A ray is incident on a prism ABC and travels | vedclass

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(B) From the geometry of the prism,the angle of incidence at the second face (the face $BC$) is $45^{\circ}$.For the ray to undergo total internal ref

Vedclass · Accepted Answer

$\sqrt{2}$

Vedclass · Answer

(B) From the geometry of the prism,the angle of incidence at the second face (the face $BC$) is $45^{\circ}$.For the ray to undergo total internal reflection at this face,the angle of incidence must be greater than or equal to the critical angle $	heta_c$.Thus,$	heta_c \leq 45^{\circ}$.We know that $\sin 	heta_c = \frac{1}{\mu}$,where $\mu$ is the refractive index of the prism.Therefore,$\frac{1}{\mu} \leq \sin 45^{\circ}$.$\frac{1}{\mu} \leq \frac{1}{\sqrt{2}}$.$\mu \geq \sqrt{2}$.Hence,the minimum refractive index is $\sqrt{2}$.

$A$ ray is incident on a prism $ABC$ and travels as shown in the figure. The minimum refractive index of the material of the prism should be .......

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