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

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]

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 .