Question

Two waves having their intensities in the ratio 9:1 produce interference. In the interference pattern, the ratio of maximum to minimum intensity is equal to

• A. 2:1
• B. 9:1
• C. 3:1
• D. 4:1

Answer 1

The correct option is D 4:1

Let the intensities of the two waves be $I_1$ and $I_2$.
Given : $I_1:I_2=9:1$
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 $\frac{I_{max}}{I_{min}}=(\frac{\sqrt{9}+1}{\sqrt{9}-1}{)}^2=(\frac{3+1}{3-1}{)}^2$
$⟹$ $\frac{I_{max}}{I_{min}}=\frac{16}{4}=\frac{4}{1}$