Question

Show that in Young's experiment the distance between successive maxima and minima are equal.

Answer 1

The condition for constructive interference:

$$d\text{ sin}\theta=m\lambda.$$

The distance between maxima for two successive m:

$$\delta=(m+1)\lambda-m\lambda=\lambda.$$

The condition for destructive interference:

$$d\text{ sin}\theta=\bigg(m+\frac12\bigg)\lambda.$$

The distance between two successive minima:

$$\delta=\bigg(m+\frac12+1\bigg)\lambda-\bigg(m+\frac12\bigg)\lambda=\lambda.$$