Two coherent light waves superpose on a screen. The maximum intensity in the pattern is 25 units and the minimum intensity is 9 units. The intensities of the two waves are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 16 units and 1 unit
Amplitudes add at a maximum and subtract at a minimum. Intensities do not add this way. Intensity is proportional to the square of the amplitude, so the amplitude is proportional to \( \sqrt{I} \).
\( \begin{aligned} \sqrt{I_1}+\sqrt{I_2} &= \sqrt{I_{max}}=\sqrt{25}=5 \\ \sqrt{I_1}-\sqrt{I_2} &= \sqrt{I_{min}}=\sqrt{9}=3 \end{aligned} \)
\( \begin{aligned} \sqrt{I_1} &= 4,\quad \sqrt{I_2}=1 \\ I_1 &= 16\ \mathrm{units},\quad I_2=1\ \mathrm{unit} \end{aligned} \)
As a check, \( (4+1)^2=25 \) and \( (4-1)^2=9 \). Hence, the intensities of the two waves are 16 units and 1 unit.
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 I0 …”