FSc Notes: FSc Part 1

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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

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

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

STATICS

Statics
Statics is the branch of mechanics which deals with the study of bodies at rest under a number of forces, the equilibrium, conditions of equilibrium, types of equilibrium and torque etc.
Equilibrium
A body is said to be in equilibrium if it is at rest or moving with uniform velocity. In other words if the linear and angular acceleration of a body are zero, the body is said to be in equilibrium. Or we can say that when two or more forces act on a body such that their resultant or combining effect on the body is Zero and the body retains its state of rest or of uniform motion then the body is said to be in equilibrium.
Example
A book lying on the table, suspended bodies, all stationary bodies , jump by using parachute.
Types of equilibrium
With respect to the state of a body, equilibrium may be divided into two categories: 1. Static equilibrium. 2. Dynamic equilibrium. For latest information , free computer courses and high impact notes visit :
Static equilibrium
If the combined effect of all the forces acting on a body is zero and the body is in the state of rest then its equilibrium is termed asstatic equilibrium. For example: All stationary bodies
Dynamic equilibrium
when a body is in state of uniform motion and the resultant of all the forces acting upon it is zero then it is said to be in dynamic equilibrium. For example: Jump by using parachute.
Conditions of equilibrium
There are two conditions of equilibrium are as follows
First condition of equilibrium
The first condition of equilibrium stated as follow:
To maintain the transitional equilibrium in a body the vector sum of all the forces acting on the body is equal to zero i.e.

AREA OF PARALLELOGRAM

COMMUTATIVE LAW OF VECTOR ADDITION
Consider two vectors and . Let these two vectors represent two adjacent sides of a parallelogram. We construct a parallelogram
OACB as shown in the diagram. The diagonal OC represents the resultant vector

	From above figure it is clear that:
	This fact is referred to as the commutative law of vectr addition .
	ASSOCIATIVE LAW OF VECTOR ADDITION
	The law states that the sum of vectors remains same irrespective of their order or grouping in which they are arranged. Consider three vectors , and
	Applying "head to tail rule" to obtain the resultant of (+ ) and (+ )
	Then finally again find the resultant of these three vectors :

	This fact is known as the ASSOCIATIVE LAW OF VECTOR ADDITION.

MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR)

MULTIPLICATION OF A VECTOR BY A SCALAR
When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector. If however a vector is multiplied by a negative number (for example -2, -3 ,-5, -60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed.


The product of a vector by a scalar quantity (m) follows the following rules:
	(m) = (m) which is called commutative law of multiplication.
	m(n) = (mn) which is called associative law of multiplication .
	(m + n) = m+ n which is called distributive law of multiplication .
	DIVISION OF A VECTOR BY A SCALAR
	The division of a vector by a scalar number (n) involves the multiplication of the vector by the reciprocal of the number (n) which generates a new vector.
	Let n represents a number or scalar and m is its reciprocal then the new vector is given by :
	where m = 1/n
	and its magnitude is given by:

	The direction of is same as that of if (n) is a positive number. The direction of is opposite as that of if (n) is a negative number.

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