MHT CET · Physics · Wave Optics

A light wave of wavelength ' \(\lambda\) 'is incident on a slit of width ' \(d\) '. The resulting diffraction pattern is observed on screen at a distance of ' \(\mathrm{D}\) '. If linear width of the principal maximum is equal to width of the slit, then the distance \(D\) is

A \(\frac{\mathrm{d}}{\lambda}\)
B \(\frac{2 \lambda^2}{d}\)
C \(\frac{2 \lambda}{d}\)
D \(\frac{\mathrm{d}^2}{2 \lambda}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\mathrm{d}^2}{2 \lambda}\)

Step-by-step Solution

Detailed explanation

The correct option is (D)
Concept: If \(\mathrm{D}>>\mathrm{d}\),
the linear width of the central principal maximum is equal to the product of angular width and the distance \(D\).
\(\beta=\frac{2 \lambda D}{d}\), where \(d\) is the width of the slit.
The linear width of the principal maximum will be equal to slit width for a value of \(\mathrm{D}\) given by
\(\frac{2 \lambda D}{d}=d\)
or
\(\mathrm{D}=\frac{\mathrm{d}^2}{2 \lambda}\)

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.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app