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Question

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 refractive index of water to be 4/3.

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Solution

Given:

The given distance between the screen and the slit, D=1m.

The wavelength of the light, λ=600nm.

Angular width of the fringe in the air, θ 1 =0.2°.

Let θ 2 be the width of the fringe in water.

Refractive index of the water, μ= 4 3 .

The relation of refractive index with the angular width is,

μ= θ 1 θ 2

Substitute values in the above equation.

4 3 = 0.2 θ 2 θ 2 = 0.2×3 4 =0.15°

Thus, the angular fringe in the water will be 0.15°.


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