Question

Two coherent sources of different intensities send waves which interfere. The ratio of the maximum intensity to the minimum intensity is $25$. The intensities are in the ratio:

Answer 1

As maximum intensity is given by
$I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2\propto (A_1+A_2{)}^2$
And minimum intensity is given by $I_{max}=(\sqrt{I_1}-\sqrt{I_2}{)}^2\propto (A_1-A_2{)}^2$
So, ratio of maximum to minimum intensity is given by
$\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2}{(\sqrt{I_1}-\sqrt{I_2}{)}^2}=\frac{(A_1+A_2{)}^2}{(A_1-A_2{)}^2}=25$
Now,
$\frac{A_1+A_2}{A_1-A_2}=5$
$\Rightarrow A_1+A_2=5(A_1-A_2)$
$\frac{A_1}{A_2}=\frac{3}{2}$
$\frac{I_1}{I_2}={\left(\frac{A_1}{A_2}\right)}^2=\frac{9}{4}$
Final answer: $\left(2.25\right)$