Two coherent sources are kept at a distance o | vedclass

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

Question

(B) The path difference $\Delta x$ at any point on the screen is given by $\Delta x = d \cos 	heta$,where $d = 2 \lambda$ is the distance between the

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) The path difference $\Delta x$ at any point on the screen is given by $\Delta x = d \cos 	heta$,where $d = 2 \lambda$ is the distance between the sources and $	heta$ is the angle with the line joining the sources.For maxima,the path difference must be an integer multiple of $\lambda$,i.e.,$\Delta x = n \lambda$.Since the screen is perpendicular to the line joining the sources,the range of $	heta$ is from $0$ to $90^\circ$ (or $0$ to $\pi/2$ radians).Thus,$\Delta x = 2 \lambda \cos 	heta$.As $	heta$ varies from $0$ to $90^\circ$,$\cos 	heta$ varies from $1$ to $0$.Therefore,the path difference $\Delta x$ varies from $2 \lambda$ to $0$.The possible values for $n$ in $\Delta x = n \lambda$ are $n = 0, 1, 2$.For $n = 2$,$\Delta x = 2 \lambda$ (at $	heta = 0$,the point on the screen closest to the sources).For $n = 1$,$\Delta x = \lambda$ (at $\cos 	heta = 0.5$,i.e.,$	heta = 60^\circ$).For $n = 0$,$\Delta x = 0$ (at $	heta = 90^\circ$,i.e.,at infinity).Since the screen is symmetric on both sides of the line joining the sources,we have:- At $	heta = 0$: $1$ central maxima $(n=2)$.- For $	heta > 0$: $2$ maximas for $n=1$ (one on each side) and $2$ maximas for $n=0$ (one on each side at infinity).However,the question typically asks for finite points on the screen. At $	heta = 90^\circ$,the path difference is $0$,which corresponds to the point at infinity. Excluding the points at infinity,we have $n=2$ (one point) and $n=1$ (two points),totaling $3$ maximas.

Two coherent sources are kept at a distance of $d = 2 \lambda$. $A$ large screen is placed perpendicular to the line joining the sources. Determine the total number of maximas observed on the screen. (Here,$\lambda$ is the wavelength of light.)

Similar Questions

Define constructive interference. $OR$ Define destructive interference.

Two point sources $X$ and $Y$ emit waves of the same frequency and speed,but $Y$ lags in phase behind $X$ by $2\pi l$ radians. If there is a maximum in direction $D$,the distance $XO$ (where $n$ is an integer) is given by:

In the phenomenon of interference :-
$(a)$ Total energy is conserved
$(b)$ Total energy is not conserved
$(c)$ Only bright fringes are formed
$(d)$ The frequency of two sources is equal

The phenomenon of interference is based on

The two coherent sources of equal intensity produce a maximum intensity of $100$ units at a point. If the intensity of one of the sources is reduced by $36\%$ by reducing its width,then the intensity of light at the same point will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module