Question

If two waves of same wavelength with their intensities in the ratio $25:9$ produce interference, then the ratio of the maximum to minimum intensity is

• A. $9:2$
• B. $9:1$
• C. $5:3$
• D. $16:3$
• E. $16:1$

Hint:

Physics Tip: In interference, convert intensity ratio into amplitude ratio first by taking square root.

Answer 1

Answer: (E)

Concept:
For two interfering waves: - Amplitude $\propto \sqrt{\text{Intensity}}$ If intensities are $I_1$ and $I_2$, then $$I_{\max}=(\sqrt{I_1}+\sqrt{I_2})^2$$ $$I_{\min}=(\sqrt{I_1}-\sqrt{I_2})^2$$
Step 1: Given intensity ratio.
$$I_1:I_2=25:9$$ So amplitudes ratio: $$a_1:a_2=\sqrt{25}:\sqrt{9}=5:3$$
Step 2: Find maximum intensity.
$$I_{\max}=(5+3)^2=8^2=64$$
Step 3: Find minimum intensity.
$$I_{\min}=(5-3)^2=2^2=4$$
Step 4: Take ratio.
$$I_{\max}:I_{\min}=64:4=16:1$$ Hence correct option is (E). :contentReference[oaicite:0]{index=0}