MHT CET · Physics · Wave Optics

In a single slit diffraction experiment, for a wavelength of light ' \(\lambda\) ', half-angular width of the principle maxima is ' \(\theta\) '. Also for wavelength of light \(\mathrm{p} \lambda\), the half angular width of the principle maxima is \(q \theta\). The ratio of the halfangular widths of the first secondary maxima in the first case to second case will be

A \(\mathrm{p}: 1\)
B \(\mathrm{q}: 1\)
C \(\mathrm{p}: \mathrm{q}\)
D \(\mathrm{q}: \mathrm{p}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\mathrm{q}: \mathrm{p}\)

Step-by-step Solution

Detailed explanation

Let \(d\) and \(d\) ' be the width of the slits in the two cases.
\(\begin{aligned}
& \therefore & \theta & =\frac{\lambda}{d} \text { and } q \theta=\frac{p \lambda}{d^{\prime}} \\
& \therefore & \frac{d}{d^{\prime}} & =\frac{q}{p}
\end{aligned}\)

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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