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Syllabus

Coherent and Incoherent Addition of Waves

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Estimated time: 4 minutes
CBSE: Class 12

Key Points: Coherent and Incoherent Addition of Waves

Coherent Sources-

Two sources are coherent if they emit waves of:

  • Same frequency
  • Constant (fixed) phase difference
  • Obtained from a single source

Two coherent sources can be created by:

  • Splitting a physical source into two
  • Generating two virtual images of the same source

Incoherent Sources-

  • Phase difference changes with time → incoherent.
  • Two independent monochromatic sources of same frequency are incoherent because atoms cannot emit light waves in same phase simultaneously.

Addition of Waves (Superposition)

Let two waves have amplitudes A₁ and A₂, same frequency, and constant phase difference φ.

  • Resultant amplitude: \[A_{res}=\sqrt{A_1^2+A_2^2+2A_1A_2\cos\phi}\]

  • Phase angle: \[\theta=\tan^{-1}\left(\frac{A_2\sin\phi}{A_1+A_2\cos\phi}\right)\]

  • Since I ∝ A2: \[I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi\]

Shaalaa.com | Wave Optics part 13 (Coherent and incoherent addition of waves)

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Related QuestionsVIEW ALL [5]

Two coherent point sources S1 and S2, vibrating in phase, emit light of wavelength \[\lambda.\] The separation between the sources is \[2\lambda.\] Consider a line passing through S2 and perpendicular to the line S1 S2. What is the smallest distance from S2 where a minimum intensity occurs?

Two source S1 and S2 of intensity I1 and I2 are placed in front of a screen [Figure (a)]. The pattern of intensity distribution seen in the central portion is given by Figure (b).


(a)

(b)

 

  1. S1 and S2 have the same intensities.
  2. S1 and S2 have a constant phase difference.
  3. S1 and S2 have the same phase.
  4. S1 and S2 have the same wavelength.

When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?

Two sources are called coherent if they produce waves ______________ .

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio ______.

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