Three rays of light,namely red (R),green (G) | vedclass

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(B) Assuming that the right-angled prism is an isosceles prism,the other two angles are $45^{\circ}$ each.$\Rightarrow$ Each incident ray strikes the

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(B) Assuming that the right-angled prism is an isosceles prism,the other two angles are $45^{\circ}$ each.$\Rightarrow$ Each incident ray strikes the face $PR$ at an angle of incidence $i = 45^{\circ}$.$\Rightarrow$ $A$ ray will emerge from the face $PR$ if the angle of incidence $i$ is less than the critical angle $	heta_{C}$ for that specific wavelength.$\Rightarrow$ The critical angle is given by $	heta_{C} = \sin^{-1}\left(\frac{1}{\mu}ight)$.$\Rightarrow$ For the red ray: $\mu_{R} = 1.27$. $	heta_{C,R} = \sin^{-1}\left(\frac{1}{1.27}ight) \approx 51.94^{\circ}$. Since $45^{\circ} $\Rightarrow$ For the green ray: $\mu_{G} = 1.42$. $	heta_{C,G} = \sin^{-1}\left(\frac{1}{1.42}ight) \approx 44.76^{\circ}$. Since $45^{\circ} > 44.76^{\circ}$,the green ray will undergo total internal reflection and will not emerge.$\Rightarrow$ For the blue ray: $\mu_{B} = 1.49$. $	heta_{C,B} = \sin^{-1}\left(\frac{1}{1.49}ight) \approx 42.15^{\circ}$. Since $45^{\circ} > 42.15^{\circ}$,the blue ray will undergo total internal reflection and will not emerge.$\Rightarrow$ Therefore,only the red ray will emerge out of the face $PR$.

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