Q143 / 160 · TS EAMCET 2022 (19 Jul Shift 2) · Physics

In a double-slit experiment performed in air the angular width of a fringe is found to be $0.15^{\circ}$ on a screen placed $80 \mathrm{~cm}$ away. The wavelength of light used is $490 \mathrm{~nm}$. The angular width of the fringe if the entire apparatus is immersed in medium of refractive index $\frac{5}{3}$ is

  • Correct answer
    A
    $0.09^{\circ}$
  • B
    $0.7^{\circ}$
  • C
    $0.9^{\circ}$
  • D
    $0.11^{\circ}$

Solution

$\begin{aligned} & \theta=\frac{\lambda}{\mathrm{d}} \Rightarrow \theta \propto \lambda \\ & \Rightarrow \quad \frac{\theta_2}{\theta_1}=\frac{\lambda_2}{\lambda_1}=\frac{\lambda}{\mu \cdot \lambda} \\ & \Rightarrow \quad \theta_2=\frac{\theta_1}{\mu}=\frac{0.15^{\circ}}{5} \times 3=0.09^{\circ}\end{aligned}$

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

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