In Fraunhoffer diffraction by a single slit, the width of the slit is 0.01 cm . If the wavelength of the light incident normally on the slit is 5000Å the angular distance of second maxima from the mid line of central maxima is __________ rad.

A 0.125
B 0.15
C 0.015
D 0.0125

Verified Solution

Answer & Solution

Correct Answer

(D) 0.0125

Step-by-step Solution

Detailed explanation

(D) 0.0125
for \(n\) the order secondary maxima,
\(
\begin{aligned}
a \sin \theta & =\left(n+\frac{1}{2}\right) \lambda \\
\sin \theta & =\left(2+\frac{1}{2}\right) \frac{\lambda}{a}(n=2) \\
\therefore \sin \theta & =\frac{5 \times 5 \times 10^{-7}}{2 \times 10^{-4}} \\
& =12.5 \times 10^{-3} \\
& =0.0125 \mathrm{rad}
\end{aligned}
\)

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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