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) 25 : 16

Answer 1

answer : option (c) 9 : 4


explanation : Two coherent sources of different intensities $I_1$ and $I_2$ do interfere.

then, maximum intensity, $I_{max}=(\sqrt{I_1}+\sqrt{I_2})^2$

minimum intensity, $I_{min}=(\sqrt{I_1}-\sqrt{I_2})^2$

a/c to question,

$\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2})^2}{\sqrt{I_1}-\sqrt{I_2})^2}$

or, $\frac{25}{1}=\frac{5^2}{1^2}=\frac{(\sqrt{I_1}+\sqrt{I_2})^2}{\sqrt{I_1}-\sqrt{I_2})^2}$

or, $\frac{5}{1}=\frac{(\sqrt{I_1}+\sqrt{I_2})}{(\sqrt{I_1}-\sqrt{I_2})}$

or, $5(\sqrt{I_1}-\sqrt{I_2})=\sqrt{I_1}+\sqrt{I_2}$

or, $4\sqrt{I_1}=6\sqrt{I_2}$

hence, $\frac{I_1}{I_2}=\frac{9}{4}$