Two coherent sources of light have intensities in the ratio $I_1/I_2=16/1$. If they interfere, what is the ratio of the maximum to minimum intensity?

Solution

1. Given the ratio of intensities $I_1/I_2=16/1$, the ratio of their amplitudes is $$\begin{array}{rl}\sqrt{I_1}/\sqrt{I_2}& =\sqrt{16/1}\\ & =4/1\end{array}$$.
2. The ratio of maximum to minimum intensity is given by the formula $\frac{I_{\text{max}}}{I_{\text{min}}}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$.
3. Substituting the amplitude ratio into the formula, we get $$\begin{array}{rl}{\left(\frac{4+1}{4-1}\right)}^2& ={\left(\frac{5}{3}\right)}^2\\ & =\frac{25}{9}\end{array}$$.
4. Hence the answer is (A).