FSc Notes: March 2014

NATURE OF LIGHT

Newton’s corpuscular theory of light
Newton’s corpuscular theory of light is based on the following points 1. Light consists of very tiny particles known as “corpuscular”. 2. These corpuscles on emission from the source of light travel in straight line with high velocity 3. When these particles enter the eyes, they produce image of the object or sensation of vision. 4. Corpuscles of different colours have different sizes.
Huygen’s wave theory of light
In 1679, Christian Huygens proposed the wave theory of light. According to huygen’s wave theory: 1. Each point in a source of light sends out waves in all directions in hypothetical medium called "ETHER". 2. Light is a form of energy 3. Light travels in the form of waves. 4. A medium is necessary for the propagation of waves & the whole space is filled with an imaginary medium called Ether 5. Light waves have very short wave length
Quantum theory of light

Quantum theory was put forward by MAX-PLANCK in 1905. According to quantum theory “Energy radiated or absorbed can not have any fractional value. This energy must be an integral multiple of a fixed quantity of energy. This quantity is called “QUANTUM” OR Energy released or absorbed is always in the form of packets of energy or bundles of energy. These packets of energy are known as QUANTA or PHOTONS

LONG SIGHTEDNESS OR HYPER METROPIA

SYMPTOMS
In HYPER METROPIA, a person can not see objects clearly which are near to him, but he can see clearly distant objects
REASON
The reason for HYPER METROPIA is that either the focal length of the lens of eye is too long or the eyeball is too short.
WHAT HAPPENS IN HYPER METROPIA
In HYPER METROPIA, light rays from a near object are focused behind the Retina.

CORRECTION OF DEFECT
This defect can be corrected by using a convex lens of suitable focal length


POWER OF LENS
Power of lens is defined as the reciprocal of the focal length of the lens in meters.
FORMULA:
Power = 1/f(in meter)
Unit of power of lens is Dioptre.
DIOPTRE
Dioptre is defined as the power of lens whose focal length is one meter
if f =1 meter then the power of the lens = 1 dioptre.

SNELL’S LAW

SNELL’S LAW

According to Snell’s law
"The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always constant. "
Mathematically,
Sine <i/sine <r = constant or sin< i/sine< r = m
where m = Refractive index of the material of medium.
TOTAL INTERNAL REFLECTION
When light rays enter from one medium to the other, they are refracted. If we increase the angle of incidence, angle of refraction will also increase. At certain angle of incidence light rays are reflected back to the first medium instead of refraction. This condition or phenomenon is called Total Internal Reflection.

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CRITICAL ANGLE
The angle of incidence at which the angle of refraction will become 90^o is called Critical Angle. If angle of incidence further increased then instead of refraction, reflection will take place.
DEFECTS OF VISION Write down the defects of the vision.
There are four common defects of vision: 1. SHORT SIGHTEDNESS OR MYOPIA 2. LONG SIGHTEDNESS OR HYPER METROPIA 3. ASTIGMATISM 4. PRESBYOPIA
SHORT SIGHTEDNESS OR MYOPIA
SYMPTOMS
In Myopia, a person can not see distant objects clearly, but he can see clearly the objects near to him.
REASON
The reason for Myopia is either the focal length of lens of eye is too short or the eyeball is very much elongated.
WHAT HAPPENS IN MYOPIA
In Myopia, light rays from a distant object are focused in front of the Retina.

CORRECTION OF DEFECT
This defect can be corrected by using a concave lens of suitable focal length

REFLECTION OF LIGHT DEFINITIONS

REFLECTION OF LIGHT
When light rays traveling is a medium reaches the boundary of other medium, they turn back to the first medium. This phenomenon of turning back of light into the same medium after striking the boundary of other medium is called Reflection of Light.

LAWS OF REFLECTION
1. The angle of incident is equal to the angle of reflection i.e. <i = <r 2. The incident ray, the reflected ray and the normal lie on the same plane.

REGULAR REFLECTION
When a beam pass of parallel light rays is incident on a smooth and plane surface, the reflected rays will also be parallel. This type of reflection is called Regular Reflection.

IRREGULAR REFLECTION
When a beam of parallel light rays is scattered in all directions. Therefore the parallel rays incident on the surface will reflect in different directions. This type of reflection is called "Irregular or Diffuse Reflection".

CENTER OF CURVATURE
Center of curvature of a lens or mirror is defined as the center of the sphere of which the less or mirror is a part. C = Center of curvature.

RADIUS OF CURVATURE
Radius of curvature is the radius of sphere of which the lens or mirror is a part.
PC = Radius of curvature OR PC = R

POLE
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The middle or center point of a lens or a mirror is called "Pole" P = Pole.
PRINCIPLE AXIS
The straight line joining the center of curvature to the pole is called Principle Axis. .

PRINCIPLE FOCUS
When a narrow beam of light, parallel to the principle axis and closed to it, is incident on the surface of a mirror or lens, the beam reflected or refracted is converged at a fixed point on the axis. This point is called Principle Axis. F = principle focus.

FOCAL LENGTH
The distance between the pole of a lens or mirror to the principal focus is called Focal Length (PF) of lens or mirror. Focal length is always equal to half of the radius of curvature of lens or mirror. f = R/2.

Write down the characteristics of image formed by a plane mirror
1. Image formed by plane mirror is laterally inverted. This means that right side of the object appears on the left side. 2. Size of image formed by plane mirror is the same as that of size of object. 3. The image formed by plane mirror is virtual because it can not be obtained on the screen. 4. The image is as far behind the mirror as the object is in front of the mirror. Fig.
DEFINE SPHERICAL MIRROR AND IT'S TWO TYPES
SPHERICAL MIRROR
Mirror obtained from a spherical surface is known as Spherical Mirror. A spherical mirror is considered as a section of hollow sphere.

TYPES OF SPHERICAL MIRRORS
There are two types of spherical mirrors. 1. Concave mirror. 2. Convex mirror.
CONCAVE MIRROR
If the inner side of the surface of a spherical mirror is polished to reflect light, the mirror is called a Concave Mirror. Concave mirror converges parallel beam of light.

CONVEX MIRROR
If the outer side of the surface of a spherical mirror is polished to reflect light the mirror is called a Convex Mirror. Convex mirror diverges parallel beam light.

MAGNIFICATION
Magnification of a mirror or lens is defined as the ratio of the size of image to the size of object.
M = height of image/height of object M = hi/ho or M = q/P
REFRACTIVE INDEX
Refractive index is defined as the ratio of sine of the angle of incidence of the sine of the angle of refraction. FORMULA :
m= sine< i/ sine< r
note :Refractive index depends upon the nature of material. It has no unit.
ANGLE OF DEVIATION
The angle at which the light ray is refracted (bend) in a prism is called angle of deviation. It is denoted by < D. Minimum value of angle of deviation is called angle of minimum deviation. It is denoted by <Dm.

SIMPLE PENDULUM

SIMPLE PENDULUM
	simple pendulum consists of a heavy mass particle suspended by a light, flexible and in-extensible string.

	MOTION OF THE BOB OF SIMPLE PENDULUM
	The motion of the bob of simple pendulum simple harmonic motion if it is given small displacement. In order to prove this fact consider a simple pendulum having a bob of mass 'm' and the length of pendulum is 'l'. Assuming that the mass of the string os pendulum is negligible. When the pendulum is at rest at position 'A', the only force acting is its weight and tension in the string. When it is displaced from its mean position to another new position say 'B' and released, it vibrates to and fro around its mean position.
	Suppose that at this instant the bob is at point 'B' as shown below :

	FORCES ACTING ON THE BOB
	1. Weight of the bob (W) acting vertically downward. 2. Tension in the string (T) acting along the string.
	The weight of the bob can be resolved into two rectangular components:
	a. Wcosq along the string. b. Wsinq perpendicular to string.
	Since there is no motion along the string, therefore, the component Wcosq must balance tension (T) i.e. Wcosq = T
	This shows that only Wsinq is the net force which is responsible for the acceleration in the bob of pendulum.
	According to Newton's second law of motion Wsinq will be equal to m x a
	i.e. Wsinq = m a
	Since Wsinq is towards the mean position, therefore, it must have a negative sign. i.e. m a = - Wsinq
	But W = mg
	m a = - mgsinq
	a = - gsinq
	In our assumption q is very small because displacement is small, in this condition we can take sinq = q
	Hence a = - gq ----------- (1)
	If x be the linear displacement of the bob from its mean position, then from figure, the length of arc AB is nearly equal to x
	From elementary geometry we know that:

	Where s= x, r = l
	Putting the value of q in equation (1)

	As the acceleration of the bob of simple pendulum is directly proportional to displacement and is directed towards the mean position, therefore the motion of the bob is simple harmonic when it is given a small displacement

WAVES AND SOUND

Define the following terms:

PERIODIC MOTION
A motion that repeats itself in equal intervals of time is called Periodic Motion.
VIBRATORY MOTION
If a particle in periodic motion moves back and forth (To and Fro) over the same path, then this type of motion is called Vibratory or Oscillatory Motion.
VIBRATION
A complete round trip of a vibrating body is called a Vibration. or The motion of a vibrating body from one extreme point to the other extreme point and back to the first extreme point is called VIBRATION.
For Example the motion of the bob of Simple Pendulum from A to B & back from B to A via point "O" is called one Vibration.


TIME PERIOD
Time required to complete one vibration is called Time Period of vibrating body. It is denoted by "T".
FREQUENCY
Number of vibrations executed by a vibrating body in one second is called its frequency. It is denoted by "f". Frequency is reciprocal of time period f = 1/T Unit of frequency : Hertz Other units : cycle/sec or vibration/sec.
DISPLACEMENT
Displacement of the vibrating body at any instant in its distance from the mean position at that instant either right or left side. Here it is denoted by "x".
AMPLITUDE
Maximum displacement of a vibrating body on either side of its equilibrium position is called amplitude of vibration. It is denoted by .
SIMPLE HERMONIC MOTION
"Type of vibratory motion in which acceleration of body is directly proportional its displacement and the acceleration is always directed towards the equilibrium (mean) position is called Simple Harmonic Motion. "
acceleration a - displacement
a a - x
Negative sign indicates that acceleration and displacement are opposite in direction.
Examples of S.H.M :
Motion of the bob of a simple pendulum, spring-mass system, guitar wires, prongs of a tuning fork

THERMAL CONDUCTIVITY

THERMAL CONDUCTIVITY

Thermal conductivity is defined as" the amount of heat conducted in one second through one cubic meter of a substance whose two opposite faces are maintained at the temperature difference of one degree centigrade." It is denoted by "K". Formula K=QL/ADTt Unit : Unit of thermal conductivity is J/mKs OR watt/m.K.
EXPRESSION FOR THERMAL CONDUCTIVITY
Experiments indicates that the amount of heat conducted through a solid block is : Directly proportional to temperature difference between two faces of block.
DQ a DT ...................... (i)
Directly proportional to the area of cross - section of block.
DQ a A ...................... (ii)

Directly proportional to the the time interval to which heat is conducted.
DQ a t ...................... (iii)
Inversly proportional to the length of block.
DQ a 1/L ...................... (iv)
Combining above facts,we get
DQ a DT.A.t /L
OR

OR

KINETIC MOLECULAR THEORY OF MATTER

KINETIC MOLECULAR THEORY OF MATTER
According to kinetic theory of matter:
Matter is made of very small particles called MOLECULES. These molecules are in a state of motion. They possess Kinetic Energy. Molecular motion may be translational , rotational or vibrational. These molecules attract each other. As the temperature of a substance is increased , its molecular speed is also increased and vice versa. If a substance is compressed , The K.E of its molecules increases and its temperature rises For latest information , free computer courses and high impact notes visit : www.citycollegiate.com
BROWNIAN MOTION
A famous scientist ROBERT BROWN observed that molecules of a substance are moved in ZIG ZAG path. Their motion is random. They collide with each other and move in a new direction after collision in ZIG ZAG fashion. This type of motion present in the molecules of matter is called "Brownian motion".
Brownian motion
ELASTICITY
The property of solid by virtue of which a solid body recovers its original shape after the removal of an applied force is called "ELASTICITY".
ELASTIC LIMIT
If applied force on a solid is gradually increased, a state is reached after which the material will not return to it original shape even after the removal of applied force. This limit is called "ELASTIC LIMIT". After elastic limit, material is permanently deformed. Different substances have different elastic limit.
STRESS
When a body is deformed, the internal force came into play per unit area to restore it to its original state is called "STRESS" OR "Stress is an opposing force expressed per unit area which resists any change in shape."
Stress is equal to the force per unit area. Mathematically:
or
Stress produces when a body is made to change in length, volume or Shape by the application of an external force

MACHINES

MACHINE
A machine is a device by means of which work can be performed easily or in a convenient manner. A machine can be used : To lift heavy loads by applying little force. To enlarge magnitude of force To increase rate of work done To change the direction of force Example of simple machines are : Lever, pulley, inclined plane, wedge, screw etc.
EFFORT OR POWER
The power directly applied to a machine to lift a load is called Effort or Power. It is denoted by ‘P’.
LOAD OR WEIGHT
The weight lifted by a machine is called Load. It is denoted by ‘W’.
MECHANICAL ADVANTAGE
The ratio of weight (load) lifted by a machine to the force(effort) applied on a machine is called mechanical advantage of the machine. Greater the value of mechanical advantage of a machine, more easier is the work done. Mathematically,
M.A = load/effort
OR
M.A = W/P
UNIT:
It has no unit.
INPUT
Amount of work done on a machine by a given effort (force) is called input of a machine.
Input = effort x distance through which effort acts OR
input = P x d
OUTPUT
Amount of work done by a machine on the load (weight) is called output of the machine.
Output = load x distance covered by the load OR
Output = W x D
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EFFICIENCY
The ratio of output of a machine to the input of machine is called its efficiency.
h = output/input h = (W x D)/(P x d) Efficiency in %: h = (W x D)/(P x d )x100
UNIT:
It has no unit.
IDEAL MACHINE
An ideal machine is a hypothetical machine whose output is equal to its input. For an ideal machine
output = input
Efficiency of an ideal machine is 100% because there is no loss of energy in an ideal machine due to friction or any other means that can waste useful energy.
M.A of an ideal machine is d / h.
_LEVER
Lever is a simple machine which is used to lift heavy bodies or heavy load in a very easy way. Lever consists of a rigid bar capable to rotate about a fixed axis called fulcrum. Effort is applied at one end of the bar and weight can be lifted from the other end.

TYPES OF LEVER
There are three kinds of lever depending upon the positions of load , effort and fulcrum.
FIRST KIND OF LEVER
In the first kind of lever, the fulcrum F lies between effort (P) and load (W).

Example: common balance, seesaw, scissors, handle of hand pump.
SECOND KIND OF LEVER
In the second kind of lever, load (W) lies between effort (P) and fulcrum (F).

Example: door, nutcracker, punching machine.
THIRD KIND OF LEVER
In the third kind of lever, effort (P) lies between load (W) and fulcrum (F). Example: forceps, jaws, human forearm, firetong.

CIRCULAR MOTION AND GRAVITATION

GRAVITATION
Every object in our universe attracts the other object with certain fore towards its center. This force of attraction is known asGRAVITATIONAL FORCE and the phenomenon is called GRAVITATION. This is gravitational force which is responsible for the uniformity or regularity in our daily astronomical life. The whole system of the universe is in order only due to this force. Due to gravitation, the system of our universe is working uniformly and smoothly. The planets around the earth or around the sun moves in an orderly motion due to gravitation.
NEWTON’S LAW OF GRAVITATION
In order to explain the gravitational force between two bodies, Newton formulated a fundamental law known after his name i.e. "NEWTON'S LAW OF GRAVITATION" Newton’s law of gravitation states that every object in the universe attracts the other object with a force and :
(1) The gravitational force of attraction between two bodies is directly proportional to the product of their masses.
F a m₁ x m₂ ------- (1)
(2) The gravitational force of attraction between two bodies is inversely proportional to the square of the distance between their centers.
F a 1/d² --------- (2)
MATHEMATICAL REPRESENTATION
Combining (1) and (2)
F a m₁m₂ /d²
F = G m₁m₂/d²
Where G = universal gravitational constant
Value of G:
G = 6.67 x 10^-11 Nm²/kg²
MASS OF THE EARTH
Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘M_e’ and radius of earth is ‘R_e’ .

Gravitational force of attraction between earth and body is
F = G m M_e/ R_e²
We know that the force of attraction of the earth on a body is equal to weight the weight of body.
i.e
F = W
therefore
W = G m M_e/ R_e²
But W = mg
mg = G m M_e/ R_e²
or g = G M_e/R_e²
or M_e = g x R_e²/G
From astronomical data: g= 9.8 m/s² R_e= 6.4 x 10⁶ m G = 6.67 x 10^-11 N-m²/kg² Putting these values in the above equation.
M_e = 9.8 (6.4 x 10⁶)²/6.67 x 10^-11 or

TORQUE - CENTER OF GRAVITY

TORQUE - CENTER OF GRAVITY

Torque
The torque or moment of force can be define as
“ The tendency of a force to produce rotation in a body about an axis is called torque or moment of force."
The turning effect of a force depends upon two factors: The magnitude of force (F) Moment arm (r) The torque about any axis is given by the product of force and moment arm

Torque = force x moment arm OR
Positive torque: If a body rotates about its axis in anti clockwise direction, then the torque is taken positive .
Negative torque: If the body rotates in the clockwise direction, then the torque is taken as negative .
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Center of gravity
The center of a body is that point in the body through which the resultant forces due to the earth’s attraction posses and through which the whole weight of the body always acts. OR Center of gravity of a body is a point where total weight of the body is concentrated. Every body posses a center of gravity and this is irrespective of the body. Its is not necessary that the center of gravity should be within the body, but it may also be situated in space out side the body. Example: center of gravity of a ring is at the center, which is in the space. Center of gravity of different objects: Rectangle Center of gravity of a rectangular is at the point of intersection of its diagonals Circle Center of gravity of a circle is at its center. Square Center of gravity of square is at the point of intersection of its diagonals. Regular bar The center of gravity of a regular bar is at its geometrical center. Triangle The center of gravity of a triangle is at the point of intersection of its medians. Cylinder The center of gravity of a cylinder is at the axis of cylinder.

STATES OF EQUILIBRIUM

States of equilibrium
There are three states of equilibrium:
Stable equilibrium Unstable equilibrium Neutral equilibrium
Stable equilibrium
When the center of gravity of a body lies below point of suspension or support, the body is said to be in STABLE EQUILIBRIUM. For example a book lying on a table is in stable equilibrium.
Explanation
A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge and then allowed to fall, it will come back to its original position. Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.
Reason of stability
When the book is lifted its center of gravity is raised . The line of action of weight passes through the base of the book. A torque due to weight of the book brings it back to the original position.

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Unstable equilibrium
When the center of gravity of a body lies above the point of suspension or support, the body is said to be in unstable equilibrium
Example
pencil standing on its point or a stick in vertically standing position.
Explanation: If thin rod standing vertically is slightly disturbed from its position it will not come back to its original position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are vertically standing cylinder and funnel etc.
Reason of instability
when the rod is slightly disturbed its center of gravity is lowered . The line of action of its weight lies outside the base of rod. The torque due to weight of the rod toppled it down.

Neutral equilibrium
When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium. Example: rolling ball.
Explanation
If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. This type of equilibrium is called NEUTRAL EQUILIBRIUM.
Reason of neutral equilibrium
If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity is at the same height as before.

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