Consider a glass prism immersed in a liquid a | vedclass

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Question

(A) The given situation is shown in the figure. The light ray enters the prism perpendicular to the face $AB$, so it passes undeviated into the prism

Vedclass · Accepted Answer

$\cos ^{-1}(0.8)$

Vedclass · Answer

(A) The given situation is shown in the figure. The light ray enters the prism perpendicular to the face $AB$, so it passes undeviated into the prism and strikes the face $AC$.In the triangle formed by the prism, the angle of incidence $i$ at the face $AC$ is $i = 90^{\circ} - 	heta$.For total internal reflection to occur at face $AC$, the angle of incidence $i$ must be greater than or equal to the critical angle $i_c$.Thus, for the largest value of $	heta$, we set $i = i_c$.Using Snell's law at the interface $AC$ for the critical angle condition:$\sin(i_c) = \frac{\mu_{	ext{liquid}}}{\mu_{	ext{glass}}}$Substituting $i = 90^{\circ} - 	heta$ and the given refractive indices:$\sin(90^{\circ} - 	heta) = \frac{1.2}{1.5}$$\cos(	heta) = \frac{12}{15} = \frac{4}{5} = 0.8$Therefore, $	heta = \cos^{-1}(0.8)$.

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