The ratio of the intensities at maxima to minima in Young's double-slit experiment is $\displaystyle 25: 9$. Calculate the ratio of intensities of the interfering waves.

\[\text { Calculating the ratio of intensities } 2 \] Given, \(\displaystyle \frac{\mathrm{I}_{\text {max }}}{\mathrm{I}_{\text {min }}}=\frac{25}{9}\) \[\frac{\mathrm{I}_{\max }}{\mathrm{I}_{\min }}=\frac{\left(a_{1}+a_{2}\right)^{2}}{\left(a_{1}-a_{2}\right)^{2}}=\frac{25}{9} \] \[3\left(a_{1}+a_{2}\right)=5\left(a_{1}-a_{2}\right) \] \[\frac{a_{1}}{a_{2}}=\frac{4}{1} \] \[\frac{\mathrm{I}_{1}}{\mathrm{I}_{1}}=\frac{16}{1} \]