Question 61 of 295

Three rays of light, namely red $\left(R\right)$, green $(G)$ and blue $(B)$ are incident on the face $PQ$ of a right angled prism $PQR$ as shown in figure.

The refractive indices of the material of the prism for red, green and blue wavelength are $1.27,1.42$ and $1.49$ respectively. The colour of the ray(s) emerging out of the face $PR$ is :

AgreenBredCblue and greenDblue

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Answer: (B) red

Assuming that the right angled prism is an isoceles prism, so the other angles will be $45^{\circ}$ each.
$\Rightarrow$ Each incident ray will make an angle of $45^{\circ}$ with the normal at face $PR$.
$\Rightarrow$ The wavelength corresponding to which the incidence angle is less than the critical angle, will pass through $PR$.
$\Rightarrow {\theta }_{C}=$ critical angle
$\Rightarrow {\theta }_{C}={\sin }^{-1}\left(\dfrac{1}{\mu }\right)$
$\Rightarrow$ If ${\theta }_{C}\geq 45^{\circ}$
the light ray will pass
$\Rightarrow {\left({\theta }_{C}\right)}_{Red}={\sin }^{-1}\left(\dfrac{1}{1.27}\right)=51.94^{\circ}$
Red will pass.
$\Rightarrow {\left({\theta }_{C}\right)}_{Green}={\sin }^{-1}\left(\dfrac{1}{1.42}\right)=44.76^{\circ}$
Green will not pass
$\Rightarrow {\left({\theta }_{C}\right)}_{Blue}={\sin }^{-1}\left(\dfrac{1}{1.49}\right)=42.15^{\circ}$
Blue will not pass
$\Rightarrow$ So only red will pass through $PR$.