If the two waves of intensities \( I_1 \) and \( I_2 \) pass through the region in the same direction and at the same time, the sum of the maximum and minimum intensities is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2(I_1 + I_2) \)
In the superposition of two coherent waves, the amplitudes add, and the intensity is proportional to the square of the amplitude, so \( a \propto \sqrt{I} \). The resultant is largest when the waves are in phase and smallest when they are opposite in phase.
\( \displaystyle I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^{2} = I_1 + I_2 + 2\sqrt{I_1 I_2} \)
\( \displaystyle I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^{2} = I_1 + I_2 - 2\sqrt{I_1 I_2} \)
Adding, the cross terms cancel:
\( I_{\max} + I_{\min} = 2(I_1 + I_2) \)