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A double slit apparatus is immersed in a...

A double slit apparatus is immersed in a liquid of refractive index 1.33. it has slit separation of 1 mm and distance between the plane of the slits and the screen is 1.33 m. the slits are illuminated by a parallel beam of light whose wavelength in air is 6300 Å. what is the fringe width?

Text Solution

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KEY IDEA
In this situation, the wavelength of the light in the medium changes. So, the fringe width will change. Also, the refractive index has to be taken relative to the medium in which interference has to be done.
Calculation: The wavelength in liquid is
`lambda_(1)=(lambda_(alpha) mu_(alpha))/(mu_(1))=(6300 Å xx 1)/(1.33)=(6.3 xx 10^(-7))/(1.33) m`
Therefore, fringe width in liquid is
`beta_(1)=(lambda_(1)D)/(d)=(6.3 xx 10^(-7) xx 1.33)/(1.33 xx 1 xx 10^(-3))=6.3 xx 10^(-4) m = 0.63 mm`.
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