Question

The ratio of intensities of two waves that produce interference pattern is 16:1, then the ratio of maximum and minimum intensities in the pattern is :

• A. 25:9
• B. 9:25
• C. 1: 4
• D. 4:1

Answer 1

The correct option is A 25:9

Let the intensities of the two waves be $I_1$ and $I_2$.
Given : $I_1:I_2=16:1$
Ratio of maximum and minimum intensities $\frac{I_{max}}{I_{min}}=(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}{)}^2$
Or $\frac{I_{max}}{I_{min}}=(\frac{\sqrt{\frac{I_1}{I_2}}+1}{\sqrt{\frac{I_1}{I_2}}-1}{)}^2$
Or $\frac{I_{max}}{I_{min}}=(\frac{\sqrt{16}+1}{\sqrt{16}-1}{)}^2=(\frac{4+1}{4-1}{)}^2$
$⟹$ $\frac{I_{max}}{I_{min}}=\frac{25}{9}$