A linear aperture whose width is \(0.02\,\, cm\) is placed immediately in front of a lens of focal length \(60\,\, cm.\) The aperture is illuminated normally by a parallel beam of wavelength \(5 \times 10^{-5}\,\, cm.\) The distance of the first dark band of the diffraction pattern from the centre of the screen is .....\(cm\)

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.