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

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 90o 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

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.

Momentum- Law of conservation of Momentum

MOMENTUM
Quantity of motion of a body is referred to as "MOMENTUM".
Definition
Momentum of a moving body defined as :
"the product of mass and velocity of a body is called MOMENTUM."
Mathematically
Momentum = mass x velocity
It is a vector quantity. Momentum is always directed in the direction of velocity.    The unit of momentum is in S.I system kg .m/s or NS.    Momentum depends upon mass and velocity of body.
LAW OF CONSERVATION OF MOMENTUM.
The law of conservation of momentum states that:
"when some bodies constituting an isolated system act upon one another, the total momentum of the system remains constant." OR "the total momentum of an isolated system of interacting bodies remains constant." OR "Total momentum of an isolated system before collision is always equal to total momentum after collision."
Consider an isolated system of two bodies 'A' and 'B' as shown. The masses of bodies are ma and mb and
MATHEMATICAL REPRESENTATION
Consider two bodies of mass m1 and m2 moving initially with velocities u1 and u2.
Total momentum before collision = m1u1 + m2u2
Let after collision their velocities become v1 and v2.
Total momentum after collision = m1v1 + m2v2
According to the law of conservation of momentum
m1u1 + m2u2 = m1v1 + m2v2

DIFFERENCE BETWEEN MASS AND WEIGHT

Mass		Weight
(1) The quantity of matter in a body is          called its mass.		(1) Weight is the force by which the earth          attracts a body towards its center.
(2) Mass is a scalar quantity.		(2) Weight is a vector quantity and is always          directed towards the center of the earth.
(3) Mass of a body is always constant          every where in the universe.		(3) Weight of a body vary place to place and          become zero on the center of earth and far          away from the surface of earth.
(4) Mass of a moving body is m=F/a.		(4) Weight of a body is W = mg.
(5) Mass can be determine by an          ordinary balance.		(5) Weight of a body is measured by spring          balance.
(6) Unit of mass in S.I system is          KILOGRAM ( kg).		(6) Unit of weight in S.I system is NEWTON (N).
FRICTION
When a body slides over the surface of another body, an opposing force is set up between them to resist    the motion. The force which opposes the motion is called friction OR Force of Friction.
Force of friction tends to decelerate a body and always acts in the opposite direction of motion.
CATEGORIES OF FRICTION    (1) Contact friction    (2) Fluid friction
LIMITING FRICTION
When an external force is applied against the force of friction, the force of friction also increases by the    same amount. Therefore, It adjusts itself in such a way that it is equal and opposite to the external    force. It has a maximum value just before the motion starts. So friction is a self-adjusting force. The    maximum force of friction that stops the body from moving is called LIMITING FRICTION.    It is denoted by Fs.    LIMITING FRICTION is directly proportional to the surface reaction.
Limiting friction Fs is:
Where R = normal reaction  but R = W and R = mg
Where = constant known as coefficient of friction.
COEFFICIENT OF FRICTION
Coefficient of friction is the ratio of LIMITING FRICTION to the NORMAL REACTION.
Coefficient of friction is constant for a given pair of surfaces but different for different pairs
Unit of :    Since it is a ratio of two similar quantities, therefore it has no unit as shown.
ROLLING FRICTION		www.citycollegiate.com
When a body rolls over a surface, the force of friction is called ROLLING FRICTION. When a sphere rolls    over a surface it experiences an opposing force called ROLLING FRICTION.    Rolling friction is much less than the sliding friction because in case of rolling contact area of two surfaces    is very small as compared to sliding.

NEWTON'S 2ND LAW OF MOTION

When an unbalanced force acts upon a body, it is accelerated in the direction of force. The magnitude of acceleration is directly proportional to the applied force and is inversely proportional to the mass of body.
MATHEMATICALLY
Combining (i) and (ii)
....
a = k (F)(1/m) here constant k=1
a= (1)(F)(1/m) Or
SECOND STATEMENT
With the help of above equation 2nd law of motion can be expressed as:
THE NET FORCE ACTING ON A BODY IS EQUAL TO THE PRODUCT OF THE MASS OF BODY AND THE ACCELERATION PRODUCED IN IT.
NEWTON'S 3RD LAW OF MOTION
STATEMENT:
"To every action there is a reaction equal in magnitude but opposite in direction"
OR
"When a body exerts a force on another body, the second body also exerts a force on the first body of same magnitude but in the opposite direction"
FACTION = -FREACTION
Force exerted by one body is called ACTION and the force exerted by the second body is called    REACTION.
EXAMPLES:    (1) Motion of rocket: fuel burns rapidly, exerts force in downward direction and rocket moves upward        as a reaction.    (2) Book lying on a table: weight of the book on the surface is action and the force exerted by the          surface (R) is the reaction.                         R = -W    (3) Walking on a street    (4) Motion of helicopter

FORCE & MOTION

"Force is an agent which changes or tends to change the state  of rest or of uniform motion of a body."
In the light of Newton's 2nd law of motion Force may be defined as :
"Force acting on a body is equal to the product of the mass and acceleration produced in the body."
i.e.
F = ma
Force can accelerate or decelerate a body.  Force is a vector quantity.
UNITS OF FORCE
(i) NEWTON (N) in S.I system    (ii) DYNE in C.G.S system    (iii) POUND (Lb) in BRITISH ENGINEERING SYSTEM (F.P.S)
NEWTON
Newton is the unit of force and can be defined as:
"The amount of force that produces an acceleration of 1 m/s2 in a body of mass 1-kg is equal to 1 NEWTON."
1 N = 1 kg x 1m/s2
[ N = kg m/s2]
NEWTON 'S FIRST LAW OF MOTION
STATEMENT:    Newton 's first law of motion states that:
"Every body remains at rest or continues to move with uniform velocity in straight line unless an unbalanced force acts upon it".
EXPLANATION
First law of motion consists of two parts:
PART NO 1:
The first part states that a body at rest remains at rest unless an unbalanced force acts upon it.    This part is in accordance with our common experience for example, a book lying on a table remains at    rest unless it is lifted or pushed by an external force.
PART NO 2 :
Second part states that a body in motion remains in motion with uniform velocity unless an unbalance    force acts upon it. This part is not self-evident because a ball pushed once does not continue its motion    forever. A little consideration however, shows that there is an opposing force like ground friction and air    friction acting in this case. These frictional forces are responsible to stop the ball. If we eliminate these    opposing forces, a body in motion will continue its motion forever.
INERTIA
"Tendency of a body by virtue of which the body at rest or moving with uniform velocity retains its state is called INERTIA."
OR
"Property of a body by which a body resists a force, applied to it to change its state of rest or of uniform velocity is called INERTIA."
INERTIA of a body is directly related to its mass. Heavy bodies have greater inertia while lighter bodies    have little inertia.
LAW OF INERTIA AND THE FIRST LAW OF MOTION
Every body in the universe opposes the force which tends to change its state of rest or of uniform    motion. This property INERTIA is a direct consequence of FIRST LAW OF MOTION. As heavy bodies due    to greater INERTIA requires forces of large magnitude and bodies of small masses require small forces.    By the above explanation of INERTIA we conclude that the state of rest or motion does not change by its    self unless an external force acts upon it, which is according to the FIRST LAW OF MOTION.    Thus the FIRST LAW OF MOTION is also called LAW OF INERTIA.

DISTRIBUTIVE LAW FOR DOT PRODUCT

DISTRIBUTIVE LAW FOR DOT PRODUCT
According to distributive law for dot product:
	PROOF
	Consider three vectors , and .Here we will use geometric interpretation of dot product by drawing projection as shown below. First we obtain the sum of vectors  and by head to tail rule then we draw projection  and from the terminal point of vector respectively onto the direction of . The dot product  is equal to the projection of vector  onto the direction of  multiplied by the magnitude of. 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.

EQUATIONS OF MOTION EQUATIONS OF MOTION

FIRST EQUATION OF MOTION Vf = Vi + at
Consider a body initial moving with velocity "Vi". After certain interval of time "t", its velocity becomes "Vf". Now
Change in velocity = Vf - Vi  OR DV =Vf – Vi
	Due to change in velocity, an acceleration "a" is produced in the body. Acceleration is given by
	a = DV/t
	Putting the value of "DV"
	a = (Vf – Vi)/t at = Vf – Vi at + Vi =VfOR
	SECOND EQUATION OF MOTION OR S = Vit + 1/2at2
	Consider a car moving on a straight road with an initial velocity equal to ‘Vi’. After an interval of time ‘t’ its velocity becomes ‘Vf’. Now first we will determine the average velocity of body.
	Average velocity = (Initial velocity + final velocity)/2 OR Vav = (Vi + Vf)/2
	but Vf = Vi + at
	Putting the value of Vf
	Vav = (Vi + Vi + at)/2 Vav = (2Vi + at)/2    Vav = 2Vi/2 + at/2   Vav = Vi + at/2                            Vav = Vi + 1/2at.......................................(i)
	we know that
	S = Vav x t
	Putting the value of ‘Vav’
	S = [Vi + 1/2at] t
	THIRD EQUATION OF MOTION OR 2aS = Vf2 – Vi2
	Initial velocity, final velocity, acceleration, and distance are related in third equation of motion.
	Consider a body moving initially with velocity ‘Vi’. After certain interval of time its velocity becomes ‘Vf’. Due to change in velocity, acceleration ‘a’ is produced in the body. Let the body travels a distance of ‘s’ meters.  According to first equation of motion:
	Vf = Vi + at      OR Vf – Vi = atOR                          (Vf – Vi)/a = t....................(i)
	Average velocity of body is given by:
	Vav = (Initial velocity + Final velocity)/2                               Vav = (Vi + Vf)/2.................. (ii)
	we know that :
	S = Vav x t.................. (ii)
	Putting the value of Vav and t from equation (i) and (ii) in equation (iii)
	S = { (Vf + Vi)/2} { (Vf – Vi)/a} 2aS = (Vf + Vi)(Vf – Vi)
	According to [ (a+b)(a-b)=a2-b2]

KINEMATICS

KINEMATICS
"Kinematics is the branch of Physics in which we discuss bodies at rest or motion without the reference of external agent that causes motion or rest."  OR "The branch of physics which deals with the description of motion of objects without reference to the force or agent causing motion in it, is called Kinematics."
REST
	"If a body does not change its position with respect to its surroundings then the body is said to be in a state of rest."
	MOTION
	"If a body continuously changes its position with respect to its surrounding than it is said to be in a state of motion."
	TYPES OF MOTION
	Motion of objects can be divided into three categories.
	(i) TRANSLATIONAL MOTION (ii) ROTATIONAL MOTION (iii) VIBRATIONAL MOTION
	TRANSLATIONAL MOTION
	"Motion of a body in which every particle of the body is being displaced by the same amount is called Translational Motion".
	EXAMPLE:  (i) Motion of a person on a road. (ii) Motion of a car or truck on a road.
	ROTATIONAL MOTION
	"Type of motion in which a body rotates around a fixed point or axis is called Rotational Motion."
	EXAMPLE:  (i) Motion of wheel (ii) Motion of the blades of a fan
	VIBRATIONAL MOTION
	"Type of motion in which a body or particle moves to and fro about a fixed point or mean position is called Vibratory Motion."
	EXAMPLE: (i) Motion of simple pendulum (ii) Motion of the wires of guitar (iii) Motion of swing
	DISPLACEMENT
	"Distance between two points in a particular direction is called Displacement." OR Displacement may also be defined as "the minimum distance between two points in a particular direction."
	It is a vector quantity and is always directed from the initial point to the terminal point. It is denoted by "d".
	SPEED
	"Distance covered by a moving body in one second is called its Speed". OR "Distance covered by a body in unit time is called Speed".
	Speed is a scalar quantity.
	FORMULA
	Speed = Distance traveled/Time taken  OR v = S/t
	UNIT
	Unit of speed in S.I system is "m/sec".
	VELOCITY
	"Distance covered by a body in a particular direction in one second is called Velocity". OR "Displacement of a body in unit time is called Velocity". OR "Change of position of a body per second in a particular direction is called Velocity."
	FORMULA
	velocity = displacement/time
	UNIT
	In S.I system unit of velocity is meter/second. It is a vector quantity.
	ACCELERATION
	"The rate of change of velocity of a body is called Acceleration." OR "Change in velocity of a body in unit time is called its acceleration."
	It is denoted by "a". It is a vector quantity. If a body moves with uniform velocity or constant velocity then its acceleration will be zero. UNIT: m/sec2.
	FORMULA
	Acceleration = change in velocity/time OR a = DV/t

Addition of vectors by Head to Tail method (Graphical Method)

Head to Tail method or graphical method is one of the easiest method used to find the resultant vector of two of more than two vectors.
	DETAILS OF METHOD
	Consider two vectors  and  acting in the directions as shown below:
	In order to get their resultant vector by head to tail method we must follow the following steps:
	STEP # 1
	Choose a suitable scale for the vectors so that they can be plotted on the paper.
	STEP # 2
	Draw representative line  of vector
	Draw representative line  of vector  such that the tail of  coincides with the head of vector .
	STEP # 3
	Join 'O' and 'B'.  represents resultant vector of given vectors  and  i.e.
	STEP # 4
	Measure the length of line segment  and multiply it with the scale choosen initially to get the magnitude of resultant vector.
	STEP # 5
	The direction of the resultant vector is directed from the tail of vector  to the head of vector .