Question

What happens to fringe width, when the separation between the slits as well as distance of the screen from the slit are halved?

Answer 1

Since fringe width,

ß = \(\frac{\lambda D}{d}\)

When D' = \(\frac{D}{2}\) and d' = \(\frac{d}{2},\) then

The new fringe width,

ß' = \(\frac{\lambda D'}{d'} = \frac{\lambda D}{2} \times \frac{2}{d}\)

= \(\frac{\lambda D}{d} = \beta\)

i.e. the fringe width remains the same.