Wave Optics

JEE Main level, single correct, medium

24 of 191

Question 24 of 191

Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is:

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Answer: (D) 491\frac{49}{1}

Intensity ∝( amplitude )2\propto(\text { amplitude })^2
I1I2=169=a12a22⇒a1=4;a2=3\begin{aligned} &\frac{I_1}{I_2}=\frac{16}{9}=\frac{a_1^2}{a_2^2} \\ &\Rightarrow \mathrm{a}_1=4 ; \mathrm{a}_2=3 \end{aligned}
Therefore the ratio of intensities of bright and dark parts
IBright IDark =(a1+a2)2(a1−a2)2=(4+3)2(4−3)2=491\frac{I_{\text {Bright }}}{I_{\text {Dark }}}=\frac{\left(a_1+a_2\right)^2}{\left(a_1-a_2\right)^2}=\frac{(4+3)^2}{(4-3)^2}=\frac{49}{1}

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