The intensity ratio of two interfering sources in Young’s double slit experiment is 4 : 1. The ratio of \( \displaystyle\frac{I_{\min}}{I_{\max}} \) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1 : 9
The intensity of a wave is proportional to the square of its amplitude, so an intensity ratio \( I_1 : I_2 = 4 : 1 \) means an amplitude ratio \( a_1 : a_2 = 2 : 1 \). At the maxima the amplitudes add, at the minima they subtract (superposition), and the intensity goes as the square of the resultant amplitude.
\( I_{\max}\propto(a_1+a_2)^{2} = (2+1)^{2} = 9 \)
\( I_{\min}\propto(a_1-a_2)^{2} = (2-1)^{2} = 1 \)
\( \displaystyle \frac{I_{\min}}{I_{\max}} = \frac{1}{9} \)