JEE Main 2021 — Ray Optics Question with Solution

Assuming that the right angled prism is an isoceles prism, so the other angles will be $45°$ each.

$\Rightarrow$ Each incident ray will make an angle of $45°$ with the normal at face $PR$.

$\Rightarrow$ The wavelength corresponding to which the incidence angle is less than the critical angle, will pass through $PR$.

$\Rightarrow {\theta }_{\mathrm{C}}=$ critical angle

$\Rightarrow {\theta }_{\mathrm{C}}={\sin }^{-1}\left(\frac{1}{\mu }\right)$

$\Rightarrow$ If ${\theta }_C\ge 45°$

the light ray will pass

$\Rightarrow {\left({\theta }_{\mathrm{C}}\right)}_{\mathrm{Red}}={\sin }^{-1}\left(\frac{1}{1.27}\right)=51.94°$

Red will pass.

$\Rightarrow {\left({\theta }_{\mathrm{C}}\right)}_{\mathrm{Green}}={\sin }^{-1}\left(\frac{1}{1.42}\right)=44.76°$

Green will not pass

$\Rightarrow {\left({\theta }_{\mathrm{C}}\right)}_{\mathrm{Blue}}={\sin }^{-1}\left(\frac{1}{1.49}\right)=42.15°$

Blue will not pass

$\Rightarrow$ So only red will pass through $PR$.