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 \(\left(\cos 0^{\circ}=1, \cos \pi=-1\right)\)

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 \(I_2=4 I_0 \cos ^2\left(\frac{\pi}{2}\right)=0\)
\(\begin{aligned}
\therefore \quad & \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{4 \mathrm{I}_0}{0}=\infty \\
& \Rightarrow \infty: 1
\end{aligned}\)