Light waves from two slits reach a screen. Their phase difference changes rapidly and randomly with time. The screen shows a uniform intensity of 6 units. Now the phase difference is kept constant, and each slit gives the same intensity as before. The intensity at a point of constructive interference is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 units
When the phase difference changes rapidly, the sources are incoherent. Their intensities just add, so the screen shows \( 2I_0 \) everywhere. Here \( I_0 \) is the intensity due to one slit.
With a constant phase difference, the waves add in amplitude. At constructive interference the amplitude is \( 2a \), so the intensity is \( 4I_0 \).
\( \begin{aligned} 2I_0 &= 6\ \mathrm{units} \\ I_0 &= 3\ \mathrm{units} \end{aligned} \)
\( \begin{aligned} I_{max} &= 4I_0 \\ &= 4\times3=12\ \mathrm{units} \end{aligned} \)
Hence, the intensity at a point of constructive interference is 12 units.
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… we will observe an average intensity that will be given by”
\( \displaystyle I=2I_0 \)\( \qquad (10.12) \)
“at all points.”
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 I0 …”