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.

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.

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.

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

MEASUREMENT

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MEASUREMENT
Meter
Meter is the unit of length in S.I. System.   Meter is defined as "The distance between the two marks on a Platinum-Iridium bar kept at 0OC in the   International Bureau of Weight and Measures in Paris."   One meter = 100 cm   One meter = 1000 mm
Kilogram
Kilogram is the unit of mass in S.I. System.   "Kilogram is defined as the mass of a platinum cylinder placed in the International Bureau of Weight and   Measures in Paris."   One kilogram = 1000gram
Second
Second is the unit of time in S.I. System.   A second is defined in terms of the time period of Cs-133 atoms.  i.e." one second is equal to 9,192,631,770 periods of vibrations of Cs-133 atoms."   60 seconds = one minute   3600 seconds = one hour
Least Count
Minimum measurement that can be made by a measuring device is known as " LEAST COUNT'.
Least count (vernier callipers) = minimum measurement on main scale / total number of divisions on                                                                                                              vernier scale
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Least count (screw gauge) = minimum measurement on main scale / total number of divisions on                                                                                                   circular scale
Smaller is the magnitude of least count of a measuring instrument, more precise the measuring   instrument is.   A measuring instrument can not measure any thing whose dimensions are less than the magnitude of   least count.   Least Count of Vernier Callipers = 0.01 cm   Least Count of Micrometer Screw gauge = 0.001 cm
Zero Error
It is a defect in a measuring device (Vernier Callipers & Screw Gauge).   When jaws of a Vernier Callipers or Screw Gauge are closed, zero of main scale must coincides with the   zero of vernier scale or circular scale in case of screw gauge.   If they do not coincide then it is said that a zero error is present in the instrument.
Types Of Zero Error
Zero error may be positive or negative.
A positive zero error in the instrument shows a larger measurement than the actual measurement.  In order to get exact measurement, positive zero error is subtracted from the total reading.
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A negative zero error in the instrument shows a smaller measurement than the actual measurement.   In order to get exact measurement, negative zero error is added to the total reading.
Pitch
"Perpendicular distance between two consecutive threads of the screw gauge or spherometer is called PITCH."
Pitch = Distance traveled on main scale / total number of rotations
Error
An error is defined as "The difference between the measured value and actual value."
If two persons use the same instrument for measurement for finding the same measurement, it is not   essential that they may get the same results. There may arises a difference between their   measurements. This difference is referred to as an "ERROR".
Types Of Error
Errors can be divided into three categories:   (1) Personal Error   (2) Systematic Error   (3) Random Error
Personal Error
An error comes into play because of faulty procedure adopted by by the observer is called "PERSONAL   ERROR".   Personal error comes into existence due to making an error in reading a scale. It is due to faulty   procedure adopted by the person making measurement.
Systematic Error
The type of error arises due to defect in the measuring device is known as "SYSTEMATIC ERROR".   Generally it is called "ZERO ERROR". it may be positive or negative error. Systematic error can be   removed by correcting measurement device.
Random Error
The error produced due to sudden change in experimental conditions is called "RANDOM ERROR".   For example:   Sudden change in temperature, change in humidity, fluctuation in potential difference (voltage).   It is an accidental error and is beyond the control of the person making measurement.