The refracting angle of a prism is 60^{circ} | vedclass

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(A) For a ray to be transmitted through the prism,the emergent ray must not undergo total internal reflection at the second face. The limiting case oc

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(A) For a ray to be transmitted through the prism,the emergent ray must not undergo total internal reflection at the second face. The limiting case occurs when the emergent ray grazes the second face,i.e.,the angle of emergence $e = 90^{\circ}$.Let $n_2 = \sqrt{7/3}$ be the refractive index of the prism and $n_1 = 1$ be the refractive index of the surroundings.Applying Snell's law at the second face $(LN)$:$n_2 \sin r_2 = n_1 \sin e$$\sqrt{7/3} \sin r_2 = 1 	imes \sin 90^{\circ} = 1$$\sin r_2 = \sqrt{3/7} \approx 0.6546$$r_2 = \arcsin(0.6546) \approx 40.89^{\circ}$Given the prism angle $A = 60^{\circ}$,we know $A = r_1 + r_2$. Therefore:$r_1 = A - r_2 = 60^{\circ} - 40.89^{\circ} = 19.11^{\circ}$Now,applying Snell's law at the first face $(LM)$:$n_1 \sin i = n_2 \sin r_1$$1 	imes \sin i = \sqrt{7/3} 	imes \sin 19.11^{\circ}$$\sin i = 1.5275 	imes 0.3273 \approx 0.5$$i = \arcsin(0.5) = 30^{\circ}$

The refracting angle of a prism is $60^{\circ}$ and the refractive index is $\sqrt{7/3}$ relative to the surroundings. The limiting angle of incidence of a ray that will be transmitted through the prism is ......$^{\circ}$

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