State two conditions to obtain sustained interference of light. In young's double slit experiment, using light of wavelength 400 nm, interference fringes of width X are obtained. The wavelength of light is increased to 600 nm and the separation between the slits is halved. if one wants the observed fringe width on the screen to be the same in the two cases, find the ratio of the distance between the screen and the plane of the slits in the two arrangements.

Answer

`3 : 1`

Explanation

Here, `lambda_(1) = 400 nm, lambda_(2) = 600 nm, d_(2) = (d_(1))/(2)`
`(D_(1))/(D_(2)) = ? As beta_(2) = beta_(1)`
`:. (lambda_(2)D_(2))/(d_(2)) = (lambda_(1)D_(1))/(d_(1))`
`:. (D_(1))/(D_(2)) = (d_(1))/(d_(2)) xx (lambda_(1))/(lambda_(2)) = 2 xx (600)/(400) = 3 : 1`