Question

Two coherent waves, each of intensity \( I_0 \), produce interference pattern on a screen. The average intensity of light on the screen is:

• A. zero
• B. \( I_0 \)
• C. \( 2I_0 \)
• D. \( 4I_0 \)

Hint:

When two coherent waves of equal intensity interfere, the average intensity on the screen is \( 2I_0 \), even though the maximum can be \( 4I_0 \) and the minimum can be zero.

Answer 1

The Correct Option is C

For an interference pattern generated by two coherent sources of identical intensity \( I_0 \), the resulting intensity at any screen location is determined by the phase difference.- For constructive interference (phase difference \( = 0, 2\pi, \ldots \)), amplitudes summate:\[I_{\text{max}} = (\sqrt{I_0} + \sqrt{I_0})^2 = (2\sqrt{I_0})^2 = 4I_0\]- For destructive interference (phase difference \( = \pi, 3\pi, \ldots \)), amplitudes cancel:\[I_{\text{min}} = (\sqrt{I_0} - \sqrt{I_0})^2 = 0\]The mean intensity across numerous fringes is:\[I_{\text{avg}} = \frac{I_{\text{max}} + I_{\text{min}}}{2} = \frac{4I_0 + 0}{2} = 2I_0\]