Refractive index of a medium is mu. If the an | vedclass

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(A) Given, angle of incidence $i = 2r$, where $r$ is the angle of refraction.According to Snell's law, $\mu_1 \sin i = \mu_2 \sin r$.Assuming the ligh

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

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(A) Given, angle of incidence $i = 2r$, where $r$ is the angle of refraction.According to Snell's law, $\mu_1 \sin i = \mu_2 \sin r$.Assuming the light travels from air $(\mu_1 = 1)$ to a medium with refractive index $\mu_2 = \mu$, we have:$1 \cdot \sin(2r) = \mu \sin r$Using the trigonometric identity $\sin(2r) = 2 \sin r \cos r$, we get:$2 \sin r \cos r = \mu \sin r$Since $\sin r 
eq 0$, we can divide both sides by $\sin r$:$2 \cos r = \mu \implies \cos r = \frac{\mu}{2}$Thus, $r = \cos^{-1}\left(\frac{\mu}{2}ight)$.Since $i = 2r$, the angle of incidence is $i = 2 \cos^{-1}\left(\frac{\mu}{2}ight)$.

Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refraction, then the angle of incidence is

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