MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Interference of Light Page 1

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1.

Principle of Superposition of Waves:w

When two, or more waves, travelling through a medium, arrive at a point of the medium simultaneously, each wave produces its own displacement at that point, independently of the other wave.

The resultant displacement at that point is equal to the vector sum of the displacements due to all the waves.

Interference of Light: The physical effect (i.e., change in intensity of light) produced due to the superposition of the waves of light is called the interference of light.

·         If two waves of light, arriving simultaneously at a point, are in phase, (crest of one wave coincides with the crest of the other wave, trough of one wave coincides with the trough of the other wave), the resultant displacement at that point is maximum, giving rise to maximum intensity and hence a point of brightness.

This phenomenon is called constructive interference.

• If two waves of light, arriving at a point at the same time, are in opposite phase (crest of one wave coincides with the trough of the other wave and vice versa), the resultant intensity at that point is minimum and hence that point is dark.

This phenomenon is called destructive interference.

Steady Interference Pattern: When the resultant maximum and minimum intensity of two interfering light waves is observed on a screen, the alternate bright and dark bands are termed as an interference pattern.

The pattern is said to be steady if the intensity of light at any given point always remains constant.

·         In a steady interference pattern, dark points remain dark and bright points remain bright.

• Alternate bright and dark bands or rings are observed (depending on the geometry of the source). These bands or rings are called interference fringes.

Conditions Necessary for Obtaining a Steady Interference Pattern:

The following conditions must be satisfied in order to observe a steady or stationary interference pattern.

• The two sources of light must be coherent, i.e., there is a constant phase difference between the light waves emitted by the two sources.

This condition is met only if the two sources are derived from the same source.

• The two sources of light must be monochromatic, i.e., the light emitted is of the same wavelength. (Though light waves of different colours interfere, the resulting interference pattern is not well defined).
• The light waves emitted by the two sources must be of equal amplitudes or the sources must be of same intensity.

For example, The interference pattern produced by
the waves (1) and (2) is not significant.

• The two sources must be narrow. Point sources of light in the form of illuminated slits are used.
• The two sources should be close to (near) each other.
For example, the distance between the coherent sources ~10-3 to 10-4 m while the interference pattern is observed on a screen placed about 1 m away from the source.
• The two sources should emit waves in nearly the same direction.

Coherent Sources: Two sources of light are called coherent sources. If there is a constant phase difference between the light waves emitted by them.

• This condition is met only if the sources are derived from the same original source.
• A steady interference pattern can be produced only if coherent sources are used.
• In Young's experiment, monochromatic light from an illuminated slit falls on two symmetrically placed parallel slits. These slits S1 and S2 act as coherent sources.

·  In a biprism experiment, two virtual images of the     illuminated slit are produced due to refraction.

These virtual images act as coherent sources.

2.

Young's Double Slit Experiment to Observe the Interference of Light:

L : monochromatic light source
S : illuminated slit
S1, S2 : Parallel slits
® coherent sources
N : Screen

• The resulting interference pattern consists of alternate dark and bright bands parallel to the slit.
• The bands are equidistant, i.e., the distance between two consecutive bright (dark) bands is constant.
• The intensity of the bright bands is the same throughout.

Significance of Young's Experiment

• The first experiment in which the interference of light was observed.
• Proved that light travels in the form of waves, hence verified Huygens' theory.
• The experiment can be used to determine the wavelength of any monochromatic light source.

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