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  4. The intensity of light coming from one of the slits in Young's double slit experiment is double the intensity from the other slit. The ratio of maximum intensity to minimum intensity in the interference pattern will be

Q. The intensity of light coming from one of the slits in Young's double slit experiment is double the intensity from the other slit. The ratio of maximum intensity to minimum intensity in the interference pattern will be

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Solution:

Given $I_1=2 I_2$ the required ratio is given by
$ \frac{I_{\max }}{I_{\min }}=\frac{\left(\sqrt{2 I_2}+\sqrt{I_2}\right)^2}{\left(\sqrt{2 I_2}-\sqrt{I_2}\right)^2}=\frac{(\sqrt{2}+1)^2}{(\sqrt{2}-1)^2}=\frac{3+2 \sqrt{2}}{3-2 \sqrt{2}}$
$ \text { or by } \frac{I_{\max }}{I_{\min }}=\frac{3+2 \times 1.414}{3-2 \times 1.414}=\frac{5.828}{0.172} \approx 34$

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