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A Young's double slit interference arran...

A Young's double slit interference arrangement with slits `S_(1)` and `S_(2)` is immersed in water (refractive index `=4//3`) as shown in the figure. The positions of maxima on the surface of water are given by `x^(2) = p^(2)m^(2)lambda^(2)-d^(2)`, where `lambda` is the wavelength of light in air (reflactive index = 1), 2d is the separation between the slits and m is an integer. The value of P is ..........

Text Solution

Verified by Experts

The correct Answer is:
3
For constructive interference `Deltax=mlambda`
`(4)/(3)sqrt(d^(2)+x^(2))-sqrt(d^(2)+x^(2))=mlambda`
`(1)/(2) sqrt(d^(2)+x^(2))=mlambda`
`x^(2)=9m^(2)lambda^(2)-d^(2)`
`p=3`
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