If the angle of incidence is twice the angle | vedclass

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(A) According to Snell's law,the refractive index $\mu$ is given by $\mu = \frac{\sin i}{\sin r}$.Given that the angle of incidence $i$ is twice the a

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$2 \cos^{-1} \left( \frac{\mu}{2} \right)$

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(A) According to Snell's law,the refractive index $\mu$ is given by $\mu = \frac{\sin i}{\sin r}$.Given that the angle of incidence $i$ is twice the angle of refraction $r$,so $i = 2r$.Substituting this into Snell's law: $\mu = \frac{\sin(2r)}{\sin r}$.Using the trigonometric identity $\sin(2r) = 2 \sin r \cos r$,we get $\mu = \frac{2 \sin r \cos r}{\sin r}$.Simplifying,we have $\mu = 2 \cos r$,which implies $\cos r = \frac{\mu}{2}$.Therefore,$r = \cos^{-1} \left( \frac{\mu}{2} \right)$.Since $i = 2r$,we get $i = 2 \cos^{-1} \left( \frac{\mu}{2} \right)$.

If the angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$,then the angle of incidence is

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