Light of wave-length λis incident on a slit of width d. The resulting diffraction pattern is obs

Name: Problem 2300, Chapter 16: JEE Physics
Uploaded: 2021-11-29T08:00:10-08:00
Duration: 56 s
Channel: Mirza Aslam Beig
Description: Light of wave-length λis incident on a slit of width d. The resulting diffraction pattern is observed on a screen placed at a distance D. The linear width of the principal maximum is equal to the width of the slit, then D= (A) (d^2 / 2 λ) (B) (2 λ^2 / d) (C) (d / λ) (D) (2 λ/ d)

step 1 Okay, in this question we are asked that light of wavelength lambda is incident on a slit of wav

Question

Light of wave-length $\lambda$ is incident on a slit of width $\mathrm{d}$. The resulting diffraction pattern is observed on a screen placed at a distance $\mathrm{D}$. The linear width of the principal maximum is equal to the width of the slit, then $\mathrm{D}=$ (A) $\left(\mathrm{d}^{2} / 2 \lambda\right)$ (B) $\left(2 \lambda^{2} / \mathrm{d}\right)$ (C) $(\mathrm{d} / \lambda)$ (D) $(2 \lambda / \mathrm{d})$

   Light of wave-length $\lambda$ is incident on a slit of width $\mathrm{d}$. The resulting diffraction pattern is observed on a screen placed at a distance $\mathrm{D}$. The linear width of the principal maximum is equal to the width of the slit, then $\mathrm{D}=$
(A) $\left(\mathrm{d}^{2} / 2 \lambda\right)$
(B) $\left(2 \lambda^{2} / \mathrm{d}\right)$
(C) $(\mathrm{d} / \lambda)$
(D) $(2 \lambda / \mathrm{d})$

JEE Physics

StemEZ 1st Edition

Chapter 16, Problem 2300

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Solved by Expert Mirza Aslam Beig

11/29/2021

Step 1

Step 1: We know that the linear width of the central maximum in a diffraction pattern is given by $2\lambda D/d$. Show more…

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Light of wave-length $\lambda$ is incident on a slit of width $\mathrm{d}$. The resulting diffraction pattern is observed on a screen placed at a distance $\mathrm{D}$. The linear width of the principal maximum is equal to the width of the slit, then $\mathrm{D}=$ (A) $\left(\mathrm{d}^{2} / 2 \lambda\right)$ (B) $\left(2 \lambda^{2} / \mathrm{d}\right)$ (C) $(\mathrm{d} / \lambda)$ (D) $(2 \lambda / \mathrm{d})$

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Key Concepts

Single-slit diffraction

This concept describes how light spreads out after passing through a narrow opening, resulting in an interference pattern of bright and dark regions. The shape and extent of the diffraction pattern, particularly the central bright maximum, depend on the slit width and the wavelength of the light.

Fraunhofer diffraction

This is the far-field approximation of diffraction where both the light source and observation screen are effectively at infinity or simulated as such using lenses. Under Fraunhofer conditions, the linear dimensions of the diffraction pattern on the screen are directly related to the geometry of the aperture and the wavelength, allowing for simple relationships between the slit width, the distance to the screen, and the size of the diffraction pattern.

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