00:02
In this question we are asked to derive law of reflection and law of refraction according to the fermat's principle.
00:13
Fermat's principle generally states that light travels between any two points in the shortest distance and the least time k.
00:24
Hence now let us take a surface, this is the polished surface in light ray coming from here will reflect at this point, let us take this is angle of incidence theta 1 and if it reflects like this and this says theta 2, then this is point b, this is point a, then time required should be the least time between the point a and point b that is what fermat's rule says.
00:56
Then let us take this distance travelled by the light as l, then this distance if we take it as x, then this will be l minus x, let us take this side h1 and this is side h2, then applying inside the formula for the least time in fermat's rule, p is equal to root of x square plus h1 square divided by p plus l minus x the whole square plus h2 square divided by p, here the whole root.
01:44
So, now derivative of p will be equal to 0 as it takes the least time, hence pt divided by px will be equal to x divided by c root of x square plus h1 square plus minus l minus x divided by c root of l minus x the whole square plus h2 square, this will be equal to 0.
02:28
So, now as dt by dx is equal to 0, we can write x divided by root of x square plus h1 square equal to l minus x divided by l minus x the whole square plus h2 square the whole root.
02:49
So, now this is nothing but the value of sin theta 1 equal to this is nothing but sin of theta 2, we can write as sin theta 1 is theta 1 equal to theta 2.
03:09
So, this is nothing but the law of reflection which says angle of incidence equal to angle of reflection...