question_answer

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

Correct Answer: A

Solution :

                 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,          \[\sin i>\sin C\]                 \[\sin {{45}^{o}}>\frac{1}{\mu }\] 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.