JEE Mains · Physics · STD 12 - 10. Wave optics

In a Young’s double slit experiment with slit separation \(0.1\, mm\), one observes a bright fringe at angle \(\frac{1}{{40}}\, rad\) by using light of wavelength \({\lambda _1}\). When the light of wavelength \(\lambda _2\) is used a bright fringe is seen at the same angle in the same set up. Given that \({\lambda _1}\) and \({\lambda _2}\) are in visible range (\(380\, nm\) to \(740\, nm\)), their values are

A \(625\, nm, 500\, nm\)
B \(380\, nm, 525\, nm\)
C \(380\, nm, 500\, nm\)
D \(400\, nm, 500\, nm\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(625\, nm, 500\, nm\)

Step-by-step Solution

Detailed explanation

For maxima, \(\operatorname{dsin} \theta=n \lambda\) \(\lambda=\frac{\mathrm{d} \theta}{\mathrm{n}}\) ( \(\because \,\sin \theta \approx \theta \) when \(\theta\) is small ) \(=\frac{2500}{n}\, n m\) Take \(n=4,5\) for \(\lambda=625\, \mathrm{nm}\) and \(500 \,\mathrm{nm}\)

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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