If I is the intensity of light and A is the amplitude of the wave, wh…

The correct answer is Option (4) → \( I\propto A^{2} \)

Option (1) \( I\propto A^{3} \) — Incorrect. Two equal coherent waves arriving in phase give twice the amplitude of one wave and four times its intensity, \( 4I_0 \). A cube law would give eight times.

Option (2) \( I\propto A^{1/2} \) — Incorrect. With this law, doubling the amplitude would raise the intensity only by a factor of about 1.4. But two equal waves in phase give \( 4I_0 \).

Option (3) I is independent of A — Incorrect. At a dark fringe the two waves are in opposite phase. The resultant amplitude is zero, and so is the intensity. So the intensity changes with the amplitude.

Option (4) \( I\propto A^{2} \) — Correct. The intensity of a wave is proportional to the square of its amplitude. So the amplitude \( 2a \) of two equal waves in phase gives four times the intensity \( I_0 \) of one wave.

NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “Since the intensity is proportional to the square of the amplitude, the resultant intensity will be given by

    \( I=4\,I_0 \)

where I₀ represents the intensity produced by each one of the individual sources; I₀ is proportional to a².”