Interference of Light Waves - Young's Double-slit Experiment

  1. Wave Nature of Light
  2. Concepts
  3. Parameters and Equations
  4. Effects of Varying Certain Variables

Wave Nature of Light

Early physicists such as Issac Newton and Christiann Huygens thought tt was a steady stream of particles and had a wave motion. Indeed, such theories were correct but were unproven because light does indeed consists of moving quantas of photons which are packets of particles of pure energy. It was not until 1802, that Thomas Young proved that light does have a wave motion. In his experiment, he hypothesized that parallel beams of light should produce a brighter area where they overlapped if light were a steady stream. Instead, they produced bright bands separated by dark bands, the result of two sets of waves coinciding or canceling each other out. Thus, light is a form of wave.


Parameters and Equations

  • d is the distance between the 2 slits
  • y is the vertical distance from the center of the screen to the position of the fringe
  • θ is the angle made by a line to P from the point midway between the slits
  • L is the distance between the slits and the screen
  • r1 is the first path
  • r2 is the second path
  • δ is the path difference
  • m is the order number of the fringe
  • S1 is the first slit
  • S2 is the second slit


path difference.

δ = r2 - r1 = d sin θ

A bright fringe can be found at points on the screen for which the path difference is equal to an integral multiple of the wavelength:

δ = d sin θ = m λ (constructive)

(m = 0, ±1, ±2, …)

Since destructive interference occurs when waves arrive at the screen 180° out of hpase, dark fringes can be found when their path lengths differ by an odd integer multiple of a half wavelength:

δ = d sin θ = (m + ½) λ (destructive)

(m = 0, ±1, ±2, …)

The position of the fringes are dependent of variables L, d and λ.

y = L tan θ ≈ L sin θ

ybright @ λ L m / d (for small θ)

ydark @ λ L (m + ½) / d (for small θ)

Effects of Varying Certain Variables

The following diagrams visually show how each variable affects y
Varying d

Increasing the length of d decreases the spacing between different fringes. This is consistent with the fact that spacings between different fringes inversely depend on d.

This second diagram shows what happens to waves as they pass through the slits as d varies. More interference occurs when d is wider.

Varying L

The spacings between different fringes decreases as the distance between the slits increases because it is dependent on L.

Varying the Wavelength

Increasing the wavelength of the light increases the spacing between different fringes since the spacing between different fringes is wavelength dependent.

Red light has the largest wavelength of the color spectrum with a range of 625 - 740 nm, while violet has the smallest wavelength with a range of 380 - 435 nm.

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