Two coherent sources produce the maximum intensity of 100 units at a point. The sources are of equal intensity. What will be the intensity of the light at the same point, if the intensity of one of the sources is reduced by 36% by reducing its width? 

$\begin{array}{l}{I}_{max}={\left({\sqrt{I}}_1\right)}^2+{\left(\sqrt{I_2}\right)}^2\\ +2\sqrt{I_1{I}_2}\end{array}$

Both have same intensity,

$I_{max}=(\sqrt{I}{)}^2+(\sqrt{I}{)}^2 +2\sqrt{I^2}$

$\begin{array}{l}+2\sqrt{I^2}\\ I_{max}=4I\\ 100=4I\\ I=25\\ I_1=25\text{ units }\end{array}$

Intensity of one of the source is reduced by 36%,

So, $I_2=25-25\times \frac{36}{100}$

$I_2=16\text{ units }$

Resultant intensity at a point is given by,

$\begin{array}{l}\mathrm{I}={\left(\sqrt{{\mathrm{I}}_1}\right)}^2+{\left(\sqrt{{\mathrm{I}}_2}\right)}^2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}\\ \mathrm{I}=\left({\sqrt{25)}}^2+(\sqrt{16}{)}^2\right.\\ +2\sqrt{25\times 16}\\ \mathrm{I}=81\text{ units }\end{array}$