A beam of light consisting of red, green and blue colours is incident on a right angled prism, fig. The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will `

Options

A. Separate the red colour part from green and blue colours
B. Separate the blue colour part from the red and green colours.
C. Separate all the three colours from one another.
D. Not separate the three colours at all

Answer

A

Explanation

In Fig. on face `AC`, `/_i = 45^(@)`
For total internal reflection, `I ge C`, so `sin I gt sin C`

As `mu = (1)/(sin C), :. sin C = (1)/(mu)`
`sin 45^(@) ge (1)/(mu), :. (1)/(sqrt(2)) ge (1)/(mu)`
or `mu ge sqrt(2) mu ge 1.414`
Since, `mu` for green colour and violet colour is greater than `1.414`, so they will undergo total internal reflection. Red colour will not undergo total internal reflection. Therefore, it will be separated.