Question

Two light waves of intensities 'I₁' and 'I₂' having same frequency pass through medium at a time in same direction and interfere. The sum of the mini- maximum intensities is

• A. (I₁ + I₂)
• B. 2(I₁ + I₂)
• C. $\sqrt{I_1}+\sqrt{I_2}$
• D. $\sqrt{I_1}-\sqrt{I_2}$

Answer 1

Answer: (B)

2(I₁ + I₂)

Answer 2

For two coherent light waves with amplitudes proportional to $\sqrt{I_1}$ and $\sqrt{I_2}$, the maximum intensity (constructive interference) is

$I_{max}=(\sqrt{I_1}+\sqrt{I_2})^2 = I_1+I_2+2\sqrt{I_1I_2}$.

The minimum intensity (destructive interference) is

$I_{min}=(\sqrt{I_1}-\sqrt{I_2})^2 = I_1+I_2-2\sqrt{I_1I_2}$.

Sum of maxi- and mini- intensities:

$I_{max}+I_{min} = [I_1+I_2+2\sqrt{I_1I_2}] + [I_1+I_2-2\sqrt{I_1I_2}] = 2(I_1+I_2)$.