Statics

Statics

CHAPTER – 6
DEFINITIONS
1. Static
Statics deals with the bodies at rest under number of forces, the equilibrium and the conditions of equilibrium.
2. Resultant Force
The net effect of two or more forces is a single force, that is called the resultant force.
3. Moment Arm
The perpendicular distance between the axis of rotation and the line of the action of force is called the moment arm of the force.
TORQUE
It is the turning effects of a force about an axis of rotation is called moment of force or torque.
FACTORS ON WHICH TORQUE DEPENDS
1. The magnitude of the applied force.
2. The perpendicular distance between axis of rotation and point of application of force.
REPRESENTATION
Torque may be represented as,
Torque = Force * moment arm
T = F * d
CENTRE OF GRAVITY
The centre of gravity is a point at which the whole weight of the body appears to act.
Centre of Gravity of Regular Shaped Objects
We can find the centre of gravity of any regular shaped body having the following shapes:
1. Triangle: The point of intersection of all the medians.
2. Circle: Centre of gravity of circle is also the centre of gravity.
3. Square: Point of intersection of the diagnonals.
4. Parallelogram: Point of intersection of the diagonals.
5. Sphere: Centre of the sphere.
Centre of Gravity of Irregular Shaped Objects
We can find the center of gravity of any irregular shaped object by using following method. Drill a few small holes near the edge of the irregular plate. Using the hole A, suspend the plate from a nail fixed horizontally in a wall. The plate will come to rest after a few moments. It will be in a position so that its centre of gravity is vertically below the point of suspension.
Now, suspend a plumb line from the supporting nail. Draw a line AA’ in the plate along the plumb line. The centre of gravity is located somewhere on this line.
Repeat the same process using the second hole B. This gives the line BB’ on the plate. Also repeat this process and use hole C and get line CC’.
The lines AA’, BB’ and CC’ intersect each other at a point. It is our required point, i.e.e the centre of gravity. We can use this procedure with any irregular shaped body and find out its centre of gravity.
EQUILIBRIUM
A body will be in equilibrium if the forces acting on it must be cancel the effect of each other.
In the other word we can also write that:
A body is said to be in equilibrium condition if there is no unbalance or net force acting on it.
Static Equilibrium
When a body is at rest and all forces applied on the body cancel each other then it is said to be in static equilibrium.
Dynamic Equilibrium
When a body is moving with uniform velocity and forces applied on the body
cancel each other then it is said to be in the dynamic equilibrium.
CONDITIONS OF EQUILIBRIUM
FIRST CONDITION OF EQUILIBRIUM
“A body will be in first condition of equilibrium if sum of all forces along X-axis and sum of all forces along Y-axis are are equal to zero, then the body is said to be in first condition of equilibrium.”
( Fx = 0 Fy = 0 )
SECOND CONDITIONS OF EQUILIBRIUM
“A body will be in second condition of equilibrium if sum of clockwise(Moment) torque must be equal to the sum of anticlockwise torque(Moment), then the body is said to be in second condition of equilibrium.”
Sum of torque = 0
STATES OF EQUILIBRIUM
There are following three states of Equilibrium:
1. First State (Stable Equilibrium)
A body at rest is in stable equilibrium if on being displaced, it has the tendency to come back to its initial position.
When the centre of gravity of a body i.e. below the point of suspension or support, then body is said to be in stable equilibrium.
2. Second State (Unstable Equilibrium)
If a body on displacement topples over and occupies a new position then it is said to be in the state of unstable equilibrium.
When the centre of gravity lies above the point of suspension or support, the body is said to be in the state of unstable equilibrium.
3. Third State
If a body is placed in such state that if it is displaced then neither it topples over nor does it come back to its original position, then such state is called neutral equilibrium.
When the centre of gravity of a body lies at the point of suspension, then the body is said to be in neutral equilibrium.

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Circular Motion and Gravitation

Circular Motion and Gravitation

CHAPTER – 7
Centripetal Force
Definition
“The force that causes an object to move along a curve (or a curved path) is called centripetal force.”

Mathematical Expression
We know that the magnitude of centripetal acceleration of a body in a uniform circular motions is directly proportional to the square of velocity and inversely proportional to the radius of the path Therefore,
a(c) < v2 (Here < represents the sign of proportionality do not write this in your examination and 2 represents square of v)
a(c) < 1/r
Combining both the equations:
a(c) < v2/r From Newton’s Second Law of Motion: F = ma => F(c) = mv2/r
Where,
Fc = Centripetal Force
m = Mass of object
v = Velocity of object
r = Radius of the curved path
Factors on which Fc Depends:
Fc depends upon the following factors:
Increase in the mass increases Fc.
It increases with the square of velocity.
It decreases with the increase in radius of the curved path.
Examples
The centripetal force required by natural planets to move constantly round a circle is provided by the gravitational force of the sun.
If a stone tied to a string is whirled in a circle, the required centripetal force is supplied to it by our hand. As a reaction the stone exerts an equal force which is felt by our hand.
The pilot while turning his aeroplane tilts one wing in the upward direction so that the air pressure may provide the required suitable Fc.
Centrifugal Force
Definition
“A force supposed to act radially outward on a body moving in a curve is known as centrifugal force.”

Explanation
Centrifugal force is actually a reaction to the centripetal force. It is a well-known fact that Fc is directed towards the centre of the circle, so the centrifugal force, which is a force of reaction, is directed away from the centre of the circle or the curved path.
According to Newton’s third law of motion action and reaction do not act on the same body, so the centrifugal force does not act on the body moving round a circle, but it acts on the body that provides Fc.
Examples
If a stone is tied to one end of a string and it is moved round a circle, then the force exerted on the string on outward direction is called centrifugal force.
The aeroplane moving in a circle exerts force in a direction opposite to the pressure of air.
When a train rounds a curve, the centrifugal force is also exerted on the track.
Law of Gravitation
Introduction
Newton proposed the theory that all objects in the universe attract each other with a force known as gravitation. the gravitational attraction exists between all bodies. Hence, two stones are not only attracted towards the earth, but also towards each other.
Statement
Every body in the universe attracts every other body with a force, which is directly proportional to the product of masses and inversely proportional to the square of the distance between their centres.
Mathematical Expression
Two objects having mass m1 and m2 are placed at a distance r. According to Newton’s Law of Universal Gravitation.
F < m1m2 ((Here < represents the sign of proportionality do not write this in your examination)
Also F < 1/r2 (Here 2 represents square of r)
Combining both the equations :
F < m1m2/r2
Removing the sign of proportionality and introducing a constant:
F = G (m1m2/r2)

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Work, Energy and Power

Work, Energy and Power

CHAPTER – 8
Definitions
1. Joule
It is the work done by a force of one Newton when the body is displaced one meter.
2. Erg
It is the work done by a force of one Dyne when the body is displaced one centimeter.
3. Foot Pound (ft-lb)
It is the work done by a force of one pound when the body is displaced one foot.
4. Force
It is an agent that moves or tends to move or stops or tends to stop a body.
5. Watt
Watt is the unit of power that is equal to the quantity of 1 Joule work done in 1 second.
Work
When a force produces displacement in a body, it is said to do work.
Units of Work

• S.I System – Joule
• C.G.S System – Erg

Explanation
When force is applied in the direction of the displacement we can find the work by using definition
Work = Force * Displacement
W = F*s
W = Fs
Suppose a man is pulling the grass cutting machine then the direction of the foce and displacement is not same. The applied force makes an angle @ with the ground while the motion takes place along the ground.
In this case force is resolved into its components.
Fx = Fcos@
Fy = Fsin@
As the machine moves along the ground, so Fx is doing the work, Hence:
W = Force * Displacement
W = Fcos@*s
W=Fscos@
Energy
Energy is define as the capability to do work. Energy is also measured in Joules.
Some Types of Energy

• Potential Energy
• Kinetic Energy
• Chemical Energy
• Heat Energy
• Light Energy
• Nuclear Energy

Potential Energy
Definition
The energy possessed by a body due to its position is known as the Potential Energy of the body. It is represented by P.E. and is measured in Joules in System International.
Examples
The energy of the following is potential energy:
A brick lying on the roof of a house.
The spring of a watch when wound up.
The compressed spring.
Water stored up in elevated reservoir in water-supply system.
Mathematical Expression
If we lift a body of mass m to a height h, then the force applied on it is the its weight and it will act through a distance h.
So,
Work = Force * Distance
W = W * h
Since W = mg, therefore:
W = mg * h
Since work is equal to energy possessed by a body:
P.E. = mgh
Kinetic Energy
Definition
The energy possessed by a body due to its motion is known as the Kinetic Energy of the body. It is represented by K.E.
Examples
The energy of the following is kinetic energy:
A bullet fired from a gun.
A railway engine moving at high speed.
Motion of a simple pendulum.
Mathematical Expression
Consider a body of mass m at rest (Vi = 0) on a frictionless surface. When a force F is applied, the body covers a distance S and its final velocity becomes Vf.
To calculate the amount of work done, we apply the formula.
W = F * S
According to Newton’s Second Law of Motion, the value of force is:
F = ma
The distance that the body traveled is calculated by using third equation of motion:
2as = vf2 – vi2 (Here 2 with Vf and Vi represents square)
We know that Vi = 0, therefore:
2as = v2
s = v2/2a
By substituting the values of F and s, we get:
W = (ma) * (v2/2a)
W = mv2/2
W = 1/2(mv2)
We know that work can be converted into Kinetic Energy, therefore:
K.E = 1/2(mv2)
So, Kinetic Energy of a body is directly proportional to the mass and square of velocity.
Factors on which Kinetic Energy Depends:
It is directly proportional to the mass of the body.
It is directly proportional to the square of the velocity.
Difference Between Kinetic Energy and Potential Energy
Kinetic Energy
1. Energy possessed by a body by virtue of its motion is known as Kinetic Energy.
2. Bodies in motion have Kinetic Energy.
3. It is calculated by K.E = 1/2 (mv2)
Potential Energy
1. Energy possessed by a body by virtue of its position is known as Potential Energy.
2. Bodies at rest have Potential Energy.
3. It is calculated by P.E. = mgh
Law of Conservation of Energy
Statement
Energy can neither be created, nor destroyed, but it can be converted from one form into the other.
Explanation
consider a body of mass mat height h above the ground. Its kinetic energy at that point A is:
K.E = 1/2(mv2)
K.E = 1/2 m * (0)
K.E = 0 …….. (i)
The potential Energy at point A is :
P.E = mgh …………(ii)
So the total energy at point A will be :
T.E = K.E + P.E
E(A) = 0 + mgh
E(A) = mgh
Suppose the body is released from this height and falls through a distance x. Its new height will be (h-x). The velocity with which it reaches point B is calculated by using the third equation of motion:
2gs = Vf2 – Vi2
As we know:
Vi = 0
S = x
Therefore,
2gx = Vf2 – 0
2gx = v2
The kinetic energy at point B is:
K.E. = 1/2 mv2
Substituting the value of v2:
K.E. = 1/2 * m * 2gx
K.E = mgx
The Potential Energy at point B is:
P.E = mgh
The height of the body is (h-x):
P.E. = mg(h-x)
The total energy at point B is :
E(B) = P.E + K.E.
E(B) = mgx + mg(h-x)
E(B) = mgx + mgh – mgx
E(B) = mgh
Hence, the total energy at point A and B are same. It means that the total value of energy remains constant.
Power
Definition
The rate of doing work is called power.
Mathematical Expression
Power = Rate of doing Work
Power = Work/Time
P = W/T
Unit of Power
The unit of Power is Joules per second (J/s) or Watt (W).
Need to Conserve Energy
The fuel that burns in running factories, transport and other activities is mainly obtained from underground deposits in the form of coal, oil, gas and other similar raw forms. These deposits are rapidly decreasing and one day all these resources of energy will be consumed. It is therefore highly important for us to avoid wastage of energy.
the consumption of two much energy is also having adverse effect on our environment. The air in big cities is heavy because of pollution caused by industrial wastes and smoke produced by automobiles. To ensure comfortable living with a neat environment, it is the responsibility of all of us as individuals to conserve energy.

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Machines

Machines

CHAPTER – 9
Definitions
1. Machine
A machine is a device by means of which useful work can be performed conveniently and it can also transfer one form of energy into another form of energy.
2. Mechanical Advantage
The ratio between the resistance or weight to the power applied in a machine is called the mechanical advantage of that machine. It is denoted by M.A.
M.A. = Weight over-comed by Machine/ Force Applied on the Machine
3. Efficiency
The ratio between the useful work done and the work done on the machine is called efficiency.
M.A = (output/Input) * 100
4. Input
Input is the work done on the machine.
5. Output
Output is useful work done by the machine.
Lever
Definition
Lever is the simplest machine in the world. It is a rigid bar, which can be rotated about a fixed point.
Principle of Lever
In the lever the moment P acts opposite to that of work W. It means that force F tends to rotate the lever in one direction which the wight W rotates in opposite direction. If the magnitude of these moments acting in opposite direction is equal, then the lever will be in equilibrium. It means that:
Moment of P = Moment of W
Mechanical Advantage
We know that according to Principle of Lever:
Moment of P = Moment of W
=> Force * Force Arm = Weight * Weight Arm
P * AB = W X BC
AB/BC = W/P
Hence,
M.A = W/P = AB/BC = Weight Arm/ Force Arm
Kinds of Lever
1. First Kind of Lever
In the first kind of lever, the fulcrum F is in the between the effort P and Weight W.
Examples
Physical Balance
Handle of Pump
Pair of Scissors
See Saw
2. Second Kind of Lever
In the second kind of lever, the weight W is in between the fulcrum F and effort P.
Examples
Door
Nut Cracker
Punching Machine
3. Third Kind of Lever
In the third kind of lever, the effortP is in between the fulcrum F and weight W.
Examples
Human forearm
Upper and Lower Jaws in the Mouth.
A Pair of Forecepes
Inclined Plane
Definition
A heavy load can be lifted more easily by pulling it along a slope rather than by lifting in vertically. Such a slope is called an Inclined Plane.
Mechanical Advantage
M.A = W/P = l/h = Length of Inclined Plane/Perpendicular Height
Pulley
A pulley consists of a wheel mounted on an axle that is fixed to the framework called the block. The wheel can rotate freely in the block. The groove in the circumference prevents the string from slipping.
Fixed Pulley
If the block of the pulley is fixed then it is called a fixed pulley.
Mechanical Advantage of Fixed Pulley
In a fixed pulley, the force P is the applied force and weight W is lifted. If we neclect the force of friction then:
Load = Effort
In the given case:
Load = W * Load Arm
Load = W * OB
Also,
Effort = P * Effort Arm
Effort = P * OA
So,
W*OB = P*OA
=> W/P = OA/OB
But, OA = OB, then
M.A = W/P = OB/OB
M.A = 1
Moveable Pulley
In this pulley, one end of the rope that is passing around the pulley is tied to a firm support and effort P is applied from its other end. The load and weight to be lifted is hung from the hook of block. In this system, the pulley can move. Such a pulley is called moveable pulley.
Mechanical Advantage of Moveable Pulley
In an ideal system of a moveable pulley, the tension in each segment of the rope is equal to the applied effort. As two segments support the weight, the ffort acting on the weight W is 2P. Therefore, according to the principle of lever:
W * Radius of the Wheel = 2P * Radius of the Wheel
=> 2P = W
The Mechanical Advantage is given by:
M.A = W/P
M.A = 2P/P
=> M.A = 2
Hence, the mechanical advantage of a moveable pulley is 2.

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Matter

Matter

CHAPTER – 10
Definition of Matter
“Anything having mass and volume is called matter.”

Kinetic Molecular Theory of Matter
The Kinetic Molecular Theory of Matter has the following postulates:

• Matter is made up of very small particles called molecules.
• These molecules are in the same state of motion, hence they possess kinetic energy. Their motion can be translatory, vibratory or rotational.
• The molecules attract each other with a force. This force depends upon the distance between them. Force is inversely proportional to the distance between the molecules.
• When a substance is heated its temperature as well as molecular motion increases. Due to this motion, kinetic energy also increases. we can say that when the kinetic energy of the molecules increases, then temperature of the substance rises.

Brownian Motion
In 1827, a scientist, Robert Brown observed the motion of molecules with the help of a microscope. He observed that the tiny particles in water are constantly moving in a zigzag path. He called the motion, Brownian Motion.
Explanation
The cause of this tiny particle motion is the rapid motion of the molecules, which collide with the particles and push them in one direction. If some molecules come from other direction and collide with the same particles, particles change their direction. This process continues and the motion becomes zigzag.
States of Matter
Matter has been classified into three states. These states are discussed below:
1.Solid

• According to the kinetic theory of matter, solid has the least kinetic energy. The properties of solids are given below:
• The particles are very close to each other.
• Their shape and volume is fixed.
• Particles in a solid vibrate to and fro from their mean position.
• On heating they melt and convert into liquid.
• Some solids also convert directly into gas on heating.

2. Liquid
According to the kinetic theory of matter, liquids have the following properties;

• They have greater kinetic energy than solids but less than that of gases.
• The volume of liquid is fixed.
• They move more freely than solids.
• The attraction between molecules is lower than solids.
• The distance between the molecules is greater than that of solids.
• On heating, they convert into vapours.
• On cooling, they convert into solid.

3. Gas
According to the kinetic molecular theory, gases possess the following properties.

• Gases possess more kinetic energy.
• Their shape and volume are not fixed.
• The distance between their molecules is large.
• Their temperature is proportional to their kinetic energy.
• Their temperature rises with increase in pressure.
• On cooling, they convert into liquid and gases.

Elasticity
Definition
” The tendency of a material to return to its original dimension after the deforming stress has been removed is known as elasticity.”

If we apply a force to a body, it is stretched. When the applied force is remove, the body returns to its original shape. The phenomenon of turning back to its original shape is called Elasticity.
Elastic Behaviour and Molecular Theory
The elastic behaviour of a material can be explained by the Kinetic Theory of Matter. Since the molecules in a solid are very close to each other, there exist strong attracting forces between them. Thus when force is removed, the attraction forces between the molecules pull them back again and the material is restored to its original shape. Different material have different elasticity depending on the nature of the material.
Elastic Limit
The maximum resisting force of a material is called the Elastic Limit of that material.
Stress
Definition
“When a body is made to change its length, volume or shape by the application of an external force, the opposing force per unit area is called Stress.”
Formula
Stress = Force / Area
o = F/A (Here o represents (Rho) do not write in your examination paper)
Units
S.I or MKS System – N/m2 or Pascal (Pa)
C.G.S system – Dyne/cm2
F.P.S or B.E System – lb/ft2 and lb/in2
(Here 2 in all above systems shows square)
Types of Stress
Following are some types of stress:
1. Tensile Stress: It is a stress tending to stretch a body.
2. Bulk Stress: It is an overall force per unit area, also known as pressure.
3. Shear Stress: It is a stress tending to produce an angular deformation.
Strain
Definition
Stress can produce a change in shape, volume or length in an object. This change in the shape of an object is called strain.
Formula
Mathematically,
Strain = Change in Length/Length or Strain = Change in volume / volume
Units
Since strain is a ratio between two similar quantities, it has no unit.
Types of Strain
Following are some types of strain.
1. Tensile Strain: It is a change in length divided by original length.
2. Bulk Strain: It is the change in volume divided by original volume.
3. Shear Strain: It is equal to the angular displacement produced.
Hook’s Law
Introduction
An English Physicist and Chemist Robert Hook discovered this law in 1678.
Statement
“Strain produced is proportional to the stress exerted within the elastic limit.”
Elastic Limit
The point at which a material becomes plastic is called elastic limit on yield point.
Yield Point
the yield point is the point at which the material begins to flow. It is also the point between elastic region and plastic region.
Elastic Region
When the material obey’s Hook’s Law, it is said to be in Elastic Region.
Plastic Region
When stress is applied beyond the elastic limit, the graph is no longer a straight line. In this case stress produces a permanent change in the material. The material is said to be in its Plastic Region.
Breaking Point
The material breaks at a certain point called the Breaking Point of the material.
Young’s Modulus
Definition
“The ratio of the stress on a on a body to the longitudinal strain produced is called Young’s Modulus.”
Mathematical Expression
According to the definition of YOung’s Modulus:
Young’s Modulus = Sress / Longitudinal Strain
Unit
In S.I system, Young’s Modulus is measured in N/m2.
Pressure
Definition
“The perpendicular force per unit area acting on a surface is called pressure.”
Mathematical Expression
Pressure = Force /Area
P = F/A
Unit
S.I or M.K.S System – N/m2 or Pascal.
C.G.S system – Dyne/cm2.
F.P.S or B.E System – lb/ft2 and lb/in2.
Pressure in Liquids
In water or other liquids, the weight exerted on a body or the bottom of the liquid is its pressure.
Pascal’s Principle
Statement
When a pressure is applied to a liquid contained in a vessel, it is transmitted undiminished equally in all directions and acts perpendicularly to the walls of the container.
Applications – Hydraulic Press
Pascal’s Principle has the application in Hydraulic press. In a hydraulic press a narrow cylinder A is connected with a wider cylinder B and they are fitted with airtight piston. It is filled with some incompressible liquid. Pressure can be applied by moving the piston cylinder A in the downward direction. Piston B is used to lift the object. The hydraulic press is provided with a rigid roof over it. When piston B moves upward, it compresses any material placed between the rigid roof and this piston. The hydraulic press is used for compressing soft materials like cotton into a cotton bale and powdered materials into compact solids.
(Diagram)
Pressure in Gases
The kinetic theory enables us to account for the pressure a gas exerts on the walls of its container. When a moving molecule strikes the walls of its container, a force is exerted on the walls during hte impact.
Atmospheric Pressure
The atmosphere, because of its weight exerts a pressure on the surface of the earth and on every object on the earth including human beings. The pressure is known as Atmospheric Pressure.
Applications of Atmospheric Pressure
The fact that the atmosphere exerts pressure has been put into use in several devices such as siphons, pumps and syringes.
Barometer
Definition
“A device for measuring the atmospheric pressure is called Barometer.”
Mercury Barometer
In the laboratory, the atmospheric pressure is measured by means of a mercury barometer. A mercury barometer consists of a thick walled glass tube of 1m length, which is opened at one end and closed from the other side. The tube is filled with mercury. The open end is firmly covered with a thumb and then carefully inverted in a vessel containing mercury. When the open end is completely immersed in the mercury, the thumb is removed. Some of the mercury from the columns drops in the vessel leaving a space. This space is called vacuum. If the mercury columns is measured, it is found to be 760 mm. This length always remains constant even if different diameter tubes are taken. The length of the mercury column is referred to as the atmospheric pressure.
Archimede’s Principle
Statement
“When an object is immersed in a liquid, an upward thrust acts upon it, which is equal to the weight of the liquid displaced by the object.”
Mathematical Expression
Mathematically, Archimede’s Principle may be represented by:
Apparent Weight = Actual Weight – Weight of the liquid displaced by the object
Buoyancy
It is the tendency of an object to float. It is equal to the up-thrust or weight of the water displaced by the object.
Conditions for Floating Bodies
A body will float in a liquid or a gas if it displaces liquid or gas whose weight is greater than the weight of the body.
A body will sink if it displaces liquid or gas whose weight is less than the weight of the body.

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Heat

Heat

Definitions
1. Internal Energy
Internal Energy of a body is the sum of all kinetic and potential energy of all molecules constituting the body.
2. Joules
It is the amount of heat required to rise the temperature of 1/4200 kg of pure water from 14.5 C to 15.5 C.
3. Calorie
It is the amount of heat required to rise the temperature of 1 g of pure water from 14.5C to 15.5C.
4. British Thermal Unit
It is the amount of heat tht is required to rise the temperature of 1 pound of pure water from 63F to 64F.
Difference Between Heat and Temperature
Heat

• Heat is the energy in transit from one body to another due to temperature difference.
• It is the total kinetic energy of the body.
• Heat is measured using Joule meter.
• Its unit is Joule.

Temperature

• Temperature is the degree of hotness or coldness of a body.
• It is the average kinetic energy of the body.
• Temperature is measured using thermometer.
• Its units are F, C and K.

Thermal Expansion
Change in length, breadth and height of a body due to heating is known as Thermal Expansion. It occurs in all the three states, i.e. solids, liquids and gases.
Thermal Expansion of Solids
Solids expand on heating. Their ability to expand depends on their molecular structure. As the temperature is increased, the average kinetic energy of the molecules increases and they vibrate with larger amplitudes. This results in increase in the distance between them. Hence, they expand on heating. Thermal Expansion of solids can be classified into three types.
1. Linear Thermal Expansion
Change in length or any one dimension of a solid on heating is known as LInear Thermal Expansion.
2. Real Expansion
The sum of the observed increase in the volume of a liquid and that of the containing vessel is called real Thermal expansion.
Real Expansion = Apparent Expansion + Expansion of the Vessel
3. Apparent Expansion
Apparent Expansion is the expansion in which only the expansion of liquid is considered and expansion of the vessel is not taken into account. Apparent expansion is less the real expansion.
Anomalous Expansion of Water
The increase in the volume of water as its temperature is lowered from 4 C to 0C is known as anomalous expansion of water.
Effects of Anomalous Expansion of Water
1. In winter, the temperature in the north and south poles of the earth falls. As the temperature fall below 4 C water on the surface expands and stays afloat. Ice continues building up at the surface while the temperature at the bottom remains at 4 C. This helps fish and other forms of marine life to live.
2. During the rainy season a lot of water seeps through the cracks in the rocks. In winter, when the water expands, the rock get broken due to this expansion.
3. In cold climate, water supply pipes burst when the water expands on cooling.
GAS LAWS
1. Boyle’s Law
The volume of a given mass of a gas is inversely proportional to the pressure, If the temperature is kept constant.
P < 1/V (Here < represents sign of proportionality. Do not write this in your examination paper)
P = C * 1/V
C = PV
The above equation is known as equation of Boyle’s Law.
2. Charle’s Law
The volume of a given mass of a gas is directly proportional to the temperature, if the pressure is kept constant.
V < T (Here < represents sign of proportionality. Do not write this in your examination paper)
V = C * T
C = V/T
The above equation is known as equation of Charle’s Law.
3. Pressure Law
The pressure of a given mass of a gas is directly proportional to the temperature, if the volume is kept constant.
P < T
P = C * T
C = P/T
The above is known as the equation of the Pressure Law.
THERMOMETER
The instrument that is used to measure temperature is called a thermometer.
Types of Thermometer
1. Ordinary Liquid-in-Glass Thermometer
Introduction
An ordinary liquid-in-glass thermometer is used in a laboratory to measure temperature within a range of -10C to 110C.
Construction
It consists of a glass stem with a capillary tube, having a small bulb at one end. This bulb is filled with a liquid, usually mercury or alcohol coloured with a red dye. The upper end of the capillary tube is sealed so that the liquid will neither spill not evaporate. The air from the capillary tube is also removed.
Working
When the bulb is heated, the liquid in it expands and rises in the tube. A temperature scale is marked on the glass stem to indicate temperatures according to the various levels of liquid in the tube.
2. Clinical Thermometer
Introduction
A clinical thermometer is a device that is used to find the temperature of the human body. It has a range from 35 C to 43 C (95F to 110F).
Construction
It consists of a glass stem with a capillary tube, having a small bulb at one end. This bulb is filled with a liquid usually mercury or alcohol colored with a red dye. The upper end of the capillary tube is sealed so that the liquid will neither spill nor evaporate. The air from the capillary tube is also removed. The glass stem of a clinical thermometer has a construction in its capillary tube near the bulb. This helps to stop the mercury thread from moving back when the thermometer is removed from the patient’s mouth.
Working
In order to find out the temperature, the thermometer is placed in the mouth or in the arm pit of the patient. The liquid in it expands and rises in the tube. A temperature scale is mrked on the glass stem to indicate temperatures according to the various levels of liquid in the tube.
3. Maximum and Minimum Thermometer
Introduction
This thermometer is used to read the maximum and minimum temperatures reached over a period of time.
Construction
This thermometer consists of a fairly large cylindrical bulb with alcohol in it. This bulb is connected through a U-shaped tube filled mercury. At the end of this U-shaped tube another bulb containing alcohol is provided.
Working
When the bulb is heated, alcohol in it expands and drives the mercury round towards the other end of the U-shaped tube. This mercury exerts pressure on the alcohol in the second bulb and its level rises. On each mercury surface, there is a small iron index provides with a light spring to hold it in position in the tube. When the mercury thread is moved, due to expansion or contraction of alcohol in the first bulb, the indices moves and are left in the extreme positions reached over a period of time. The lower end of the index on the left indicates the minimum and that on the right indicates the maximum temperature.
Heat Transfer
There are three methods of transferring heat from one place into another.
1. Conduction
Conduction is a mode of heat transfer by atomic or molecular collisions, without the movement of a bulk of a substance from one position to another, in a body. It mostly occurs in solids.
2. Convection
Convection is a mode of heat transfer by the actual movement of the bulk of the substance from one place to another through large distances. It mostly occurs in liquids and gases.
3. Radiation
Radiation is a mode of heat transfer which requires no material medium. Heat energy is carried by infra red electromagnetic waves from one place to another.
Bi-Metallic Strips
A bi-metallic strip is made of pieces of two different metals of different expansion rates, e.g. iron and brass. When it is heated, it bends with the brass on the outside of the curve because brass expands more quickly than iron.
1. Bi-metal Thermometer
Introduction
A bi-metal thermometer is made of a bi-metallic coil. No liquid is used in such type of thermometer.
Construction
It consists of a bi-metallic strip in the form of a long spiral. One end of the spiral is kept fixed, while a light pointer is attached to the other end.
Working
When the temperature rises, the bi-metal strip coil itself into an even tighter spiral due to different expansion rates of the two metals. the pointer moves across the temperature scale and in this way reading is noted.
2. Fire Alarm
Introduction
A fire alarm is used to warn people when there is a fire.
Construction
In a fire alarm, one end of a bi-metal strip is firmly fixed, while the other is free. One terminal of a 6 volt battery is connected to the fixed end of the strip through a 6 volt bulb or bell. The other terminal of the battery is connected with a metallic contact which is just above the free end of the bi-metallic strip.
Working
When a fire starts, heat energy is given off. It raises the temperature of the bi-metallic strip and its free end bends towards the contact. On touching the contact, electric circuit gets completed and the bulb starts to glow or in case of a bell, it rings warning about the fire.
Latent Heat of Fusion
The quantity of heat required to transform 1 kg of ice completely melts into water at 0C is known as Latent Heat of Fusion.
Latent Heat of Vaporization
the quantity of heat required to transform 1 kg of water completely into steam at 100 C is known as Latent Heat of Vaporization.
Effect of Pressure on Melting Point (Regelation)
The melting point of those substances, which expand on freezing, gets lowered when pressure oever one atmosphere is exerted on them.
Experiment
Take a bare copper wire with weights on its both ends. Place it across a block of ice. The copper wire sinks slowly through the block and weight falls to the floor. Pressure exerted by the copper wire lowers the freezing point of ice and the ice beneath the wire melts. The water flows round the wire and re-freezes on getting above the wire, releasing latent heat energy. This energy is conducted through the copper wire, which helps to melt the ice below the wire. In this way, ice below the wire melts while water above the wire freezes. This process continues until the wire cuts through the ice block.
Effect of Pressure on Boiling Point
If the pressure on the surface of a liquid is increased above the normal atmospheric pressure, its boiling point increases.
Experiment
Fill a round bottom flask to half its capacity. After boiling the water fro a few minutes, remove the burner and place a cork in the flask. Invert the flask and pour some cold water on the bottom of the flask. After some time, water starts to boil again although no more heat has been provided to it. The reason is that, when the water was boiled, it expelled all the air from the flask. When the flask was corked and allowed to cool the steam condensed into water. Since, no fresh air could enter the flask the pressure inside the flask lowered. This decreased the boiling point of water and water started to boil at normal temperature.
Evaporation
The process of change of a liquid into vapour without boiling is called evaporation.
Factors on which Evaporation Depends
Evaporation depends on the following factors:
1. Nature of Liquid: If the boiling point of a liquid is low, then they evaporate much quickly e.g. Alcohol and Ether.
2. Temperature of Liquid: If the surface temperature of a liquid is increased, then rate of evaporation also increases, e.g. ironing of clothes.
3. Surface Area of Liquid: If the surface area of a liquid is increased, then the rate of evaporation increases, e.g. liquids spread over large areas evaporate more quickly.
4. Dryness of Air: If there is more dryness in the air, then the rate of evaporation increases, e.g. in humid weather, clothes take a longer time to dry.
5. Wind speed: If the wind speed is greater, then evaporation rate increases.
6. Air Pressure on the Surface of The Liquid: If the pressure on the surface of the liquid is increased, the rate of evaporation decreases.
Law of Heat Exchange
For an isolated system comprising mixture of hot and cold substances, the heat lost by hot substances is equal to the heat gained by cold substances.
Heat lost by hot body = Heat gained by cold body
Refrigerator
Introduction
A refrigerator is a device that is used to keep fruits, vegetables and other eatables cool.
Construction
A refrigerator consists of a compressor, condenser and evaporator.
Refrigerant
Freon is used as the refrigerant in a referigerator. This gas liquifies at normal temperature if the pressure is increased.
Working
1. Compression: Freon gas is first compressed in the compressor of a refrigerator. It is then fed into the condenser.
2. Condensation: In the condenser, the gas is liquified under pressure. It converts into a liquid at normal temperature. This gas is then allowed to pass through a valve into the evaporator.
3. Evaporation: The pressure in the evaporator is comparatively less than in the condenser. Therefore, when liquid Freon enters the evaporator, it evaporates absorbing a large amount of heat. This results in cooling the area around the evaporator. This is where we keep our eatables.
(Diagram)
The gas is then again fed into the compressor and the process continues.

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Waves and Sound

Waves and Sound

CHAPTER – 12
Definitions
1. Vibration
One complete round trip of a simple harmonic motion is called vibration.
or
If a body in periodic motion moves to and fro over the same path, this motion is called Oscillation.

2. Time Period (T)
The time required to complete vibration is known as time period.

3. Frequency
It is the number of vibrations executed by an oscillating body in one second.
4. Displacement
It is the distance of a vibrating body at any instant from the equilibrium position.

5. Amplitude
The maximum distance of the body on either side of its equilibrium position is known as amplitude.

6. Wave Length
The distance between two consecutive crests and troughs is called wavelength.

7. Natural Frequency
The frequency at which an object will vibrate freely (without any external periodic force or resistance) is known as natural frequency of that object.
8. Audible Sound
Our ear can hear only those sounds whose frequency is between 20Hz and 20000Hz. This range is known as audible sound.

9. Ultrasonic Sound
Sound with frequency greater than 20000 Hz is known as ultrasonic sound.

10. Octave
The interval between a waveform and another of twice the frequency is known as Octave.
Units
Frequency: Cycles per second (eps) or Hertz (hz)
Wavelength: Meter
Intensity of Sound: Watt/meter2 or W/m2
Noise: Decibel (DB)
Simple Harmonic Motion (S.H.M)
Definition
“To and fro motion of a body in which acceleration is directly proportional to displacement and always directed towards mean position is known as Simple Harmonic Motion.”
Condition for S.H.M
The conditions for simple Harmonic Motion are given below:

• Some resisting force must act upon the body.
• Acceleration must be directly proportional to the displacement.
• Acceleration should be directed towards mean position.
• System should be elastic.

Examples
Following are the examples of S.H.M:

• Body attached to a spring horizontally on an ideal smooth surface.
• Motion of a simple and compound pendulum.
• Motion of a swing.
• Motion of the projection of a body in a circle with uniform circular motion.

Resonance
Definition
“The large amplitude vibration of an object when given impulses at its natural frequency is known as Resonance.”
Experiment
Consider a long string stretched tightly between two pegs. Four pendulums A, B, C and D of different lengths are fastened to the string. Another pendulum E of same length as A is also fastened.
When pendulum E is set to vibrate, it will be observed that all the pendulums start to swing but pendulum A begins to vibrate with larger amplitude, as pendulum E is set into vibration. It imparts its motion to the string. This string in turn imparts the same periodic motion to the pendulums. The natural frequency of all other pendulums except A is different. Due to the same natural frequency only A vibrates as the same vibration of E. This phenomenon under which pendulum A begin to vibrate is called resonance.
Example
March of Soldiers while Crossing the Bridge
Each bridge has its own natural frequency and marching of soldiers is another vibrating system. So there may occur a force on vibration in bridge. This may damage the bridge. So, for safely precautions, it is written that soldiers must march out of stop while crossing the bridge.
Wave
Definition
” A method of energy transfer involving some form of vibration is known as a wave.”
Wave Motion
Wave motion is a form of disturbance, which travels through a medium due to periodic motion of particles of the medium about their mean position.
Experiment
We see that if we dip a pencil into a tap of water and take it out a pronounced circular ripple is set up on the water surface and travels towards the edges of the tub. However if we dip the pencil and take it out many times, a number of ripples will be formed one after the other.
Waves can also be produced on very long ropes. If one end of the rope is fixed and the other end is given sudden up and down jerk, a pulse-shaped wave is formed which travels along the rope.
Transverse Wave
Definition
“The wave in which amplitude is perpendicular to the direction of wave motion is known as Transverse Wave.”
Examples

• Radio Waves
• Light Waves
• Micro Waves
• Waves in Water
• Waves in String

Longitudinal Wave
Definition
“The wave in which amplitude is parallel to wave motion is called longitudinal wave.”
Example

• Sound Waves
• Seismic Waves

Sound
Definition
“A vibration transmitted by air or other medium in the form of alternate compressions and rarefactions of the medium is known as Sound.”
Production of Sound
Sound is produced by a vibrating body like a drum, bell, etc, when a body vibrates. due to the to and fro motion of the drum, compressions and rarefactions are produced and transmitted or propagated in air.
Propagation of Sound Waves
When a body vibrates in air, it produces longitudinal waves by compressions and rarefactions. These compressions and rarefactions are traveled by the particles of the medium and transferred into the next particles. Due to this transference, sound propagates in a medium.
Experiment
(Diagram)
Suspend an electric bell in a jar by its wires through a cork fixed in its mouth. Switch on the bell, we will hear the sound of the bell. Now start removing air from jar with the help of an exhaust (vacuum) pump. The sound will decrease, although the hammer is still seen striking the bell. This experiment shows that air or any other medium is necessary for the propagation of sound.
Velocity of Sound
It is a matter of common experience that the flash of lightning is seen earlier than hearing the thunder of cloud. Similarly when a gun is fired its sound is heard a little after seeing its flash. The reason is that light is faster than sound. Due to its slow velocity sound lags behind.
Experiment
Select two stations at a distance of 8 km (or any more distance) such that there is no obstacle between them. Fire a gun at station A and note the time of sound taken for such distance. Repeat the process and note the time taken by the sound to travel from B to A. If we substitute the mean of the two times recorded and distance S (8km) in the formula V = S/t, we will get the velocity of sound.
Factors Effecting Velocity of Sound
The factors are given below:

• Velocity of air or any other medium.
• Density of the medium.
• Temperature of the medium.
• Nature of the medium

Characteristics of Sound
The characteristic properties of sound by which we can distinguish between noise and music, shrill and grave sounds or sound of men and women are known as characteristics of sound. The properties of sound are given below:
1.Loudness
Definition
“Loudness is the magnitude of auditory sensation produce by sound.”
Intensity can be defined as the energy carried by the sound waves through a unit area placed perpendicular to the direction of waver per second.
Factors Effecting Loudness of Sound
Loudness depend on following factors:
Area of Vibration of Body: Greater will be the surface area more will be the loudness.
Amplitude of Motion of Vibrating Object: Greater will be the amplitude, more will be the loudness.
Density of Medium: Loudness is directly proportional to the density of medium.
Motion and Direction: If source of sound is moving towards the listener loudness will be greater or if wind supports the velocity of sound the loudness will be greater.
2. Pitch
Definition
“The sensation that a sound produces in a listener as a result of its frequency is known as Pitch.”
This is the property of sound by virtue of which we can distinguish between a shrill and grave sound.
Factors Effecting Pitch of Sound
Pitch depends on following factors:
Frequency of Vibrating Body: The greater the fundamental frequency, more shrill will be the sound.
Relative Motion of Sound: If source and listener both are coming closer pitch will increase.
3. Quality or Timbre or Tone
Definition
“The characteristic of a musical note that is determined by the frequency present is known as Quality or Timbre or Tone of that sound.”
This is the property of sound by virtue of which it is possible to identify a sound of the same loudness and pitch but originating from different instrument.
Factors Effecting Quality
Quality depends upon the following factors:

• Phase of the Sound Wave.
• Shape of Waves

Harmful Effects of Sound (Noise)
Nowadays noise is considered as a great pollution, which is very dangerous for us. Some of them are as follows:

• Continuous noise damages hearing and can result in complete deafness.
• Noise has become a great cause for depression and blood pressure.
• Mental system shows less efficiency due to noise.
• Consequently it is harmful in all respects for living body.

Musical Sound
The sound producing pleasing effect on our ears are called musical sounds.
Difference Between Longitudinal and Transverse Waves
Longitudinal Waves
1. In longitudinal waves, particles of the medium vibrate in the direction of the waves.
2. The portion of wave in which particles of medium are very close to each other is called compression.
3. Examples of longitudinal waves are sound wave and seismic waves.
4. Distance between the centre of two compressions and rarefactions is called wavelength.
Transverse Waves
1. In transverse waves, particles of the medium vibrate in the direction perpendicular to the direction of wave.
2. The portion in which particles of medium are higher than their normal position is called crest.
3. Examples of transverse wave are microwaves and radio waves.
4. Distance between two crests and troughs is called wavelength.

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Propagation and Reflection of Light

Propagation and Reflection of Light

CHAPTER – 13
Definitions
1. Incident Ray
The ray that strikes the surface of the medium is known as Incident Ray.

2. Reflected Ray
The ray that is sent back into the same medium after reflection is known as reflected ray.

3. Plane Mirror
A flat smooth reflecting surface, which shows regular reflection is known as plane mirror.

4. Normal
Perpendicular line on the reflecting surface is known as normal.

5. Pole
The centre of the spherical mirror is called pole.
6. Angle of Incidence
The angle subtended by the incident ray to the normal is known as angle of incidence.
7. Angle of Reflection
The angle subtended by the reflected ray to the normal is known as angle of reflection.

8. Center of Reflection
The center of the hollow sphere of which the mirror is a part is called center of curvature.

9. Principle Axis
The straight line passing through center of curvature nad the pole is known as principle axis.

10. Principle Focus
The ray coming parallel to principal axis after converges to or diverges from a point, which is called principle focus.

11. Focal Length
The distance between the principle focus and pole of the mirror is called Focal Length.

12. Radius of Curvature
The distance between the center of curvature and the pole is called radius of curvature.

13. Real Image
The image that can be seen on a screen is known as a real image.

14. Virtual Image
The image that cannot be seen on a screen is known as a virtual image.

15. Magnification
The ratio between the image height and object height is known as magnification.

or
The ratio between the image distance to the object distance is known as magnification.
Reflection of Light
Definition
“The process in which light striking the surface of another medium bounces back in the same medium is known as Reflection of Light.”
Laws of Reflection
1. The angle of reflection, is equal to the angle of incidence: n 2. The incident ray, reflected ray and normal, all lie in the same plane.

Kinds of Reflection
There are two types of Reflection:
1. Regular Reflection
Definition
When parallel rays of light strike a surface and most of them are reflected in a same particular direction or same angle, they are said to be regularly reflected and the phenomenon is known as regular reflection.

Regular reflection occurs when parallel rays of light strike with an ideal smooth plane surface. In regular reflection parallel rays remain parallel after reflection.
(Diagram)
2. Irregular Reflection
Definition
When some rays of light strikes a surface and the reflected rays scatter in different directions, this type of reflection is called irregular reflection.

It occurs when parallel rays strike with an irregular rough surface. In this case rays does not remain parallel after reflection and they scattered.
(Diagram)
Advantages of Irregular Reflection

• Due to this reflection, sunlight reaches us before sunrise and persists for some time even after the sunset.
• Due to this reflection we get sufficient light in our rooms and other places where sunlight do not reach directly.
• Due to this reflection sunlight reaches to each of the leaves of a tree and photosynthesis takes place on large scale.
• Due to this reflection, we can see luminous objects.

Image Formed by a Plane Mirror
Consider a mirror MM’, AP is an object. Consider that a point P lies on the tip of the object. From P as ray travels and strikes mirror and reflect back to the eye, they appear to come back. From Point P’ as shown in the figure. Hence P’ is the image of P. Similarly, infinite points lying an object produces infinite images of points and complete image of an object is formed.
Characteristics of Image Formed by a Plane Mirror

• Image is same in size as that of the object.
• The distance of object and image are equal from the mirror.
• The image formed is virtual and inverted.

Spherical Mirrors
Definition
“A spherical mirror is a section of a of a hollow sphere.”

Types of Spherical Mirrors
There are two types of spherical mirror:
1. Concave Mirror (Converging Mirror)
2. Convex Mirror (Diverging Mirror)
1. Concave Mirror
Definition
“The spherical mirror in which inner side of the surface is polished for reflection is called a concave mirror.”
Properties

• The bulging side is polished.
• Reflection occurs from its hollow side.
• They converge the parallel rays at a point.
• They can form real and imaginary, both types of images.

2. Convex Mirror
Definition
“The spherical mirror in which inner side of the surface is polished for reflection is called concave mirror.”
Properties

• The bulging side is polished.
• Reflection occurs from its hollow side.
• They converge the parallel rays at a point.
• They can form real and imaginary, both type of images.

Formation of Image by Concave Mirrors
There are six cases to form an image by concave mirror.
1. Object at Infinity
(Diagram)
If the object is placed at infinity from the mirror, the rays coming from the object are parallel to principal axis. After reflection, they meet at principal focus and image is formed at the focus.
Details of Image

• Formed at F.
• Extremely Small
• Real
• Inverted

2. Object Beyond C
(Diagram)
If the object is placed beyond C, rays coming from the object are not parallel. They meet after reflection between the focus and center of curvature. Therefore, image is formed between the focus and center of curvature.
Details of Image

• Formed between F and C.
• Small in size.
• Real
• Inverted

3. Object at Center of Curvature ‘C’
When object is placed at the centre of curvature, the image formed at the same place.
(Diagram)
Details of Image

• Formed at C
• Equal in size
• Real
• Inverted

4. Object Between F and C
(Diagram)
When the object is placed between the focus and Centre of curvature, the image is formed beyond the centre of curvature.
Details of Image

• Formed beyond C.
• Large in size.
• Real
• Inverted

5. Object at F
(Diagram)
When object is placed at focus the reflected rays become parallel to each other. The two parallel lines meet at infinity. Therefore, we say the image is formed at infinity.
Details of Image

• Formed at Infinity.
• Extremely Large
• Real
• Inverted

6. Object between P and F
(Diagram)
For locating object between pole and focus the rays reflected do not meet because they diverge. But they meet backward. So, the image is formed backward or behind the mirror.
Details of Image

• Formed behind the mirror.
• Large in size
• Virtual
• Erect

Uses of Spherical Mirror
Spherical mirrors are used in several places. Some of them are given below:
Shaving: A concave mirror is used to enlarge the image.
Microscope: A convex mirror is used for magnification in a microscope.
Telescope: The convex mirror is used.
In Searchlights and Headlights: Concave mirror is used to form the rays in searchlights and headlights, used for different purposes.
For Rear View: The convex mirror is used in automobiles.
In Medical Examination (Opthalmoscope): Doctors use concave mirror for the examination of ear, nose, throat and eyes of patients.

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Refraction of Light and Optical Instruments

CHAPTER – 14
Definitions
1. Emergent Ray
The ray after passing the second medium comes again in the first medium. It is called emergent ray.

2. Emergence Angle
The angle formed by the emergent ray and normal is called emergence angle denoted by <e.
3. Optical Center
The middle point of the lens is called optical center. The ray passing through this point does not bend.

4. Accommodation
The ability of the eye to change the focal length of its lens so as to form a clear image of an object on its retina is called is power of accommodation.

5. Persistence of Vision
When an object is seen by an eye, its image forms on retina. If the object is removed, the impression of image persists in the eye for about 1/10 second. This interval is called Persistence of Vision.

6. Power of Lens
The power of the lens is the reciprocal of the focal length measured in meter. Its unit is Dioptre.
Refraction of Light
Definition
“The change in the direction and velocity of light as it enters from one medium to another is known as Refraction of Light.”
Laws of Refraction

• The incident ray, refracted ray and the normal at the point of incidence all lie in the same plane.
• The ratio of sine of angle of incidence (i) to the sine of angle of refraction (r) is constant for all rays of light from one medium to another. This constant is known as Refractive Index (u). This ratio is also equal to the ratio of the speeds of light in one medium to another.

Refractive Index = sin
Refractive Index
The ratio between the sine of the angle of incidence to the sine of angle of refraction is known as Refractive Index.
Refractive Index = sin
Snell’s Law
The refractive index between two particular mediums is equal to the ratio of speed of light in first medium and speed of light in second medium equal to the ratio between sin



Refractive Index = sin
Prism
Definition
“Prism is a transparent piece of glass. It has three rectangular sides and two triangular sides.
Refraction Through a Prism
(Diagram)
where,

• <i = angle of incidence
• <i = angle of refraction
• <e = angle of emergence
• <d = angle of deviation

Total Internal Reflection
(Diagram)
If the value of angle of incidence is increased so much so that it becomes greater than tht of the critical angle then no more refraction occurs but on the other hand refracted ray again comes back in the denser medium. Actually at that time, the surface of denser medium acts as a plane mirror and the incident ray bends in the same medium. This phenomenon is called Total Internal Reflection. It is used in Periscope, Optical Fibers and other instruments.
Total Reflecting Prism
Total internal reflection is used in prism. In prism the angle between two opposite sides is 90 and other two angles are 45 each. If we arrange a ray so that it falls perpendicular to the AB side then it will refract without bending and strike the side AC with angle 45. Then it totally reflects to the side BC.
Conditions for Total Internal Reflection
The ray of light should travel from denser to rarer medium.
The angle of incidence should be greater than the critical angle.
Lenses
Definition
A transparent and smooth glass or any refracting medium surrounded by two spherical surfaces is known as lens.

Types of Lenses
There are two types of lenses:
1. Convex Lens
If the glass is thick at the center and thin at the edges then it is known as convex lens. It is a converging lens.
(Diagram)
It has three types:

• Double Convex Lens
• Plano Convex Lens
• Concavo Convex Lens

2. Concave Lens If the lens is thinner in the center and thicker at the edges then it is known as a concave lens. It is a diverging lens.
(Diagram)
It has three types:

• Double Concave Lens
• Plano Concavo Lens
• Convex Concave Lens

Formation of Image by Convex Lens
1. Object at Infinity
When object is placed at infinite distance from convex lens the rays coming from the object are parallel to each other and they meet after refraction at the focus.
Details of Image

• Formed at Focus
• Real
• Inverted
• At opposite side
• Highly diminished

2. Object Beyond 2F
When object is placed at some distance from 2F then image is formed between the focus and center of curvature (2F).
Details of Image

• Between F and 2F
• Opposite side of Lens
• Real
• Inverted
• Small in size

3. Object at 2F
When object placed at center of curvature, image is formed at center of curvature at the opposite side.
Details of Image

• Real
• Inverted
• At 2F
• Same in size
• At the opposite side of the Lens

4. Object between F and 2F
When object is placed between the focus and center of curvature then the image is formed on opposite side beyond the center of curvature.
Details of Image

• Real
• Inverted
• Large in size
• Opposite side of lens
• Beyond 2F

5. Object at F
When object is placed at focus the refracted rays are parallel to each other and meet at infinity.
Details of Image

• Real
• Inverted
• Extremely Large
• Opposite side of Lens
• At infinity

6. Object between F and O
When object is placed between the lens and principal focus, then the refracted rays does not meet at opposite side but image is formed at the same side where the object is placed.
Details of Image

• Virtual
• Erect
• Large
• Same side of lens
• Beyond the object

Optical Instruments
1. THE EYE
(Diagram)

Functions of the Parts of Eye
1. Sclera Scelortic
It is a layer enclosed in cavity filled with a fluid called Vitrous Humour. It is the outer coating of eye.
2. Choroid
It is a dark membranous coating. This is coated with black pigments. It keeps the inner parts of the eye ball light proof.
3. Retina
It is semi-transparent membranes of nerve fibers forming the innermost coating of the eye and sensitive to light. It is a screen on which image is formed.
4. Cornea
It allows light into the eyes. It is transparent and bulging in shape.
5. Iris
It is like diaphragm of a camera. It has a tiny opening at its center called pupil, which regulates the quantity of light entering the eye.
6. Crystalline Lens
This is a lens that automatically contracts and expands, alters the focal length of eye lens.
7. Ciliary Body
It holds crystalline lens in the proper position.
8. Aqueous Humour and Vitrous Humour
The place between cornea and the lens is filled by a transparent liquid called Aqueous Humour. The large chamber of the eye between the lens and the back of eye is filled with a jelly like substance called Vitreous Humour. These liquids serve mainly to keep the spherical shape of the eye.
Main Defects of Eye
1. Short Sightedness (Myopia)
If a person can see object placed near, but cannot see distant object, this defect is known as short sightedness.
Causes
This defect appears due to increase in thickness of eyeball. The focal length decreases making the image to form before retina.
(Diagram)
Removal of Defect
It is removed by using a concave lens of suitable focal length.
(Diagram)
2. Long Sightedness (Hypermetropia)
If a person can see distant objects, but not near objects, this defect is called long sightedness.
Causes
This defect appears due to decrease in thickness of ball. The focal length increases so that the image is formed beyond the retina.
(Diagram)
Removal of Defect
It is removed by sing a convex lens of suitable focal length.
(Diagram)
3. Astigmatism
It is the defect in which the clear image of an object does not form on the retina.
Causes
This defect appears due to non-sphericity of the cornea.
Removal
This defect can be removed by using lenses of different focal length.
4. Presbyopia
The accommodation power of eye loses by which a person suffers a long sightedness. This defect is called Presbyopia or Lack of Accommodation.
Causes
This defect appears due to loss of accommodation power of the lens of the eye.
Removal
This defect can be removed by using convex lens.
2. CAMERA
Definition
A camera is an optical device for obtaining still photographs or for exposing cinematic films.
Construction
It consists of a light proof box with a lens at one end and a photographic plate or film at other end and a shutter to control the light rays.
Working
To make an exposure, the shutter is opened and an image is formed by lens on the photographic plate or film, small in size. Photographic plate or film saves this image. In this way an image is obtained.
3. COMPOUND MICROSCOPE
Construction
It consist of two convex lenses at the end of two tubes. One tube can slide into other so that the distance between them can be change. The lens near the object is the small convex lens of short focal length is called objective. The lens near the eye is the larger convex of longer focal length is called eyepiece.
(Diagram)
Working
The object is placed between F and @F and its real, inverted and magnified image A’B’ is formed. The eyepiece is brought close to it so that it comes within its focal length. The first image A’B’ acts as an object and a virtual, erect and magnified final image A”B” is formed. The magnification of a microscope can be varied by using different objectives.
4. ASTRONOMICAL TELESCOPE
It is used to see heavenly bodies.
Construction
It consists of two convex lenses at the end of the two metallic tubes. One tube can slide into other so that the distance between can be changed. The lens near the object is a convex lens of longer focal length called the objective, while the lens near the eye is a small convex lens of shorter focal length called the eyepiece.
(Diagram)
Working
The rays from distant object entering the objective and form a real, inverted and diminished image A’B’ near the principal focus. The eyepiece is adjusted so that the image formed by the objective comes within its focal length. Thus the eyepiece acts as a magnifying glass and a virtual, erect and magnified image A”B” is formed by the first image.
Difference between Real Image and Virtual Image
Real Image
1. Real image is formed when rays after reflection actually meet at a point.
2. Real image is inverted and can be seen on a screen.
3. It has a physical existence.
Virtual Image
1. Virtual image is formed when rays do not actually meet but appear to diverge from a point.
2. Virtual image is erect and cannot be seen on a screen.
3. It does not have a physical existence.

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Nature of Light and Electromagnetic Spectrum

Nature of Light and Electromagnetic Spectrum

CHAPTER – 15
Definitions
1. Dual Nature of Light
Light has dual nature, it behaves not only as a particle (photon) but also as a wave. This is called dual nature of light.

2. Dispersion of Light
When a beam of sunlight falls on a prism, the light is split up in seven colours. This phenomenon is called Dispersion of Light.

3. Rainbow
The rainbow is an arc of spectral colours formed across the sky during or after rainfall in the morning or when the sun is behind us.

4. Photons (Quantum)
Photons are tiny packets of energy. They behave as particles but actually they are not particles.
Newton’s Corpuscular Theory of Light
This theory which was proposed by Newton is as follows:

• Light is emitted from a luminous body in the form of tiny particles called corpuscles.
• The corpuscles travel with the velocity of light.
• When corpuscles strike the retina they make it sense light.
• Medium is necessary for the propagation of light.
• Velocity of light is greater in denser medium.

Wave Theory of Light
In 1676, Huygen proposed this theory. According to this theory:

• Light propagates in space in the form of waves.
• It can travel in space as well as in a medium.
• Light does not travel in a straight line but in sine wave form.
• Velocity of light is greater in rarer medium.
• Medium is not necessary for propagation.

Quantum Theory of Light
According to this theory of Max Plank:

• Light is emitted from a source discontinuously in the form of bundles of energy called Photons or Quantum.
• It travels in space as well as a medium.
• Speed of light is greatest in space or vacuum.

How A Rainbow is Formed?
As we know a prism disperses sunlight into a series of seven colours. When rain falls, raindrops behave like a prism and white light entering the raindrop splits up into seven colours on refraction. These are appeared as Rainbow.
Spectrum
After the dispersion of light or any electromagnetic wave, a band of colours is formed, which is known as a spectrum.

Electromagnetic Spectrum
Electromagnetic spectrum is a result obtained when electromagnetic radiation is resolved into its constituent wavelength.
Waves of Electromagnetic Spectrum
Radio Waves
It has a large range of wavelengths from a few millimeters to several meters.
Microwaves
These radio waves have shorter wavelength between 1mm and 300 mm. Microwaves are used in radars and ovens.
Infrared Waves
It has a long range. Its mean wavelength is 10 micrometers.
Visible Waves
It has a range of 400 nm to 700 nm.
Ultraviolet Waves
Their wavelength ranges from 380nm onwards. These are emitted by hotter start (about 25000 C).

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