MHT CET · Physics · Wave Optics

In Young's double slit experiment, the intensity at a point where the path difference is \(\frac{\lambda}{4}\) [ \(\lambda\) is wavelength of light used] is ' \(I\) '. If ' \(\mathrm{I}_0\) ' is the maximum intensity, then \(\frac{\mathrm{I}}{\mathrm{I}_0}\) is equal to

A \(3: 2\)
B \(2: 3\)
C \(3: 4\)
D \(1: 2\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(1: 2\)

Step-by-step Solution

Detailed explanation

If I' is the intensity of each wave, then resultant intensity is given by
\(
\mathrm{I}=4 \mathrm{I} \cos ^2 \frac{\phi}{2}
\)
I will have maximum value when \(\cos ^2 \frac{\phi}{2}=1\)
\(\therefore\) maximum intensity, \(\mathrm{I}_0=4 \mathrm{I}\)
When path difference is \(\frac{\lambda}{4}\), the phase difference, \(\phi=\frac{\pi}{2}\)
The resultant intensity, \(I=4 I^{\prime} \cos ^2 \frac{\pi}{4}=4 I^{\prime} \times \frac{1}{2}=2 I^{\prime}\)
\(
\therefore \frac{\mathrm{I}}{\mathrm{I}_0}=\frac{1}{2}
\)

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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