First slide

Ray optics

Question

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index 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 be

Difficult

A

not separate the three colours at all
B

separate the red colour part from the green and blue colours
C

separate the blue colour part from the red and green colours
D

separate all the three colours from one another

Solution

(b): As beam of light is incident normally on the face AB of the right angled prism ABC, so no refraction occurs at face AB and it passes straight and strikes the face AC at an angle of incidence i=45°.
$For total reflection to take place at face A C,$
$i > i_{c} or \sin i > \sin i_{c}$
$where i_{c} is the critical angle.$
$But as here i = 45 ° and \sin i_{c} = \frac{1}{μ}$
$∴ \sin 45 ° > \frac{1}{μ} or \frac{1}{\sqrt{2}} > \frac{1}{μ}$
$or μ > \sqrt{2} = 1.414$
$As μ_{red} (= 1.39) < μ (= 1.414) while μ_{green} (= 1.44) and μ_{blue} (= 1.47) > μ$
(=1.414), so only red colour will be transmitted through face AC while green and blue colours will suffer total internal reflection. So the prism will separate red colour from the green and blue colours as shown in the following figure.

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