Question

1. A ray of light strikes a transparent surface from air at an angle . If the angle between the reflected and
refracted ray is a right angle. the refractive index of the other surface is given by
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Answer 1

Explanation:

Let i be the angle of incidence & reflection & r be the angle of refraction in the optical medium.

As per given condition, the angle between reflected & refracted rays is 90∘ hence we have

i+r+90∘=180∘

r=90∘−i

If n is the refractive index of optical medium w.r.t. air then using Snell’s Law as follows

sini=nsinr

sini=nsin(90∘−i)

sini=ncosi

n=tani

where , i is the angle of incidence on transparent (optical) surface which should be known