Question

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio
(a) 25 : 1
(b) 5 : 1
(c) 9 : 4
(d) 625 : 1

Answer 1

(c) 9 : 4

Ratio of maximum intensity and minimum intensity is given by
$$\begin{gathered} \frac{I_{max}}{I_{min}}=\frac{{\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2}{{\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2}=\frac{25}{1} \\ \Rightarrow \sqrt{I_1}=3and\sqrt{I_2}=2 \\ \Rightarrow I_1=9and{I}_2=4 \end{gathered}$$
Then,
$\frac{I_1}{I_2}=\frac{9}{4}$