Ray Optics

JEE Main level, single correct, medium

269 of 295

Question 269 of 295

A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face ABA B. The refractive indices of the material for the above red, green and blue colours are 1.39,1.441.39,1.44 and 1.471.47 respectively. A person looking on surface ACA C of the prism will see

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Answer: (D) red colour only

For light to come out through face 'AC', total internal reflection must not take place.
 i.e., θ<c⇒sin⁡θ<sin⁡c⇒sin⁡θ<1μ\begin{aligned} & \text { i.e., } \theta < c \Rightarrow \sin \theta < \sin c \\ & \Rightarrow \sin \theta < \frac{1}{\mu} \end{aligned}
or μ<1sin⁡θ⇒μ<1sin⁡45∘\quad \mu \lt \frac{1}{\sin \theta} \Rightarrow \mu \lt \frac{1}{\sin 45^{\circ}}
⇒μ<2⇒μ<1.414\Rightarrow \mu < \sqrt{2} \Rightarrow \mu < 1.414

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