JEE Main 2022 · Physics · Ray and Wave Optics · medium

In a single-slit diffraction experiment the slit width is 0.2 mm and the screen is 2 m from the slit. The whole apparatus is immersed in a liquid of…

Numerical answer

In a single-slit diffraction experiment the slit width is

0.2\ \mathrm{mm}

and the screen is

2\ \mathrm{m}

from the slit. The whole apparatus is immersed in a liquid of refractive index

1.25

and illuminated with light of wavelength

500\ \mathrm{nm}

measured in air. The width of the central maximum on the screen, in mm, is

Show answer and solution

Answer: 8

In the liquid the wavelength becomes

\lambda'=\dfrac{\lambda}{\mu}=\dfrac{500}{1.25}=400\ \mathrm{nm}

. The central maximum extends between the first minima, so its width is

\dfrac{2\lambda'D}{a}=\dfrac{2\times400\times10^{-9}\times2}{0.2\times10^{-3}}=8\times10^{-3}\ \mathrm{m}=8\ \mathrm{mm}

. In air the width would have been

10\ \mathrm{mm}

, so immersion shrinks the pattern by the factor

\mu

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