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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=0.24/3=0.15
So, the correct choice is (a).

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