Question

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. 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

• A. separate part of the red colour from the green and blue colours
• B. separate part of the blue colour from the red and green colours
• C. separate all the three colours from one another
• D. not separate even partially any colour from the other two colours

Answer 1

Answer: (A)

The situation is shown in figure.

At face $AB,i=0.$
So, $r=0$, i.e., light will be incident on face $AC$ at an angle of incidence $45^{\circ }$.
The face $AC$ will not transmit the light for which $i>C$
ie, $\sin i>\sin C$
$\sin 45^{\circ }>\frac{1}{\mu }$
Or $\frac{1}{\sqrt{2}}>\frac{1}{\mu }$
Or $\mu >\sqrt{2}$
As refractive index for red colour is $1.39$ which is less than
$\sqrt{2}$, so red will be transmitted through face $AC$ while green and blue will be reflected.