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

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

Question

(C) The intensity $I$ at any point in an interference pattern is given by $I = I_{max} \cos^2(\phi/2)$,where $\phi$ is the phase difference.Given $I =

Vedclass · Accepted Answer

$\sin^{-1}(\lambda/3d)$

Vedclass · Answer

(C) The intensity $I$ at any point in an interference pattern is given by $I = I_{max} \cos^2(\phi/2)$,where $\phi$ is the phase difference.Given $I = I_{max}/4$,we have $I_{max}/4 = I_{max} \cos^2(\phi/2)$.This simplifies to $\cos^2(\phi/2) = 1/4$,so $\cos(\phi/2) = 1/2$.Thus,$\phi/2 = \pi/3$,which means the phase difference $\phi = 2\pi/3$.The relation between phase difference $\phi$ and path difference $\Delta x$ is $\phi = (2\pi/\lambda) \Delta x$.Substituting $\phi = 2\pi/3$,we get $2\pi/3 = (2\pi/\lambda) \Delta x$,which gives $\Delta x = \lambda/3$.For a point at angular position $	heta$,the path difference is $\Delta x = d \sin 	heta$.Therefore,$d \sin 	heta = \lambda/3$,which implies $\sin 	heta = \lambda/(3d)$.Hence,$	heta = \sin^{-1}(\lambda/3d)$.

In Young's double slit experiment,the intensity at a point is $1/4$ of the maximum intensity. The angular position of this point is:

Similar Questions

In Young's double slit experiment,white light is used. The separation between the slits is $b$. The screen is at a distance $d$ $(d >> b)$ from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

In an interference pattern,the fringe width is $\beta$. If the frequency of the source is doubled,the fringe width becomes .....

Two slits are separated by a distance of $0.5\, mm$ and illuminated with light of $\lambda = 6000\ \mathring A$. If the screen is placed $2.5\, m$ from the slits,the distance of the third bright fringe from the centre will be........$mm$.

In the Young's double slit experiment with sodium light,the slits are $0.589 \ m$ apart. The angular separation of the third maximum from the central maximum will be (given $\lambda = 589 \ nm$):

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module