Assertion: The refractive index of diamond is | vedclass

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(C) Given: Refractive index of diamond with respect to air,$\mu_d = \sqrt{6}$. Refractive index of liquid with respect to air,$\mu_l = \sqrt{3}$.The r

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If the Assertion is correct but Reason is incorrect.

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(C) Given: Refractive index of diamond with respect to air,$\mu_d = \sqrt{6}$. Refractive index of liquid with respect to air,$\mu_l = \sqrt{3}$.The refractive index of diamond with respect to the liquid is given by $\mu = \frac{\mu_d}{\mu_l} = \frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2}$.For total internal reflection to occur,the angle of incidence $i$ must be greater than the critical angle $C$. The critical angle $C$ is given by $\sin C = \frac{1}{\mu} = \frac{1}{\sqrt{2}}$.Thus,$C = 45^{\circ}$.Since the given angle of incidence $i = 30^{\circ}$ is less than the critical angle $C = 45^{\circ}$,total internal reflection will not occur. Therefore,the Assertion is incorrect.The Reason states $\mu = \frac{1}{\sin C}$,which is the correct formula for the critical angle where $\mu$ is the refractive index of the denser medium with respect to the rarer medium. Thus,the Reason is correct.

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