The index of refraction for violet light in silica flint gla

The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 60.0° if the angle of incidence is 45.0°?

Solution

From Law of Refraction, we write, sin theta 2 = sin theta 1 /n

For Violet, sin theta 2 = sin45/1.66 = 27.10 degrees

For Red, sin theta 2 = sin45/1.62 = 27.77 degrees

Theta 3 = 60 - Theta 2

For Violet, Sin theta4 = 1.66* sin (60-27.10) = 67.65 degrees

For Red, Sin theta4 = 1.62* sin (60-27.77) = 62.41 degrees

Angular Dispersion = 67.65-62.41 = 5.23 Degrees