COMEDK · Physics · 26. Wave Optics

In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio between bright and dark fringes is 3 . Then, the value of the ratio of the amplitudes of the wave that arrive there is

A \(\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)\)
B \(\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)\)
C \(\sqrt{3}: 1\)
D \(1: \sqrt{3}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Here, } \frac{I_{\text {bright }}}{I_{\text {dark }}}=\frac{I_{\max }}{I_{\min }}=3 (given) \\ & \Rightarrow \quad \frac{\left(a_1+a_2\right)^2}{\left(a_1-a_2\right)^2}=\frac{3}{1} \Rightarrow \frac{a_1+a_2}{a_1-a_2}=\sqrt{3} \\ & \Rightarrow \quad…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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