Two coherent light sources have intensities in the ratio 25 : 16. The ratio of the intensities of maxima to minima, in the interference pattern due to them would be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 81 : 1 \)
The intensity of a source is proportional to the square of its amplitude, so \( a_1/a_2 = \sqrt{I_1/I_2} \). In interference the maximum has amplitude \( a_1 + a_2 \) and the minimum \( a_1 - a_2 \).
\( \displaystyle \frac{a_1}{a_2} = \sqrt{\frac{25}{16}} = \frac{5}{4} \)
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \left(\frac{a_1 + a_2}{a_1 - a_2}\right)^{2} = \left(\frac{5 + 4}{5 - 4}\right)^{2} = \frac{81}{1} \)
So the ratio is \( 81:1 \).