Two waves having the intensities in the ratio of \( 9 : 1 \) produce interference. The ratio of maximum to minimum intensity in the interference pattern is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 4 : 1 \)
Intensity is proportional to the square of the amplitude. In interference the amplitudes add at a maximum and subtract at a minimum.
\( \displaystyle \frac{I_1}{I_2} = \frac{9}{1} \Rightarrow \frac{a_1}{a_2} = \sqrt{\frac{9}{1}} = \frac{3}{1} \)
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \frac{(a_1 + a_2)^{2}}{(a_1 - a_2)^{2}} = \frac{(3 + 1)^{2}}{(3 - 1)^{2}} = \frac{16}{4} = \frac{4}{1} \)