(a) Find the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity I_0 each, have a path…

(a) Finding the intensity for path difference of

(i) \[\begin{aligned} \Delta \phi & =\frac{2 \pi}{\lambda} \cdot \Delta x \\ \Delta \phi & =\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{3}=\frac{2 \pi}{3} \\ \mathrm{I} & =4 \mathrm{I}_{0} \cos ^{2} \frac{\phi}{2} \\ \mathrm{I} & =4 \mathrm{I}_{0} \cos ^{2} \frac{\pi}{3} \\ \mathrm{I} & =\mathrm{I}_{0} \end{aligned} \]

(ii) \(\displaystyle \Delta \phi=\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{2}=\pi\) \[\begin{aligned} & \mathrm{I}=4 \mathrm{I}_{0} \cos ^{2} \frac{\pi}{2} \\ & \mathrm{I}=0 \end{aligned} \]

(b) \[\begin{aligned} & \frac{\mathrm{n}_{2}}{\mathrm{v}}-\frac{\mathrm{n}_{1}}{\mathrm{u}}=\frac{\mathrm{n}_{2}-\mathrm{n}_{1}}{\mathrm{R}} \\ & \frac{1.5}{\mathrm{v}}-\frac{1}{(-12)}=\frac{1.5-1}{30} \\ & \mathrm{v}=-22.5 \mathrm{~cm} \end{aligned} \]

Image is virtual and erect.