Double Slit Interference

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Young's double slit experiment 1

  • The wave nature of light was first suggested by Christiaan Huygens in the 17th century but it was rejected at the time in favour of Sir Isaac Newton's corspuscular theory of light. Newton considered that light was composed of tiny particles, which he referred to as corspuscles, and he was able to explain reflection and refraction using his theory. Huygens was also able to explain reflection and refraction using his wave theory. However, because of Newton's much stronger scientific reputation, Newton's theory of light remained unchallenged for over a century until 1803, when Thomas Young demonstrated interference of light.
  • To observe interference of light, we can illuminate two closely spaced parallel slits using a suitable light source, as described below. The two slits act as coherent sources of waves, which means that they emit light waves with a constant phase difference and the same frequency.
  • 1) Young would have used a candle instead of a light bulb to illuminate a narrow single slit. The double slit arrangement is illuminated by light from the narrow single slit. Alternate bright and dark fringes, referred to as Young's fringes, can be seen on a white screen placed where the diffracted light from the double slits overlap. The fringes are evenly spaced and parallel to the double slits
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Young's double slit experiment 2

  • 2) A laser beam from a low power laser could be used instead of the light bulb and the single slit. The fringes must be displayed on a screen, as a beam of laser light will damage the retina if it enters the eye.

The fringes are formed due to interference of light from the two slits:

  • Where a bright fringe is formed, the light from one slit reinforces the light from the other slit. In other words, the light waves from each slit arrive in phase with each other.
  • Where a dark fringe is formed, the light from one slit cancels the light from the other slit. In other words, the light waves from the two slits arrive 180° out of phase.
  • The distance from the centre of a bright fringe to the centre of the next bright fringe is called the fringe seperation. This depends on the slit spacing (s) and the distance (D) from the slits to the screen, in accordance with the equation:
  • Fringe Seperation (w) = (λD)/s, where λ is the wavelength of the light.
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Young's double slit experiment 3

The equation shows that the fringes become more widely spaced if:

  • the distance (D) from the slits to the screen is increased
  • the wavelength (λ) of the light used is increased
  • the slit spacing (s) is reduced. Note that the slit spacing is the distance between the centres of the slits.
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The theory of the double slit equation

At a point (p) on the screen where the fringes are observed, light emitted from s1 arrives later than light from s2 emitted at the same time as the distance S1P is greater than the distance S2P. The difference between the two distances is the path difference.

  • For reinforcement  at P, the path difference S1P- S2P = Mλ, where m = 0, 1, 2 etc.

Light emitted simultaneously from S1 and S2 arrives in phase at P so reinforcement occurs at this point.

  • For cancellation at P, the path difference S1P - S2P = (M + 1/2)λ, where m = 0, 1, 2 etc.

Light emitted simultaneously from S1 and S2 arrives at P out of phase by 180(o), so cancellation occurs at P.

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The theory of the double slit equation 2

  • Path difference = QP
  • Consider triangles S1S2Q and MOP, where M is the midpoint between the two slits and O is the midpoint of the central bright fringe of the pattern. The two triangles are very nearly similar in shape, as angles S1S2Q and PMO are almost equal and the long sides of each trianglle are of almost equal length. Therefore:
  • (S1Q)/(S1S2) = (OP)/(OM)
  • If P is the mth bright fringe from the centre then S1Q = Mλ and OP = mw, where w is the distance between the centres of adjacent bright fringes. Also,m OM = distance (D) and S1S2 = slit spacing (s). Therefore:
  • (mλ)/S = (mw)/D. Rearranging this gives: λ = (sw)/D or w = (λD)/s
  • By measuring the slit spacing (s) the fringe seperation (w) and the slit-screen distance (D),the wavelength λ of the light used can be calculated. The formula is valid only if the fringe seperation, (w) is much less than the distance (D) from the slits to the screen. This condition is to ensure that the triangles S1S2Q and MOP are very nearly similar in shape
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