Physics - Wave Optics Question with Solution | TestHub

If I' is the intensity of each wave, then resultant intensity is given by $$\mathrm{I}=4\mathrm{I}{\cos }^2\frac{\varphi }{2}$$ I will have maximum value when ${\cos }^2\frac{\varphi }{2}=1$ $\therefore$ maximum intensity, ${\mathrm{I}}_0=4\mathrm{I}$ When path difference is $\frac{\lambda }{4}$, the phase difference, $\varphi =\frac{\pi }{2}$ The resultant intensity, $I=4I^{\prime }{\cos }^2\frac{\pi }{4}=4I^{\prime }\times \frac{1}{2}=2I^{\prime }$ $$\therefore \frac{\mathrm{I}}{{\mathrm{I}}_0}=\frac{1}{2}$$