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  4. In Young's double slit experiment, if the widths of the slits are in the ratio 4: 9, the ratio of the intensity at maxima to the intensity at minima will be

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Q. In Young's double slit experiment, if the widths of the slits are in the ratio $4: 9$, the ratio of the intensity at maxima to the intensity at minima will be

Wave Optics

Solution:

Slit width ratio $=4: 9$;
hence $I_{1}: I_{2}=4: 9$
$\therefore \frac{a_{1}^{2}}{a_{2}^{2}}=\frac{4}{9} $
$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{3}$
$\therefore \frac{I_{\max }}{I_{\min }}=\frac{\left(a_{1}+a_{2}\right)^{2}}{\left(a_{1}-a_{2}\right)^{2}}=\frac{25}{1}$