S_{1} and S_{2} are coherent point sources of | vedclass

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

Question

(B) For constructive interference,the path difference $\Delta x$ between the two waves must be an integral multiple of the wavelength,i.e.,$\Delta x =

Vedclass · Accepted Answer

$(4\lambda, 0)$

Vedclass · Answer

(B) For constructive interference,the path difference $\Delta x$ between the two waves must be an integral multiple of the wavelength,i.e.,$\Delta x = n\lambda$,where $n = 0, 1, 2, \dots$.Let the point be $P(x, 0)$ on the $x$-axis.The distance from $S_{1}(0,0)$ to $P(x,0)$ is $r_{1} = \sqrt{(x-0)^{2} + (0-0)^{2}} = x$.The distance from $S_{2}(0,3\lambda)$ to $P(x,0)$ is $r_{2} = \sqrt{(x-0)^{2} + (0-3\lambda)^{2}} = \sqrt{x^{2} + 9\lambda^{2}}$.The path difference is $\Delta x = |r_{2} - r_{1}| = |\sqrt{x^{2} + 9\lambda^{2}} - x|$.Testing option $(B)$ $(4\lambda, 0)$:$r_{1} = 4\lambda$.$r_{2} = \sqrt{(4\lambda)^{2} + (3\lambda)^{2}} = \sqrt{16\lambda^{2} + 9\lambda^{2}} = \sqrt{25\lambda^{2}} = 5\lambda$.Path difference $\Delta x = |5\lambda - 4\lambda| = \lambda$.Since $\Delta x = 1\lambda$,which is an integral multiple of $\lambda$,constructive interference occurs at $(4\lambda, 0)$.

$S_{1}$ and $S_{2}$ are coherent point sources of light located in the $xy$-plane at points $(0,0)$ and $(0,3\lambda)$ respectively. Here $\lambda$ is the wavelength of light. At which one of the following points (given as coordinates) will the intensity of interference be maximum?

Similar Questions

The wave nature of light is confirmed because:

$A$ laser is a coherent source because it contains

Coherent sources are characterized by the same

The essential condition for obtaining a sustained interference pattern is that the two sources must . . . . . .

For a distinct interference pattern to be observed,the necessary condition is that the ratio of the intensity of light emission by both sources should be

Vedclass Test Series

Exam Paper Generator

Online Exam Module