Interference of Light Waves�

Presesnted By:

Saloni Sharma

Nature of light

• Wave nature (electromagnetic wave)
• Particle nature (bundles of energy called photons)
• The wave nature of light is needed to explain various phenomena such as interference, diffraction, polarization, etc

Past- Separate Theories of Either Wave or Particle Nature

• Corpuscular theory of Newton (1670)
• Light corpuscles have mass and travel at extremely high speeds in straight lines

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• Huygens (1680)
• Wavelets-each point on a wave-front acts as a source for the next wave-front

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Proofs of Wave Nature

• Thomas Young's Double Slit Experiment (1807)

bright (constructive) and dark (destructive) fringes seen on screen

• Thin Film Interference Patterns

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• Poisson/Arago Spot (1820)

• Diffraction fringes seen within and around a small obstacle or through a narrow opening

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Proof of Particle Nature�Photoelectric Effect

• Light energy is quantized
• Photon is a quantum or packet of energy
• Heinrich Hertz first observed the photoelectric effect in 1887
• Einstein explained it in 1905 and won the Nobel prize for this

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Interference

• Light waves interfere with each other much like mechanical waves do.

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• All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine.

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• When two or more light waves pass through a given point, their electric fields combine according to the principle of superposition.

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Principle of Linear Superposition

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The waves emitted by the sources start out in phase and arrive at

point P in phase, leading to constructive interference.

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The waves emitted by the sources start out in phase and arrive at

point P out of phase, leading to destructive interference.

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Sustained Interference Pattern: Coherent Sources

• If constructive or destructive interference is to continue occurring at a point, the sources of the waves must be coherent sources.

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• Two sources are coherent if the waves they emit maintain a constant phase relation.

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• The waves must have identical wavelengths.

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Producing Coherent Sources

• Old method: light from a monochromatic source is allowed to pass through a narrow slit

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• The light from the single slit is allowed to fall on a screen containing two narrow slits; the first slit is needed to ensure the light comes from a tiny region of the source which is coherent.

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• Currently, it is much more common to use a laser as a coherent source.

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• The laser produces an intense, coherent, monochromatic beam, which can be used to illuminate multiple slits directly.

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Young’s Double Slit Experiment

• Light is incident on a screen with a narrow slit, S_o

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• The light waves emerging from this slit arrive at a second screen that contains two narrow, parallel slits, S₁ and S₂

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• The narrow slits, S₁ and S₂ act as sources of waves

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• The waves emerging from the slits originate from the same wave front and therefore are always in phase

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Thomas Young

(1773 – 1829)

Interference fringes

• The light from the two slits form a visible pattern on a screen, which consists of a series of bright and dark parallel bands called fringes
• Constructive interference occurs where a bright fringe appears.
• Destructive interference results in a dark fringe

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Constructive Interference

• Constructive interference occurs at the center point

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• The two waves travel the same distance, therefore they arrive in phase

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• The upper wave has to travel farther than the lower wave

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• The upper wave travels one wavelength farther

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• Therefore, the waves arrive in phase and a bright fringe occurs

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Destructive Interference

• The upper wave travels one-half of a wavelength farther than the lower wave

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• The trough of the bottom wave overlaps the crest of the upper wave

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• A dark fringe occurs

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• This is destructive interference

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Young’s Double slit experiment

• The path difference, δ, is found from the tan triangle: δ = r₂ – r₁ = d sin θ

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• This assumes the paths are parallel

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• Although they are not exactly parallel, but this is a very good approximation since L is much greater than d

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• For a bright fringe, produced by constructive interference, the path difference must be either zero or some integral multiple of the wavelength:

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δ = d sin θ_bright = m λ; m = 0, ±1, ±2, …

where m is called the order number

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• When m = 0, it is the zeroth order maximum and when m = ±1, it is called the first order maximum, etc.

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Position of Maxima

• Within the assumption L >> y (θ is small), the positions of the fringes can be measured vertically from the zeroth order maximum
• y = L tan θ ≈ L sin θ ;

sin θ ≈ y / L

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• δ = d sin θ_bright = m λ; m = 0, ±1, ±2

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• sin θ_bright = m λ / d

​

• y = m λ L / d

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Interference Fringes

The waves coming from the slits interfere constructively or

destructively, depending on the difference in distances between

the slits and the screen.

Interference Equations

• When destructive interference occurs, a dark fringe is observed
• This needs a path difference of an odd half wavelength

δ = d sin θ_dark = (m + ½) λ; m = 0, ±1, ±2, …

• Thus, for bright fringes

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• And for dark fringes

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White Light and Young’s Experiment�

• The figure shows a photograph that illustrates the kind of interference fringes that can result when white light is used in Young’s experiment

Interference in Thin Films

Phase Changes Due To Reflection

• An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling (similar to a reflected pulse on a string

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Phase Changes Due To Reflection

There is no phase change when the wave is reflected from a boundary leading to a medium of lower index of refraction (similar to a pulse in a string reflecting from a free support)

Interference in Thin Films

• Interference effects are commonly observed in thin films (e.g., soap bubbles, oil on water, etc.)

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• The interference is due to the interaction of the waves reflected from both surfaces of the film

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• Recall: the wavelength of light λ_n in a medium with index of refraction n is λ_n = λ / n where λ is the wavelength of light in vacuum

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Interference in Thin Films

• Recall: an electromagnetic wave traveling from a medium of index of refraction n₁ toward a medium of index of refraction n₂ undergoes a 180° phase change on reflection when n₂ > n₁ and there is no phase change in the reflected wave if n₂ < n₁

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• Ray 1 undergoes a phase change of 180° with respect to the incident ray

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Interference in Thin Films

• Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave; ray 2 also travels an additional distance of 2t before the waves recombine

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• For constructive interference, taking into account the 180° phase change and the difference in optical path length for the two rays:

2 t = (m + ½) (λ / n)

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2 n t = (m + ½) λ; m = 0, 1, 2 …

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Interference in Thin Films

• Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave; ray 2 also travels an additional distance of 2t before the waves recombine

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• For destructive interference:

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2 t = m (λ / n)

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2 n t = m λ; m = 0, 1, 2 …

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Interference in Thin Films

• Two factors influence thin film interference: possible phase reversals on reflection and differences in travel distance

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• The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface

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• If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed.

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Interference in Thin Films

Wedge Shaped Film

The wedge of air formed

between two glass plates

causes an interference

patter of alternating dark

and bright fringes

Consider two plane glass surfaces GH and G1H1, both are inclined at angle at an angle (α), so that air film of increasing thickness is formed between both of two surfaces. Let (μ) be the refractive index of the material film. Interference in wedge shape film can be studied only when this film is illuminated by source of monochromatic light.

Wedge Shaped Film

• Suppose a beam of monochromatic light AB incident at an angle (i) at a point (B) on the upper surface G1H1 .Then a part of this light will be reflected in the direction BR and a part of this light be refracted in a direction BC, this refracted ray will be incident at an angle (r+ α) at a point (C).

Then a part of this refracted will be reflected at the denser surface in the direction CD and comes out in the form of ray DR1. Our aim is to be study interference between two reflected ray BR and DR1. From the fig. it is observed that ray BR and DR1 are not parallel so that they appear to diverge from a point (S) means interference take place at S which is virtual. So that intensity at a point S is maximum or minimum depend upon the path difference between the two reflected ray BR and DR1.

Newton’s Rings

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