MHT CET · Physics · Wave Optics

In a diffraction pattern, light of wavelength \(580 \mathrm{~nm}\) is incident normally on a slit of width ' \(a\) ' The distance between slit and the screen is \(2.5 \mathrm{~m}\) and the distance of the second order maximum from the center of the screen is \(14.5 \mathrm{~mm}\). The value of ' \(a\) ' is

A \(0.26 \times 10^{-3} \mathrm{~m}\)
B \(0.36 \times 10^{-3} \mathrm{~m}\)
C \(0.50 \times 10^{-3} \mathrm{~m}\)
D \(0.12 \times 10^{-3} \mathrm{~m}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(0.26 \times 10^{-3} \mathrm{~m}\)

Step-by-step Solution

Detailed explanation

Distance of \(2^{\text {nd }}\) order maximum from the centre of the screen
\(x=\frac{5 D \lambda}{2 d}\)
Here, \(\mathrm{D}=2.5 \mathrm{~m}, \mathrm{x}=14 \mathrm{~mm}=14 \times 10^{-3} \mathrm{~m}\)
\(\lambda=580 \mathrm{~nm}=580 \times 10^{-9} \mathrm{~m}\)
\(\therefore \mathrm{d}=\frac{5 \mathrm{D} \lambda}{2 \mathrm{x}}=\frac{\left(5 \times 2.5 \times 580 \times 10^{-9} \mathrm{~m}\right)}{2 \times 14 \times 10^{-3} \mathrm{~m}}\)\(=259 \mu \mathrm{m}=0.26 \times 10^{-3} \mathrm{~m}\)

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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