Two coherent sources of intensities I_{1} and | vedclass

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

Question

(A) The intensity $I$ of a wave is proportional to the square of its amplitude $a$,i.e.,$I \propto a^{2}$.This implies that the amplitude $a$ is propo

Vedclass · Accepted Answer

$(\sqrt{I_{1}}+\sqrt{I_{2}})^{2}$

Vedclass · Answer

(A) The intensity $I$ of a wave is proportional to the square of its amplitude $a$,i.e.,$I \propto a^{2}$.This implies that the amplitude $a$ is proportional to the square root of the intensity,i.e.,$a \propto \sqrt{I}$.Let the amplitudes of the two coherent sources be $a_{1}$ and $a_{2}$,where $a_{1} \propto \sqrt{I_{1}}$ and $a_{2} \propto \sqrt{I_{2}}$.In an interference pattern,the maximum intensity $(I_{\max})$ occurs at points of constructive interference,where the phase difference is an even multiple of $\pi$ $(2n\pi)$.At these points,the resultant amplitude is the sum of the individual amplitudes: $A_{\max} = a_{1} + a_{2}$.Since $I_{\max} \propto A_{\max}^{2}$,we have $I_{\max} \propto (a_{1} + a_{2})^{2}$.Substituting the expressions for $a_{1}$ and $a_{2}$,we get $I_{\max} = (\sqrt{I_{1}} + \sqrt{I_{2}})^{2}$.

Two coherent sources of intensities $I_{1}$ and $I_{2}$ produce an interference pattern on a screen. The maximum intensity in the interference pattern is

Similar Questions

Two coherent sources of intensity ratio $x^2$ interfere. In the interference pattern,which of the following relations is correct?

$PQ$ represents a wavefront and $AO$ and $BP$ are the corresponding two rays. Find the condition on $Q$ for constructive interference at $P$ between ray $BP$ and the reflected ray $OP$.

The resultant amplitude of coherent sources depends on ......

Two light sources are said to be coherent if they are obtained from

The contrast in the fringes in an interference pattern depends on

Vedclass Test Series

Exam Paper Generator

Online Exam Module