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 ..........

Answer

C

Explanation

3 For maxima
Path defference`=mlamda`
`:'``S_2A-S_1A=mlamda`
`[(n-1)sqrt(d^2+x^2)+sqrt(d^2+x^2]]-sqrt(d^2-x^2)=mlamda`
`(n-1)sqrt((d^2+x^2))=mlamda`
`sqrt(d^2+x^2)=3mlamda`
`d^2+x^2=9m^2lamda^2`
`x^2=9m^2lamda^2`
`x^2=9m^2lamda^2-d^2`
`p^2=9` `impliesp=3`