MHT CET · Physics · Wave Optics
Consider the following statements about interference of light
A. The interference fringes are equally bright and equally spaced
B. At the centre of a bright fringe, the intensity is four times the intensity of the incident wave
C. For constructive interference of two waves, the crest of one wave coincides with trough of another wave.
Which of the above statements are correct?
- A A and B only
- B A and C only
- C All A, B and C
- D B and C only
Answer & Solution
Correct Answer
(A) A and B only
Step-by-step Solution
Detailed explanation
In interference, the fringes are equally bright and equally spaced and intensity of the bright fringe is four times the intensity of each incident wave.
Resultant intensity at a point is given by
\(I=I_1+I_2+2 \sqrt{I_1} \sqrt{I_2} \cos \delta\)
where, \(I_1\) is the intensity of the wave from source \(1, I_2\) is the intensity of the wave from source 2 . No two sources in nature can be coherent. So, sources are made from one source by either splitting the amplitude or the wave fronts, by means of double-slit or Fresnel's prism or Lloyd's mirror etc. Further, to get a high contrast \(I_1=I_2=I\).
So, for constructive interference and at the central maxima \(\delta=0\),
\(I_{\max }=2 I+2 I \cos \delta=2 I(1+\cos \delta)=4 I \cos ^2\left(\frac{\delta}{2}\right)=4 I\)
So at central maxima intensity is four times the incident wave.
Resultant intensity at a point is given by
\(I=I_1+I_2+2 \sqrt{I_1} \sqrt{I_2} \cos \delta\)
where, \(I_1\) is the intensity of the wave from source \(1, I_2\) is the intensity of the wave from source 2 . No two sources in nature can be coherent. So, sources are made from one source by either splitting the amplitude or the wave fronts, by means of double-slit or Fresnel's prism or Lloyd's mirror etc. Further, to get a high contrast \(I_1=I_2=I\).
So, for constructive interference and at the central maxima \(\delta=0\),
\(I_{\max }=2 I+2 I \cos \delta=2 I(1+\cos \delta)=4 I \cos ^2\left(\frac{\delta}{2}\right)=4 I\)
So at central maxima intensity is four times the incident wave.
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