Diffraction of Light Experiments

Diffraction of Light

• A laser beam is passed through a double slit to observe the intensity patterns created by diffraction and interference.
• The experimental set-up involves a one-meter long optical rail with a laser source, diffracting element, and a photodetector.
• The locations of the components can be controlled with a precision of mm and micron.

Theoretical Background

• Light travels in a straight line, but bending occurs when it's partially obstructed by an opaque screen with an aperture or a knife edge. This phenomenon is known as diffraction.
• Diffraction can be explained by Huygen's principle: each point on the wavefront acts as a source of spherical waves. These secondary waves interfere on the screen, creating a diffraction pattern.
• The aperture width (d) should be larger than the wavelength (λ) of the monochromatic light for diffraction to occur.
• The distance between the diffracting obstacle and the screen (D) plays a role in the type of diffraction pattern observed:
  • Fraunhofer or far field diffraction pattern: D is large compared to the slit width (d).
  • Fresnel or near field diffraction pattern: D is smaller than the slit width (d).
  • This experiment focuses on Fraunhofer patterns.

Diffraction by a Single Slit

• The intensity pattern on the screen generated by the interference of waves from a single slit follows the equation: I(θ) = I₀ (sinβ²/β²), where β = (πd / λ)sinθ.
• Minima occur when βm = ± mπ, where m = 1, 2... This corresponds to angles θ = ± sin⁻¹(mλ / d).
• The central maxima occurs at θ = 0.
• Other maxima occur when βm = ± (2m + 1)π / 2, where m = 1, 2... This corresponds to angles θ = ±sin⁻¹[(2m + 1)λ / 2d].
• The slit width (d) can be calculated using the positions of the maxima: d = mλ / sin θm.
• The angle θm is experimentally determined by recording ym (the y-position of the minima) and using the relationship tan θm = ym / D.

Diffraction by a Double Slit

• Light from a laser source hits two narrow slits, acting as in-phase point sources.
• Waves from the slits travel different distances to reach the screen, creating a path difference (δ = d sin  = λ).
• The path difference causes a phase shift between the waves, creating position-dependent interference patterns on the screen.
• The intensity pattern for double-slit diffraction is described as: 𝐼(𝜃) = 𝐼₀ cos²(πdsinθ / λ)(sinβ²/β²), where β = (πa / λ)sinθ, a being the width of each slit, and d being their separation.
• The phase shift determines constructive interference (even multiples of π) and destructive interference (odd multiples of π).
• Maxima occur when d sin  = mλ, and minima occur when d sin  = (m + (1/2))λ.

Interesting Facts about Diffraction

• Babinet's principle: the diffraction pattern of a single slit of width d is the same as that of a thin wire of width d. This is because the net electric field at the screen is zero when the slit and wire are superimposed.
• Fresnel diffraction pattern for a circular aperture shows a central minima in the near field compared to a bright central Airy disc in the far field.
• Diffraction limits the resolution of optical microscopes to 0.25 microns.

Applications of Diffraction

• Determining track width on a CD by analyzing reflected laser light.
• Measuring the wavelength (λ) of laser light using double-slit width.
• Measuring the thickness of fine fibers, such as human hair.
• Measuring the size of red blood cells.

Experimental Procedure for Double Slit / Single Slit

• Set up the laser, slit, and detector on the rail to ensure a clear pathway.
• Adjust the distance between the slit and detector (D) to obtain a sharp pattern.
• Record the maximum intensity detected when the laser beam is directly incident on the detector.
• Scan the diffraction pattern by rotating the circular scale.
• Record current (microA) versus detector position (millimeter) data.

Data Analysis for Double Slit

• Plot current versus position. Identify five maxima (one central and two on each side).
• Calculate the slit separation (d) using the distance between the central maxima and the side maxima.
• Calculate the average d and its error (standard deviation).

Safety Instructions

• Avoid looking directly into the laser beam as it can cause retinal damage.
• Exercise caution when handling diffraction slits and other components.
• Do not touch the inner surface of the diffraction cell.
• Avoid backlash error while moving the micrometer scale on the detector.