Physics - Wave Optics Question with Solution | TestHub

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

Substituting $\Delta x=\frac{\lambda }{6}$:

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{6}=\frac{\pi }{3}$

The intensity at a point on the screen is given by $I=I_0{\cos }^2\left(\frac{\varphi }{2}\right)$

Substituting $\varphi =\frac{\pi }{3}$:

$I=I_0{\cos }^2\left(\frac{\pi }{6}\right)=I_0{\cos }^2(30^{\circ })$

Given $\cos 30^{\circ }=\frac{\sqrt{3}}{2}$:

$I=I_0{\left(\frac{\sqrt{3}}{2}\right)}^2=I_0\times \frac{3}{4}=0.75I_0$

The ratio $\frac{I}{I_0}=0.75$

Answer: $0.75$