Light waves from two coherent sources arrive at two points on a screen with path difference of zero and…
Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $\frac{\lambda^{\prime}}{2}$. The ratio of intensities at the points is $\left(\cos 0^{\circ}=1, \cos \pi=-1\right)$
$2: 1$
$1: 1$
$1: 2$
$\infty: 1$
Solution
Given: Wave length $=\frac{\lambda}{2}$
Path difference of first wave $\Delta x_1=0$
Path difference of second wave $\Delta x_2=\frac{\lambda}{2}$
$\therefore \quad \Delta \phi_1=\frac{2 \pi}{\lambda} \cdot \Delta x_1=0$
Similarly,
$\Delta \phi_2=\frac{2 \pi}{\lambda} \cdot \Delta x_2=\pi$
$\therefore \quad$ Intensity of first wave $\mathrm{I}_1=4 \mathrm{I}_0 \cos ^2(0)=4 \mathrm{I}_0$ Similarly,
Intensity of second wave $I_2=4 I_0 \cos ^2\left(\frac{\pi}{2}\right)=0$
$\begin{aligned}
\therefore \quad & \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{4 \mathrm{I}_0}{0}=\infty \\
& \Rightarrow \infty: 1
\end{aligned}$