Wave Optics - Result Question 1
1. The periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:
[2008]
(a) $I_1+I_2$
(b) $(\sqrt{I_1}+\sqrt{I_2})^{2}$
(c) $(\sqrt{I_1}-\sqrt{I_2})^{2}$
(d) $2(I_1+I_2)$
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Solution:
- (d) The resultant intensity of two periodic waves at a point is given by
$I=I_1+I_2+2 \sqrt{I_1 I_2} \cdot \cos f$.
Resultant intensity is maximum if $\cos \phi=-1$
i.e. $I _{\max }=I_1+I_2+2 \sqrt{I_1 I_2}$
Resultant intensity is minimum if $\cos \phi=+1$
i.e, $I _{\min }=I_1+I_2-2 \sqrt{I_1 I_2}$
Therefore, the sum of the maximum and minimum intensities is $I _{\max }+I _{\text{min }}$
$=I_1+I_2+2 \sqrt{I_1 I_2}+I_1+I_2-2 \sqrt{I_1 I_2}$
$=2(I_1+I_2)$
