Physics - Wave Optics Question with Solution | TestHub

Let the resultant amplitude of the bright fringe be $A_{max}$ and the resultant amplitude of the dark fringe be $A_{min}$.

The intensity of a fringe is directly proportional to the square of its resultant amplitude, i.e., $I\propto A^2$.

Given the ratio of the intensity of the bright fringe to the dark fringe is:
$\frac{I_{max}}{I_{min}}=\frac{5}{1}$

Therefore, the ratio of their resultant amplitudes is:
$\frac{A_{max}}{A_{min}}=\sqrt{\frac{I_{max}}{I_{min}}}$

$\frac{A_{max}}{A_{min}}=\sqrt{\frac{5}{1}}=\frac{\sqrt{5}}{1}$

The ratio of resultant amplitudes of bright fringe to dark fringe is $\sqrt{5}:1$.

Answer: $\sqrt{5}:1$