# Answer to Question #23143 in Optics for Mohan

Question #23143

A ray of Light at an angle of 60 degree on one face of a prism angle 30 degree. The ray emerging out of the prism makes an angle of 30 degree with the incident ray. Calculate the refractive index of the material of the prism.

Expert's answer

On the entrance to the prism,

sin (60 deg) = n * sin (alpha)

On the exit, n*sin(beta) = sin (gamma)

from knowing the prism angle,

60 deg = 30 deg + gamma

from where,

gamma = 30 deg

beta = 60 - alpha.

The resulting system is

sin (60 deg) = n * sin (alpha)

sin (30 deg) = n * sin (60 deg - alpha)

From solving it,

n = sqrt((4+sqrt(3))/3) = 1.3823...

Answer: 1.38.

sin (60 deg) = n * sin (alpha)

On the exit, n*sin(beta) = sin (gamma)

from knowing the prism angle,

60 deg = 30 deg + gamma

from where,

gamma = 30 deg

beta = 60 - alpha.

The resulting system is

sin (60 deg) = n * sin (alpha)

sin (30 deg) = n * sin (60 deg - alpha)

From solving it,

n = sqrt((4+sqrt(3))/3) = 1.3823...

Answer: 1.38.

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