In Young's double slit experiment,the sli | vedclass

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

Question

(B) The intensity at any point in an interference pattern is given by $I = I_0 \cos^2\left(\frac{\phi}{2}\right)$,where $\phi$ is the phase difference

Vedclass · Accepted Answer

$\sin^{-1}\left(\frac{1}{6}\right)$

Vedclass · Answer

(B) The intensity at any point in an interference pattern is given by $I = I_0 \cos^2\left(\frac{\phi}{2}ight)$,where $\phi$ is the phase difference.
Given $I = \frac{I_0}{4}$,we have $\frac{I_0}{4} = I_0 \cos^2\left(\frac{\phi}{2}ight)$,which implies $\cos^2\left(\frac{\phi}{2}ight) = \frac{1}{4}$.
Taking the square root,$\cos\left(\frac{\phi}{2}ight) = \frac{1}{2}$,so $\frac{\phi}{2} = \frac{\pi}{3}$,which gives $\phi = \frac{2\pi}{3}$.
The path difference $\Delta x$ is related to the phase difference by $\Delta x = \frac{\lambda}{2\pi} \phi = \frac{\lambda}{2\pi} \left(\frac{2\pi}{3}ight) = \frac{\lambda}{3}$.
From the geometry of the setup,the path difference is $\Delta x = d \sin 	heta$. Given $d = 2\lambda$,we have $\frac{\lambda}{3} = 2\lambda \sin 	heta$.
Solving for $\sin 	heta$,we get $\sin 	heta = \frac{\lambda/3}{2\lambda} = \frac{1}{6}$.
Therefore,$	heta = \sin^{-1}\left(\frac{1}{6}ight)$.

In Young's double slit experiment,the slits are horizontal. The intensity at a point $P$ on the screen is $\frac{I_0}{4}$,where $I_0$ is the maximum intensity. If the distance between the two slits $S_1$ and $S_2$ is $d = 2 \lambda$,then the value of $\theta$ is:

Similar Questions

In Young's double slit experiment, for the $n^{th}$ dark fringe $(n = 1, 2, 3, \dots)$ the phase difference of the interfering waves in radian will be

Two slits are made one millimetre apart and the screen is placed one metre away from the slits. The fringe width when light of wavelength $500 \,nm$ is used is

In Young's double-slit experiment,which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module