Two coherent sources of light with intensities I₁ and I₂ produce an interference pattern on a screen. Which of the following mathematical relations for the average intensity ( I_ avg ) over the entire screen correctly demonstrates that the principle of conservation of energy holds true?

Step-by-step solution

The intensity at any point in an interference pattern is given by I = I₁ + I₂ + 2 I₁ I₂ , where is the phase difference between the two waves. To find the average intensity over the entire screen, we take the average of the intensity expression over a full cycle of phase difference. The average value of over a complete cycle is zero. Therefore, I_ avg = I₁ + I₂ + 2 I₁ I₂ (0) = I₁ + I₂ . This relation shows that the total energy distributed over the screen is exactly equal to the sum of the individual energies from