AP EAMCET · PHYSICS · Wave Optics

A Fraunhofer diffraction pattern due to a narrow slit is obtained on a screen placed at a distance \(D\) from the slit whose slit width is \(a\). The distance of first secondary maximum from the central maximum is

A \(\frac{3 D \lambda}{a}\)
B \(\frac{3 D \lambda}{2 a}\)
C \(\frac{2 D \lambda}{3 a}\)
D \(\frac{2 D \lambda}{a}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{3 D \lambda}{2 a}\)

Step-by-step Solution

Detailed explanation

In Fraunhofer diffraction pattern, the direction of secondary maximum is given as \(\begin{aligned} \theta & =(2 n+1) \frac{\lambda}{2 a}=(2 \times 1+1) \frac{\lambda}{2 a} \\ \Rightarrow \theta & =\frac{3 \lambda}{2 a} \end{aligned}\) \(\therefore\) Distance of first secondary…

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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