In a single slit diffraction experiment, for a wavelength of light ' $\lambda$ ', half-angular width of the…
In a single slit diffraction experiment, for a wavelength of light ' $\lambda$ ', half-angular width of the principle maxima is ' $\theta$ '. Also for wavelength of light $\mathrm{p} \lambda$, the half angular width of the principle maxima is $q \theta$. The ratio of the halfangular widths of the first secondary maxima in the first case to second case will be
$\mathrm{p}: 1$
$\mathrm{q}: 1$
$\mathrm{p}: \mathrm{q}$
$\mathrm{q}: \mathrm{p}$
Solution
Let \(d\) and \(d\) ' be the width of the slits in the two cases.
\(\begin{aligned}
& \therefore & \theta & =\frac{\lambda}{d} \text { and } q \theta=\frac{p \lambda}{d^{\prime}} \\
& \therefore & \frac{d}{d^{\prime}} & =\frac{q}{p}
\end{aligned}\)