MHT CET · Physics · Wave Optics

In Fraunhofer diffraction pattern, slitwidth is 0.5 mm and screen is at 2 m away from the lens. If wavelength of light used is \(5500 Å\), then the distance between the first minimum on either side of the central maximum is \((\theta\) is small and measured in radian)

A 1.1 mm
B \(\quad 2.2 \mathrm{~mm}\)
C 4.4 mm
D 5.5 mm

Verified Solution

Answer & Solution

Correct Answer

(C) 4.4 mm

Step-by-step Solution

Detailed explanation

Distance of \(1^{\text {st }}\) minima from central maxima
\(y_{1 d}=\frac{\lambda D}{a}\)
Distance between two minima on either side of the central maxima is
\(2 \mathrm{y}_{1 \mathrm{~d}}=\frac{2 \lambda \mathrm{D}}{\mathrm{a}}=\frac{2 \times 5500 \times 10^{-10} \times 2}{0.5 \times 10^{-3}}=4.4 \mathrm{~mm}\)

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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