In Fig. 6(b).80, light rays of blue, green and red wavelength are incident on an isoscels right angled prism. Explain with reason which ray of light will be transmitted through the face `AC`. The refractive index of the prism for red, green and blue light are `1.39, 1.424` and `1.476` respectively.

Answer

Red rays will be transmitted

Explanation

As `ABC` is an isoceles right angled prism, angle of incidence of each ray is `45^(@)`. If critical angle `C` is less than `45^(@)`, the ray will be totally internally reflected at `AC`. When `/_C gt 45^(@)`, the ray will be transmitted through the face `AC`.
For red ray, `mu = 1.39`
`sin C = (1)/(mu) = (1)/(1.39) = 0.719, C = 46.0^(@)`
`:.` Red ray will be transmitted.
For green ray, `mu = 1.476`,
`sin C = (1)/(mu) = (1)/(1.424) = 0.702, C = 44.6^(@)`
`:.` green ray will be reflected at face `AC`.
For blue ray, `mu = 1.476`,
`sin C = (1)/(mu) = (1)/(1.476) = 0.678, C = 42.6^(@)`
`:.` Blue ray will also be reflected at face `AC`.