Principle of Interference of Light Waves: Young’s Double Slit Experiment �

Presented 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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�Photoelectric Effect: Proof of Particle Nature of light�

• 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 Superposition

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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Superposition of Light waves and Interference

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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Young’s Double slit experiment

• 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

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• 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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Fringe width

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

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