In the figure,ABC is the cross-section of a r | vedclass

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(A) The light ray is incident normally on face $AB$,so it enters the prism without deviation.It strikes the face $BC$ at an angle of incidence $i = 90

Vedclass · Accepted Answer

$	heta \leq 37^o$

Vedclass · Answer

(A) The light ray is incident normally on face $AB$,so it enters the prism without deviation.It strikes the face $BC$ at an angle of incidence $i = 90^o - 	heta$.For the light not to cross the face $BC$,it must undergo Total Internal Reflection $(TIR)$ at the interface $BC$.The condition for $TIR$ is $i \geq 	heta_c$,where $	heta_c$ is the critical angle.The refractive index of the prism is $n_1 = 3/2$ and the refractive index of the slab is $n_2 = 6/5$.The critical angle $	heta_c$ is given by $\sin 	heta_c = \frac{n_2}{n_1} = \frac{6/5}{3/2} = \frac{6}{5} 	imes \frac{2}{3} = \frac{4}{5}$.Thus,$	heta_c = \sin^{-1}(4/5) = 53^o$.Applying the condition $i \geq 	heta_c$:$90^o - 	heta \geq 53^o$$90^o - 53^o \geq 	heta$$	heta \leq 37^o$.

In the figure,$ABC$ is the cross-section of a right-angled prism and $BCDE$ is the cross-section of a glass slab. The value of $\theta$ so that light incident normally on the face $AB$ does not cross the face $BC$ is (given $\sin^{-1}(3/5) = 37^o$):

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