A light ray is incident on a medium of refrac | vedclass

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Question

(B) According to Snell's law,$\mu = \frac{\sin i}{\sin r}$,where $i$ is the angle of incidence and $r$ is the angle of refraction.Given that $i = 2r$.

Vedclass · Accepted Answer

$2\cos^{-1}(\mu/2)$

Vedclass · Answer

(B) According to Snell's law,$\mu = \frac{\sin i}{\sin r}$,where $i$ is the angle of incidence and $r$ is the angle of refraction.Given that $i = 2r$.Substituting this into Snell's law: $\mu = \frac{\sin(2r)}{\sin r}$.Using the trigonometric identity $\sin(2	heta) = 2\sin	heta \cos	heta$,we get $\mu = \frac{2\sin r \cos r}{\sin r} = 2\cos r$.Therefore,$\cos r = \frac{\mu}{2}$,which implies $r = \cos^{-1}(\frac{\mu}{2})$.Since $i = 2r$,we have $i = 2\cos^{-1}(\frac{\mu}{2})$.

$A$ light ray is incident on a medium of refractive index $\mu$. The angle of incidence is twice the angle of refraction. The angle of incidence is:

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