Ncert Exercises & Solutions

10.7 In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take the refractive index of water to be 4/3.

Hint: Refractive index is related to angular width as: $\mu=\frac{\theta _{1}}{\theta _{2}} $

Step 1: Find the angular width of the fringe.
The distance of the screen from the slits, D= 1 m
The wavelength of light used, $λ_{1}$ = 600 nm
The angular width of the fringe in air $θ_{1} = 0.2 °$
The angular width of the fringe in water = $θ_{2}$
The Refractive index of water, $μ = 4 / 3$

$\begin{aligned} μ & = \frac{θ_{1}}{θ_{2}} \\ θ_{2} & = \frac{3}{4} θ_{1} \\ = \frac{3}{4} \times 0 .2 = 0.15° \end{aligned}$

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