Physics - Wave Optics Question with Solution | TestHub

The intensity at any point in Young's double slit experiment is given by $I=I_0{\cos }^2\left(\frac{\varphi }{2}\right)$

Given that $I=\frac{I_0}{4}$

$\frac{I_0}{4}=I_0{\cos }^2\left(\frac{\varphi }{2}\right)$

$\cos \left(\frac{\varphi }{2}\right)=\pm \frac{1}{2}$

$\frac{\varphi }{2}=n\pi \pm \frac{\pi }{3}$

$\varphi =2n\pi \pm \frac{2\pi }{3}$

The phase difference $\varphi$ is related to the path difference $\Delta x$ by $\varphi =\frac{2\pi }{\lambda }\Delta x$

$\frac{2\pi }{\lambda }\Delta x=2\pi \left(n\pm \frac{1}{3}\right)$

$\Delta x=\left(n\pm \frac{1}{3}\right)\lambda$

Answer: $\left(n\pm \frac{1}{3}\right)\lambda ,n=0,1,2$