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  4. Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is

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Q. Two coherent beams of light of same wavelengths superpose in a certain region of space. If the intensity of one beam is 4 times that of the other, then the ratio of intensity at a bright point to that at a dark point is

Wave Optics

Solution:

$\frac{I_{\max }}{I_{\min }}=\frac{\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}}{\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}},$
Now $I_{1}=4 I_{2}$
$\Rightarrow \frac{I_{\max }}{I_{\min }}=\frac{(\sqrt{4}+1)^{2}}{(\sqrt{4}-1)^{2}}=\frac{9}{1}$