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Q.
In Young's double-slit experiment, the ratio of intensities of a bright band and a dark band is $16:1$ . The ratio of amplitudes of interfering waves will be
NTA AbhyasNTA Abhyas 2022
Solution:
Since $\frac{I_{m a x .}}{I_{m i n .}}=\frac{16}{1}$
$\frac{\left(\right. \sqrt{I_{1}} + \sqrt{I_{2}} \left.\right)^{2}}{\left(\right. \sqrt{I_{1}} - \sqrt{I_{2}} \left.\right)^{2}} = \frac{16}{1}$
$\sqrt{I_{1}} + \sqrt{I_{2}} = 4 \sqrt{I_{1}} - 4 \sqrt{I_{2}}$
$A_{1} + A_{2} = 4 A _{1} - 4 A_{2}$
$3 A_{1} = 5 A_{2}$
$\Rightarrow \frac{A_{1}}{A_{2}} = \frac{5}{3}$