A double slit produces a diffraction pattern that is a combination of single- and double-slit interference. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single-slit pattern falls on the fifth maximum of the double-slit pattern.

The ratio of the width of the slits to the separation between them is 1:5

Explanation:

Given that:

Specific minimum for single slit = m₁ =1

Specific maximum of double slit = m₂ = 5

Formula for single slit differential minimum

here W is slit thickness, m is minimum order. For given case m=1

Formula for double slit differential maxima:

d is separation between slits, m is order for constructive interference i.e m =5.

λ is the wave length of light.

We have to find the ratio of the width of the slits to the separation between them, if the first minimum of the single-slit pattern falls on the fifth maximum of the double-slit pattern.

So dividing (1) by (2)