Physics - Wave Optics Question with Solution | TestHub

The distance of the $n^{\text{th}}$ bright band from the central bright band in an interference pattern is given by

$X_n=n\frac{\lambda D}{d}$

The distance of the $m^{\text{th}}$ dark band from the central bright band is given by

$X_m^{\prime }=\left(m-\frac{1}{2}\right)\frac{\lambda D}{d}$

Taking the ratio of their distances, we get

$\frac{X_n}{X_m^{\prime }}=\frac{n\frac{\lambda D}{d}}{\left(m-\frac{1}{2}\right)\frac{\lambda D}{d}}=\frac{n}{m-\frac{1}{2}}$

Thus, the required ratio is $n:\left(m-\frac{1}{2}\right)$.

Answer: $n:\left(m-\frac{1}{2}\right)$