Question:
Two beams of light having intensities I and 4I interfere to
produce a fringe pattern on a screen. The phase difference
between the beams is $\pi/2$ at point A and $\pi$ at point B. Then
the difference between resultant intensities at A and B is
Two beams of light having intensities I and 4I interfere to
produce a fringe pattern on a screen. The phase difference
between the beams is $\pi/2$ at point A and $\pi$ at point B. Then
the difference between resultant intensities at A and B is
Updated On: Jan 18, 2023
- 2 I
- 4 I
- 5 I
- 7 I
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The Correct Option is B
Solution and Explanation
$I(\phi)=I_1+I_2+2 \sqrt{I_1 I_2} cos \, \phi \hspace20mm ...(i)$
Here,$ \, \, \, \, \, I_1=I \, and \, I_2=4I$
At point A, $\phi=\frac{\pi}{2}$
$\therefore \, \, \, \, \, \, \, \, I_A=I+4I=5I$
At point B, $\phi=\pi$
$\therefore \, \, \, \, \, \, \, \, \, I_B=I+4I-4I=I$
$\therefore \, \, \, I_A-I_B=4I$
NOTE E (i) for resultant intensity can be applied only when the
sources are coherent. In the question it is given that the rays
interfere. Interference takes place only when the sources are
coherent. That is why we applied equation number (i). When the
sources are incoherent, the resultant intensity is given by I = $I_1+I_2$
Here,$ \, \, \, \, \, I_1=I \, and \, I_2=4I$
At point A, $\phi=\frac{\pi}{2}$
$\therefore \, \, \, \, \, \, \, \, I_A=I+4I=5I$
At point B, $\phi=\pi$
$\therefore \, \, \, \, \, \, \, \, \, I_B=I+4I-4I=I$
$\therefore \, \, \, I_A-I_B=4I$
NOTE E (i) for resultant intensity can be applied only when the
sources are coherent. In the question it is given that the rays
interfere. Interference takes place only when the sources are
coherent. That is why we applied equation number (i). When the
sources are incoherent, the resultant intensity is given by I = $I_1+I_2$
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Concepts Used:
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In the single-slit diffraction experiment, we can examine the bending phenomenon of light or diffraction that causes light from a coherent source to hinder itself and produce an extraordinary pattern on the screen called the diffraction pattern.
Read More: Difference Between Diffraction and Interference
Central Maximum
