Question 342: Waves Optics

Question

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

Accepted Answer

Given: Wave length $$=\frac{\lambda}{2}$$
Path difference of first wave $$\Delta x_1=0$$
Path difference of second wave $$\Delta x_2=\frac{\lambda}{2}$$
$$\begin{aligned}
	herefore \quad & \Delta \phi_1=\frac{2 \pi}{\lambda} \cdot \Delta x_1=0 \
& 	ext { Similarly, } \
& \Delta \phi_2=\frac{2 \pi}{\lambda} \cdot \Delta x_2=\pi
\end{aligned}$$
$$	herefore \quad$$ Intensity of first wave $$\mathrm{I}_1=4 \mathrm{I}_0 \cos ^2(0)=4 \mathrm{I}_0$$
Similarly,
Intensity of second wave $$I_2=4 I_0 \cos ^2\left(\frac{\pi}{2}ight)=0$$
$$\begin{aligned}
	herefore \quad & \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{4 \mathrm{I}_0}{0}=\infty \
& \Rightarrow \infty: 1
\end{aligned}$$

Answer

$$2: 1$$

Answer

$$1: 1$$

Answer

$$1: 2$$

Answer

$$\infty: 1$$

Waves Optics

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)

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