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
Given intensity ratio: $I_1 : I_2 = 25 : 16$
Therefore, amplitude ratio: $\frac{a_1}{a_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{25}{16}} = \frac{5}{4}$
For interference pattern:
Maximum intensity, $I_{max} = (a_1 + a_2)^2$
Minimum intensity, $I_{min} = (a_1 - a_2)^2$
Hence,
$\frac{I_{max}}{I_{min}} = \left(\frac{a_1 + a_2}{a_1 - a_2}\right)^2 = \left(\frac{5 + 4}{5 - 4}\right)^2 = 9^2 = 81$
∴ Ratio of intensities of maxima to minima = 81 : 1