Question

A ray of light passes from vacuum into a medium of refractive index µ, the angle of incidence is found to be twice the

angle of refraction .Then the angle of incidence is​

Answer 1

This the angle of incidence is i = 2 cos^-1 ( n / 2)

Explanation:

Let i be the incident angle and r be the refracted angle

We are given

i = 2r  r = i / 2

The refractive index of vacuum is 1 and that of another medium is n

From snell's law,

1 sin i = n sin r

Sini = n sin(   i / 2  )

2 sin (   i / 2  ) cos (   i / 2  ) =  n sin(   i / 2  )

2 sin (   i / 2  ) [ 2 cos (   i / 2  ) - n ] = 0

2 sin (   i / 2  ) = 0 = sinπ

i = 2π

[ 2 cos (   i / 2  ) - n ] = 0

i = 2 cos^-1 ( n / 2)

This the angle of incidence is i = 2 cos^-1 ( n / 2)