The ratio of intensities of two interfering waves is 1:9. The ratio of intensities at maxima and minima in the interference pattern will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4:1
Intensity is proportional to the square of the amplitude. At a maximum the amplitudes add, and at a minimum they subtract.
\( \displaystyle \frac{a_1}{a_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{1}{9}} = \frac{1}{3} \)
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \frac{(a_1 + a_2)^{2}}{(a_2 - a_1)^{2}} = \frac{(1 + 3)^{2}}{(3 - 1)^{2}} = \frac{16}{4} = \frac{4}{1} \)