Ray Optics and Optical Instruments - Result Question 56
58. 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. [2015 RS]
Theprism will:
(a) separate all the three colours from one another
(b) not separate the three colours at all
(c) separate the red colour part from the green and blue colours
(d) separate the blue colour part from the red and green colours
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Answer:
Correct Answer: 58. (c)
Solution:
- (c) For total internal reflection, incident angle (i) $>$ critical angle $(i_C)$
So, $\sin i>\sin i_c$
$\sin 45^{\circ}>\frac{1}{\mu}$
$\Rightarrow \mu>\sqrt{2} \Rightarrow 1.414$
Since refractive index $\mu$ of green and voilet are greater than 1.414 so they will total internal reflected. But red colour will be refracted.
According to Snell’s law $\mu=\frac{\sin i}{\sin r}$
$\Rightarrow$ (1) $\sin 2 A=(\mu) \sin A \Rightarrow \mu=2 \cos A$
