Q141 / 160 · TS EAMCET 2023 (13 May Shift 1) · Physics

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

  • Correct answer
    A
    $\cos ^{-1}\left(\frac{\mu}{2}\right)$
  • B
    $\sin ^{-1}\left(\frac{\mu}{2}\right)$
  • C
    $2 \cos ^{-1}\left(\frac{\mu}{2}\right)$
  • D
    $\sin ^{-1}(\mu)$

Solution

Given, angle of incidence, $\mathrm{i}=2 \times$ angle of refraction, $\mathrm{r}$ from Snell's law $$ \begin{aligned} & \mu_1 \sin \mathrm{i}=\mu_2 \sin r \\ & 1 \times \sin 2 r=\mu \sin r \\ & 2 \sin r \cos r=\mu \sin r \end{aligned} $$ $\operatorname{Cos} r=\frac{\mu}{2}$

Hence, the correct answer is option: 'A'.

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