Interference of Waves
1. Superposition of waves
When two or more waves travel simultaneously in a medium (superimposes), and then the resultant displacement at any point is due to the algebraic sum of the displacements of the individual waves.
When two light waves superimpose then the resultant amplitude (or intensity) in the region of superposition is different than the amplitude (or intensity) of individual waves. The modification in the distribution of amplitude (intensity) in the region of superposition is called Interference”. There are two types of interferences depending on the intensity.
2. Constructive Interference
When the resultant amplitude is equal to the sum of the amplitudes due to individual waves and the intensity of light becomes maximum then that interference is known as constructive interference in which bright band is formed.
3. Destructive Interference
When the resultant amplitude is equal to the difference of the amplitudes due to individual waves and the intensity of light becomes minimum then that interference is known as destructive interference in which a dark band is formed.
4. Condition for sustained interferenc
- The two sources should be coherent.
- The two sources must emit continuous waves of same wavelength and frequency.
- The two sources should be monochromatic.
- The amplitude of interfering waves should be equal.
- The distance between the two sources (2d) should be small.
- The distance between sources and screen (D) should be large.
- The background should be dark.
5. Coherence
Two sources are said to be coherent, if their waves have (i) same wavelength (ii) same amplitude and (iii) constant phase difference. Only such waves on superposition give rise to interference pattern.
Multiple Choice Questions (MCQs)
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Interference of light occurs due to:
- a) Reflection of light
- b) Superposition of two or more light waves
- c) Refraction of light
- d) Diffraction of light
Answer
b) Superposition of two or more light waves
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The condition for constructive interference is:
- a) Path difference = \( (2n + 1)\frac{\lambda}{2} \)
- b) Phase difference = \( \pi \)
- c) Path difference = \( n\lambda \)
- d) Phase difference = \( \frac{\pi}{2} \)
Answer
c) Path difference = \( n\lambda \)
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The condition for destructive interference is:
- a) Path difference = \( n\lambda \)
- b) Path difference = \( (2n + 1)\frac{\lambda}{2} \)
- c) Phase difference = 0
- d) Path difference = 0
Answer
b) Path difference = \( (2n + 1)\frac{\lambda}{2} \)
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Interference fringes are produced only when:
- a) Light from two independent sources is used
- b) Coherent sources are used
- c) The light is unpolarized
- d) The light beams are of different frequencies
Answer
b) Coherent sources are used
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In an interference pattern, the bright and dark fringes are due to:
- a) Different intensities caused by constructive and destructive interference
- b) Change in color
- c) Refraction of waves
- d) Polarization of light
Answer
a) Different intensities caused by constructive and destructive interference