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

In the Young's double slit experiment, the distance between the slits varies in time as \({d}({t})={d}_{0}+{a}_{0}\, sin\omega \,t\) ; where \({d}_{0}, \omega\) and \(a_{0}\) are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

A \(\frac{\lambda D}{d_{0}+a_{0}}\)
B \(\frac{2 \lambda \cdot D a_{0}}{\left(d_{0}^{2}-a_{0}^{2}\right)}\)
C \(\frac{2 \lambda {D}\left({d}_{0}\right)}{\left({d}_{0}^{2}-{a}_{0}^{2}\right)}\)
D \(\frac{\lambda D}{d_{0}^{2}} a_{0}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2 \lambda \cdot D a_{0}}{\left(d_{0}^{2}-a_{0}^{2}\right)}\)

Step-by-step Solution

Detailed explanation

Fringe Width, \(\beta=\frac{\lambda D }{ d }\) \(\beta_{\max } \Rightarrow d _{\min } \text { and } \beta_{\min } \Rightarrow d _{\max }\) \(d = d _{0}+ a _{0} \sin \omega t\) \(d _{\max }= d _{0}+ a _{0} \text { and } d _{\min }= d _{0}- a _{0}\)…

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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