COMEDK · Physics · 26. Wave Optics

A source of light of wavelength \(5000 Å\) is placed at one end of a table \(2 \mathrm{~m}\) long and \(5 \mathrm{~mm}\) above its flat well polished top. The fringe width of the interference bands seen on a screen located at the end of the table is

A \(2 \times 10^{-5} \mathrm{~m}\)
B \(2 \times 10^{-4} \mathrm{~m}\)
C \(2 \times 10^{-3} \mathrm{~m}\)
D \(2 \times 10^{-2} \mathrm{~m}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \times 10^{-4} \mathrm{~m}\)

Step-by-step Solution

Detailed explanation

Given, wavelength of light used, \[ \begin{aligned} \lambda &=5000 Å=5 \times 10^{-7} \mathrm{~m} \\ D &=2 \mathrm{~m} \\ d &=5 \mathrm{~mm}=5 \times 10^{-3} \mathrm{~m} \end{aligned} \] \(\therefore\) Fringe width, \(\beta=\frac{D \lambda}{d}\)…

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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