Physics - Wave Optics Question with Solution | TestHub

If $\mathrm{I}$ ' is the intensity of each wave, then the resultant intensity at a point is given by $$\mathrm{I}=4{\mathrm{I}}^{\prime }{\cos }^2\frac{\varphi }{2}$$ For maximum intensity, phase difference $\varphi =0$ $$\therefore {\mathrm{I}}_0=4{\mathrm{I}}^{\prime }{\cos }^{2}0=4{\mathrm{I}}^{\prime }$$ At a point where path difference is $\frac{\lambda }{6}$, hence phase difference is $$\begin{array}{rl}& \frac{\pi }{3}.\\ & \therefore \mathrm{I}=4{\mathrm{I}}^{\prime }{\cos }^2\frac{\pi }{6}=3{\mathrm{I}}^{\prime }\\ & \therefore \frac{\mathrm{I}}{{\mathrm{I}}_0}=\frac{3}{4}\end{array}$$