Question

In the phenomenon of interference of two waves

• A. Sources of the two waves must be coherent
• B. Amplitude of the two waves must be same
• C. Wavelength of two waves must be same
• D. Intensities of the two waves can be different

Answer 1

Answer: (A), (C), (D)

Intensities of the two waves can be different

In the phenomenon of interference, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe.

For this to happen, sources must be coherent, i.e. fixed phase difference $\left(\varphi \right)$.

If phase difference is not fixed (varying with time), then we take average value of $\cos \varphi$ in net intensity, $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$ over a period $(0,2\pi )$ which comes out to be zero.

Hence, intensities are the same at all points. Therefore, no interference will occur.

Also, phase difference does not depend on amplitudes and intensities, hence, they may have different values.

Phase difference depends on wavelength, i.e. $\varphi =\frac{2\pi }{\lambda }\Delta x$, where $\Delta x$ is path difference.

For stable interference at a point as wavelengths must be same.

So, option $\text{(A), (C) and (D)}$ are correct.