Question

In Young’s double slit experiment, show that fringe width ω (fringe separation) is given by

ω = `(lambda D)/d`

where the terms have their usual meaning.

Answer 1

Because θ is small,

tan θ ≈ sin θ

`(y_m)/D = (BN)/(AB) = (m lambda)/d`

y_m = `(m lambda)/d`

ω = `y_m - y_(m - 1)`

= `(m lambda D)/d - (m - 1) (lambda d)/d`

= `(lambda D)/d`

Hence proved.