21. In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water ? ( $μ_{water}$ = 4/3)

21. In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water ? (μ_water = 4/3)

(a) 0.266°

(b) 0.15°

(c) 0.05°

(d) 0.1°

Answer :  (b) 0.15°

\( \theta_w = \dfrac{\lambda}{d} = \dfrac{400 \, \text{nm}}{d} = 0.2^\circ \)

\( \theta_w = \dfrac{\lambda_{\text{water}}}{d} = \dfrac{\tfrac{400 \, \text{nm}}{\mu}}{d} = \theta_{w_{\text{water}}} \)

\( \mu = \dfrac{0.2^\circ}{\theta_{w_{\text{water}}}} \)

\( \theta_{w_{\text{water}}} = \dfrac{0.2^\circ}{\mu} \)

\( = \dfrac{0.2^\circ}{\tfrac{4}{3}} \)

\( = \dfrac{0.6^\circ}{4} \)

\( = 0.15^\circ \)