Question 234: Wave Optics

Question

The ratio of the distance of $n^{	ext {th }}$ bright band and $\mathrm{m}^{	ext {th }}$ dark band from the central bright band in an interference pattern is

Accepted Answer

Distance of $\mathrm{n}^{	ext {th }}$ bright fringe from centre
$$ y_n=\frac{n \lambda D}{d}=n W \quad\left(\because W=\frac{\lambda D}{d}ight) $$
Distance of $\mathrm{m}^{	ext {th }}$ dark fringe from centre
$$ \begin{array}{ll}  & y_n^{\prime}=\left(m-\frac{1}{2}ight) \frac{\lambda D}{d}=\left(m-\frac{1}{2}ight) W \ 	herefore \quad & 	ext { Ratio }=\frac{y_n}{y_m^{\prime}}=\frac{n W}{\left(m-\frac{1}{2}ight) W}=\frac{n}{\left(m-\frac{1}{2}ight)} \ & 	ext { Ratio }=n:\left(m-\frac{1}{2}ight) \end{array} $$

Answer

$n: m$

Answer

$m: n$

Answer

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

Answer

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

Wave Optics

The ratio of the distance of n^{\text {th }} bright band and \mathrm{m}^{\text {th }} dark band from the central bright band in an interference pattern is

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