In a YDSE with two identical slits,when the u | vedclass

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

Question

(A) Let the phase difference introduced by the mica sheet be $\phi$. The intensity at the center of the screen is given by $I = I_0 \cos^2(\phi/2)$. G

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(A) Let the phase difference introduced by the mica sheet be $\phi$. The intensity at the center of the screen is given by $I = I_0 \cos^2(\phi/2)$. Given $I = 0.75 I_0$,we have $\cos^2(\phi/2) = 3/4$,which implies $\cos(\phi/2) = \pm \sqrt{3}/2$. Thus,$\phi/2 = n\pi \pm \pi/6$,or $\phi = 2n\pi \pm \pi/3$. For $n=1$,$\phi = 2\pi \pm \pi/3$,giving $\phi = 5\pi/3$ or $7\pi/3$. For $n=2$,$\phi = 4\pi \pm \pi/3$,giving $\phi = 11\pi/3$ or $13\pi/3$. For $n=3$,$\phi = 6\pi \pm \pi/3$,giving $\phi = 17\pi/3$ or $19\pi/3$. The condition that the second minimum is above the center and the third maximum is below the center constrains the value of $\phi$. Based on the shift analysis,the phase difference $\phi$ must satisfy $3\pi < \phi < 4\pi$. Among the options,$\pi/3$ does not fall in the required range.

Similar Questions

In $Y.D.S.E.,$ the slits are $0.2 \, cm$ apart and are illuminated by yellow light $(\lambda = 600 \, nm).$ What would be the fringe width on a screen placed $1 \, m$ from the plane of the slits if the whole system is immersed in water of refractive index $\mu = \frac{4}{3}$ (in $, mm$)?

In Young's double-slit experiment,when two light waves form the third minimum,they have:

In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The distance between the two coherent sources is $d$ and $D$ is the distance between the source and the screen. The possible wavelengths used are inversely proportional to

Light of wavelength $600 \, nm$ is incident on a double slit and the interference fringes are formed on a screen $1 \, m$ apart. The separation between two consecutive dark fringes on a screen is found to be $1.2 \, mm$. What is the separation between the slits in $mm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module