Q142 / 160 · AP EAMCET 2024 (19 May Shift 2) · Physics

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^{\circ}$. The light ray is also found to be refracted at an angle of $30^{\circ}$. Then the refractive index of the liquid is

  • Correct answer
    A
    $\sqrt{2}$
  • B
    $\sqrt{3}$
  • C
    $\sqrt{\frac{3}{2}}$
  • D
    $\frac{3}{2}$

Solution

For prism, $\mathrm{s}_{\mathrm{m}}=30^{\circ}, \mathrm{r}=30^{\circ}$ $\therefore \quad A=2 r=2 \times 30^{\circ}=60^{\circ}$ $\therefore$ Refractive index, $\mu=\frac{\sin \left(\frac{A+S_m}{2}\right)}{\sin \frac{A}{2}}$ $=\frac{\sin \left(\frac{60+30}{2}\right)}{\sin \left(\frac{60}{2}\right)}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}=\sqrt{2}$

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

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