In Young's double slit experiment interference fringes `1^(@)` apart are produced on the screen, the slit separation is `(lambda = 589 nm)`

Explanation

The fringe width , `beta = (lambda D)/(d)`
The angular separation of the fringes is given by
`theta = (beta)/(D) = (lambda)/(d)`
Given , `theta = 1^(0) = (pi)/(180) rad`
`lambda = 589 nm`
`:. d = (lambda)/(theta) = (589 xx 180 xx 10^(-9))/(pi)`
= 0 . 0 337 m m