MHT CET · Physics · Wave Optics

Light of wavelength $' λ^{'}$ is incident on a single slit of width ‘a’ and the distance between slit and screen ‘D’. In diffraction pattern, if slit width is equal to the width of the central maximum then ‘D’ is equal to

A $\frac{a}{2 λ}$
B $\frac{a^{2}}{2 λ}$
C $\frac{a}{λ}$
D $\frac{a^{2}}{λ}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{a^{2}}{2 λ}$

Step-by-step Solution

Detailed explanation

The width of central maximum is given by

2 y = \frac{2 D λ}{a}

…. (i)
where,

λ =

wavelength of incident light.
Here, a =2y, then from Eq. (i) we get

a = \frac{2 D λ}{a} \Rightarrow D = \frac{a^{2}}{2 λ}

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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Light of wavelength 'λ' is incident on a single slit of width ‘a’ and the distance between slit and screen ‘D’. In diffraction pattern, if slit width is equal to the width of the central maximum then ‘D’ is equal to

Step-by-step Solution

Light of wavelength $' λ^{'}$ is incident on a single slit of width ‘a’ and the distance between slit and screen ‘D’. In diffraction pattern, if slit width is equal to the width of the central maximum then ‘D’ is equal to