Question

Two coherent light sources whose intensity ratio is $81:1$ produce interference fringes. If the ratio of intensities of maxima and minima in the fringe system is x:y. Find x-y?

Answer 1

It is given that $\frac{I_1}{I_2}=\frac{81}{1}$

Since, $\frac{I_1}{I_2}=\frac{A_1^2}{A_2^2}$

It is given that, ratio of intensities of maxima and minima is $\frac{x}{y}$

So,

$\frac{x}{y}=\frac{{(\sqrt{I_1}+\sqrt{I_2})}^2}{{(\sqrt{I_1}-\sqrt{I_2})}^2}$

$\frac{x}{y}=\frac{{(\sqrt{81}+1)}^2}{{(\sqrt{81}-1)}^2}$

$\frac{x}{y}={\left(\frac{10}{8}\right)}^2$

$\frac{x}{y}=\frac{25}{16}$

So, $x-y=9$