Question

prove that i=e with Snell's law​

Answer 1

your question is wrong

sin i/ sin r = constant..

Perhaps this will help, if you are looking at a non Calculus approach.enter image description here Consider two parallel rays A and B coming through the medium 1 (say air) to the medium 2 (say water). Upon arrival at the interface L between the two media (air and water), they continue their parallel course in the directions U and V respectively.

Let us assume that at time t=0, light ray A arrives at the interface L at point C, while ray B is still shy of the surface by a distance PD. B travels at the speed v1=cn1 and arrives at D in t seconds. During this time interval, ray A continues its journey through the medium 2 at a speed v2=cn2 and reaches the point Q.

We can formulate the rest, geometrically (looking at the parallel lines) from the figure. Let x denote the distance between C and D.

xsin(θi)xsin(θr)======PDv1tcn1tCQv2tcn2t

Thus,

n1sin(θi)n2sin(θr)==cxtcxt

Re arranging this will take us to the Snell's law as we know.

n2n1=sin(θi)sin(θr)

Answer 2

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