Question

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

• A. 4 : 1
• B. 9 : 1
• C. 2 : 1
• D. 10 : 8

Answer 1

Answer: (A)

4 : 1

Let the intensity of the two waves be $I_1$ and $I_2$

Given: $I_2:I_1=9:1⟹I_2=9I_1$

Now $\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2}{(\sqrt{I_2}-\sqrt{I_1}{)}^2}=\frac{(\sqrt{I_1}+\sqrt{9I_1}{)}^2}{(\sqrt{9I_1}-\sqrt{I_1}{)}^2}=\frac{16I_1}{4I_1}$

$⟹I_{max}:I_{min}=4:1$