Question
Two coherent waves of equal amplitude produce interference pattern in Young’s double slit experiment. What is the ratio of intensity at a point where phase difference is $\frac{\pi}{2}$ to intensity at centre?
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Answer
$\text{I}_\frac{\pi}{2}=\text{a}^2_1+\text{a}^2_2+\text{2a}_1\text{a}_2\cos\varphi$
$=\text{a}^2+\text{a}^2+2\text{a}^2\cos\frac{\pi}{2}=2\text{a}^2$
$\text{I}_\max=(\text{a}_2+\text{a}_2)^2=(\text{a}+\text{a})^2=4\text{a}^2$
$\therefore\frac{\text{I}_\frac{\pi}{2}}{\text{I}_\max}=\frac{2\text{a}^2}{\text{4a}^2}=\frac{1}{2}.$
$=\text{a}^2+\text{a}^2+2\text{a}^2\cos\frac{\pi}{2}=2\text{a}^2$
$\text{I}_\max=(\text{a}_2+\text{a}_2)^2=(\text{a}+\text{a})^2=4\text{a}^2$
$\therefore\frac{\text{I}_\frac{\pi}{2}}{\text{I}_\max}=\frac{2\text{a}^2}{\text{4a}^2}=\frac{1}{2}.$
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