Question

In a double slit experiment the angular width of a fringe is found to be 0.2∘ on a screeen 1 m away. The wavelength of light used is 6000 Å. What will be the angular width of a fringe if the entire experimental arrangement is immersed in water? Refractive index of water =43.

A
0.15
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B
0.18
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C
0.2
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D
0.27
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Solution

The correct option is A 0.15∘ The angular width of a fringe is given by θ=λd In air: θa=λad In water: θw=λwd ∴θwθa=λwλa or θw=λwθaλa ...(1) Now, refractive index is defined as μw=speed of light in airspeed of light in water =vavw=νλaνλw=λaλw ...(2) where ν is the frequency of light which remains unchanged. Using Eq. (2) in Eq. (1) we have θw=θaμw=0.2∘4/3=0.15∘ So, the correct choice is (a).

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