Assertion: The maximum refractive index of th | vedclass

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(D) For total internal reflection to occur at the prism-liquid interface,the angle of incidence $i$ must be greater than or equal to the critical angl

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If both the Assertion and Reason are incorrect.

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(D) For total internal reflection to occur at the prism-liquid interface,the angle of incidence $i$ must be greater than or equal to the critical angle $c$.In the given figure,the ray strikes the interface at an angle of incidence $i = 45^o$.For total internal reflection,we require $i \ge c$,so $45^o \ge c$,or $\sin 45^o \ge \sin c$.Since $\sin c = \frac{\mu_{liquid}}{\mu_{prism}}$,and assuming the prism is glass with $\mu_{prism} \approx 1.5$,the condition for total internal reflection is $\sin 45^o \ge \frac{\mu_{liquid}}{\mu_{prism}}$.However,the question asks for the maximum refractive index of the liquid such that total internal reflection still occurs. This occurs when $c = 45^o$.Using the relation $\sin c = \frac{\mu_{liquid}}{\mu_{prism}}$,we get $\mu_{liquid} = \mu_{prism} \sin 45^o = 1.5 	imes \frac{1}{\sqrt 2} \approx 1.06$.The assertion states the value is $\sqrt 2$,which is incorrect as it assumes the prism refractive index is $2$. Given the standard context of such problems,the assertion and reason are both technically incorrect based on standard glass prisms.

Assertion: The maximum refractive index of the liquid for total internal reflection of the ray passing through the prism as shown in the figure must be $\sqrt 2$.
Reason: Here,the critical angle is $45^o$.

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Assertion: The maximum refractive index of the liquid for total internal reflection of the ray passing through the prism as shown in the figure must be $\sqrt 2$.Reason: Here,the critical angle is $45^o$.