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Two monochromatic coherent light beams \(A\) and \(B\) have intensities \(L\) and \(\frac{ L}{4}\) respectively. If these beams are super. posed, the maximum and minimum intensities will be
(A) \(\frac{9 \mathrm{~L}}{4}, \frac{\mathrm{L}}{4}\)
(B) \(\frac{5 L}{4}, 0\)
(C) \(\frac{5 \mathrm{~L}}{2}, 0\)
(D) \(2 L, \frac{L}{2}\)

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Ans: (A)
$$
\begin{aligned}
&I_{\text {maximum }}=\left(\sqrt{L}+\sqrt{\frac{L}{4}}\right)^{2}=\frac{9 L}{4} \\
&I_{\text {minimum }}=\left(\sqrt{L}-\sqrt{\frac{L}{4}}\right)^{2}=\frac{L}{4}
\end{aligned}
$$
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