Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

Wave Optics PYQ — JEE Main 2019 · 9 Jan · Shift 1 · Q66 with Solution

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Correct answer: B

Let the intensities of the two coherent sources be $I_1$ and $I_2$ .
For interference of two coherent waves: $I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2$ $I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2$
Given: $\frac{I_{\max}}{I_{\min}} = 16$

So, $\frac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_1} - \sqrt{I_2})^2} = 16$
Taking square root on both sides: $\frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} = 4$
Let $\sqrt{I_1} = a, \quad \sqrt{I_2} = b$ Then, $\frac{a+b}{a-b} = 4$

Cross-multiplying: $a+b = 4a - 4b$ $5b = 3a$ $\frac{a}{b} = \frac{5}{3}$
Therefore, $\frac{I_1}{I_2} = \frac{a^2}{b^2} = \left(\frac{5}{3}\right)^2 = \frac{25}{9}$
Hence, the ratio of the intensities is: $25:9$
Checking options:
- A: $16:9$ ❌
- B: $25:9$ ✅
- C: $4:1$ ❌
- D: $5:3$ ❌

Therefore, the correct option is B.