Sodium light of wavelengths 650, nm and 655, | vedclass

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

Question

(C) For a single slit diffraction,the condition for the $n^{th}$ maxima is given by $a \sin 	heta = (n + \frac{1}{2}) \lambda$.For the first maxima,$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) For a single slit diffraction,the condition for the $n^{th}$ maxima is given by $a \sin 	heta = (n + \frac{1}{2}) \lambda$.For the first maxima,$n = 1$,so $a \sin 	heta = \frac{3 \lambda}{2}$.Since $	heta$ is very small,$\sin 	heta \approx 	heta = \frac{y}{L}$,where $y$ is the distance from the central maxima and $L$ is the distance to the screen.Thus,$y = \frac{3 \lambda L}{2 a}$.The separation between the first maxima for two wavelengths $\lambda_1 = 650\, nm$ and $\lambda_2 = 655\, nm$ is $\Delta y = y_2 - y_1 = \frac{3 L}{2 a} (\lambda_2 - \lambda_1)$.Given $L = 2.0\, m$,$a = 0.5\, mm = 0.5 	imes 10^{-3}\, m$,$\lambda_1 = 650 	imes 10^{-9}\, m$,and $\lambda_2 = 655 	imes 10^{-9}\, m$.$\Delta y = \frac{3 	imes 2.0}{2 	imes 0.5 	imes 10^{-3}} 	imes (655 - 650) 	imes 10^{-9}$.$\Delta y = \frac{6}{10^{-3}} 	imes 5 	imes 10^{-9} = 6 	imes 5 	imes 10^{-6} = 30 	imes 10^{-6} = 3 	imes 10^{-5}\, m$.Comparing with $x 	imes 10^{-5}\, m$,we get $x = 3$.

Similar Questions

Light of wavelength $6000 \, \mathring A$ is incident on a slit of width $0.30 \, mm$. $A$ screen is placed at a distance of $2 \, m$ from the slit. Find the position of the first minimum.

On which factor does the number of interference fringes in a given width of a diffraction peak depend?

In the case of Fraunhofer diffraction at a single slit,which of the following statements correctly describes the diffraction pattern on the screen?

Angular width of the central maximum of a diffraction pattern due to a single slit does not depend upon:

$A$ light wave of wavelength $\lambda$ is incident on a slit of width $d$. The resulting diffraction pattern is observed on a screen at a distance $D$. If the linear width of the principal maxima is equal to the width of the slit,then the distance $D$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module