In a Fraunhofer diffraction of a single slit, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The angular width of the central maximum in a single-slit Fraunhofer diffraction is given by $	heta = \frac{2\lambda}{a}$, where $\lambda$ is the

Vedclass · Accepted Answer

$4860$

Vedclass · Answer

(C) The angular width of the central maximum in a single-slit Fraunhofer diffraction is given by $	heta = \frac{2\lambda}{a}$, where $\lambda$ is the wavelength of light and $a$ is the slit width.Let the initial wavelength be $\lambda_1 = 6480 	ext{ Å}$ and the initial angular width be $	heta_1 = \frac{2\lambda_1}{a}$.When the wavelength is changed to $\lambda_2 = \lambda$, the new angular width is $	heta_2 = \frac{2\lambda}{a}$.According to the problem, the angular width decreases by $25\%$, so $	heta_2 = 	heta_1 - 0.25	heta_1 = 0.75	heta_1$.Substituting the expressions for $	heta_1$ and $	heta_2$:$\frac{2\lambda}{a} = 0.75 	imes \frac{2\lambda_1}{a}$.This simplifies to $\lambda = 0.75 	imes \lambda_1$.$\lambda = 0.75 	imes 6480 	ext{ Å} = 4860 	ext{ Å}$.

Similar Questions

For an aperture of $5 \times 10^{-3} \ m$ and a monochromatic light of wavelength $\lambda$, the distance for which ray optics becomes a good approximation is $50 \ m$, then $\lambda=$ (in $\text{Å}$)

The limit of resolution of a telescope and a microscope is imposed because of which phenomenon?

The condition for observing Fraunhofer diffraction from a single slit is that the wave front incident on the slit should be ............

The cause of Fraunhofer lines is

$A$ plane wavefront of wavelength $6000 \, \mathring A$ is incident on a slit of width $0.2 \, mm$. $A$ Fraunhofer diffraction pattern is obtained on a screen at a distance of $2 \, m$ from the slit. What is the width of the central maximum in $mm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module