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

3

Explanation

`x_(1)=sqrt(x^(2)+d^(2))`
`x_(2)=(4)/(3)sqrt(x^(2)+d^(2))`
`Deltax=((4)/(3)-1)sqrt(x^(2)+d^(2))=nlamda`
`(1)/(3)sqrt(x^(2)+d^(2))=nlamda`
`(x^(2)+d^(2))=9n^(2)lamda^(2)`
`therefore(P=3)`