Question

A beam of light consisting of red green and blue colours is incident on a right-angle prism. The refractive indexes of the material of the prism for the above red, green and blue wavelength are 1.39, 1.44 and 1.47 respectively. The prism will:

A) separate the red color part from the green and blue colours
B) separate the blue color part from the red and green colours
C) separate all three colours from one another
D) not separate the three colours at all

Answer 1

Hint :The refractive index is the ratio of the speed of light in a vacuum to the speed of the light in a prism. If the refractive index of the light is greater than the refractive index of any medium, then the light gets reflected from that medium. The light whose refractive index is less than the refractive index of medium gets refracted from the medium.

Complete Step By Step Answer:
The incident angle for light of all colours is $ i = 90^\circ $ , the refraction angle is $ r = 45^\circ $ refractive index of red light is $ {n_r} = 1.39 $ , refractive index of green light is $ {n_g} = 1.44 $ and refractive index of blue light is $ {n_b} = 1.47 $ .
Use Snell's law to find the refractive index of the prism. The expression is given as,
 $ n = \dfrac{{\sin i}}{{\sin r}}......\left( 1 \right) $
Substitute $ 90^\circ $ for $ i $ and $ 45^\circ $ for r in the equation (1) to find the refractive index of the prism.
 $ n = \dfrac{{\sin 90^\circ }}{{\sin 45^\circ }} $
 $ n = \sqrt 2 $
 $ n = 1.414 $
Compare the refractive index of prism with the refractive index of red light.
 $ n\left( {1.414} \right) > {n_r}\left( {1.39} \right) $
Compare the refractive index of prism with the refractive index of green light.
 $ n\left( {1.414} \right) < {n_g}\left( {1.44} \right) $
Compare the refractive index of prism with the refractive index of blue light.
 $ n\left( {1.414} \right) < {n_b}\left( {1.47} \right) $

From the above comparison of the refractive index of the prism with refractive indices of red, green and blue lights, it shows the green and blue lights get reflected and red light gets refracted from the prism.
Therefore, the prism will separate the red colour part from the green and blue colours.
The option (A) is correct.

Note :
The total internal reflection is the process of the returning of the light to the incident medium from a less dense medium. The refraction is the process of deflection from the original path of the light. Be careful in applying the Snell’s law and remember that the refractive index is the ratio of the sine of an incident angle to the sine of the refracted angle.