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

In an interference pattern formed by two coherent sources of equal intensity \( I_0 \), the resultant intensity at any point on the screen depends on the phase difference. - At a point of constructive interference (phase difference \( = 0, 2\pi, \ldots \)), the amplitudes add up: \[ I_{\text{max}} = (\sqrt{I_0} + \sqrt{I_0})^2 = (2\sqrt{I_0})^2 = 4I_0 \] - At a point of destructive interference (phase difference \( = \pi, 3\pi, \ldots \)), the amplitudes cancel: \[ I_{\text{min}} = (\sqrt{I_0} - \sqrt{I_0})^2 = 0 \] The average intensity over many fringes is: \[ I_{\text{avg}} = \frac{I_{\text{max}} + I_{\text{min}}}{2} = \frac{4I_0 + 0}{2} = 2I_0 \]