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  4. A ray falls on a prism ABC.(AB = BC) and travels as shown in figure. The least value of refractive index of material of the prism, should be:

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Q. A ray falls on a prism $ABC.(AB = BC)$ and travels as shown in figure. The least value of refractive index of material of the prism, should be:Physics Question Image

Delhi UMET/DPMTDelhi UMET/DPMT 2005Ray Optics and Optical Instruments

Solution:

Ray inside the prism is suffering total internal reflection.
The given prism is a right angled prism, and angle $\angle L M N=45^{\circ}$, and since the ray is suffering total internal reflection the critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is $90^{\circ}$, that is $C=45^{\circ}$.
From Snells law $\mu=\frac{1}{\sin C}$
$\mu=\frac{1}{\sin 45^{\circ}}=\sqrt{2}$.

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