Two identical light waves, propagating in the same direction, have a phase difference $\delta$. After they superpose the intensity of the resulting wave will be proportional to
- $cos\, \delta$
- $cos\, (\delta /2)$
- $cos^{2} (\delta/2)$
- $cos^{2}\delta$
The Correct Option is C
Solution and Explanation
The resulting intensity of two identical light waves, which have a phase difference of δ and propagate in the same direction, is
\(I_r=I+I+2I\cosδ=4I\cos^2(\frac{δ}{2})\)
Therefore, the resulting intensity of the wave is directly proportional to \(\cos^2\frac{δ}{2}\)
So, the correct option is (C) : \(\cos^2(\frac{δ}{2})\)
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Concepts Used:
Wave interference
What is Interference?
When two or more waves meet each other then interference happens . Interference is a phenomenon in which 2 or more waves superpose to form a resultant wave of greater, lower or the same amplitude.
There are two types of wave interference:
- Constructive interference
- Destructive interference
The principle of superposition of waves refers that when two or more waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves. If the crest of a wave meets the crest of another wave of the same frequency at the same point, sum of individual amplitudes is called as constructive interference.The destructive interference occurs when the maxima of the two waves are at 180 degrees out of phase and a positive displacement of one wave is cancelled exactly by a negative displacement of the other wave.