Diffraction Of Light At A Single Slit

Interactive Tutorials

Diffraction of Light

  • Diffraction by a Single Slit Example 35-1: Single-slit diffraction maximum. Light of wavelength 750 nm passes through a slit 1.0 x 10-3 mm wide. How wide is the central maximum (a) in degrees, and (b) in centimeters, on a screen 20 cm away? Sin D sin Dsin 020 486 0227 486 1010 7510 First minimum: 6 7 1 1 u q ¸¸ q ¹.
  • Diffraction pattern from a single slit A laser illuminates a single slit and the resultant patten is projected on a distant screen. The sketch shows the view from above a single slit. Let's assume that the slit is constant width and very tall compared with that width, so that we can consider the system as two-dimensional.

Several of the classical and most fundamental experiments that help explain diffraction of light were first conducted between the late seventeenth and early nineteenth centuries by Italian scientist Francesco Grimaldi, French scientist Augustin Fresnel, English physicist Thomas Young, and several other investigators. These experiments involve propagation of light waves though a very small slit (aperture), and demonstrate that when light passes through the slit, the physical size of the slit determines how the slit interacts with the light. This interactive tutorial explores the diffraction of a monochromatic light beam through a slit of variable aperture.

The tutorial initializes with a beam of monochromatic red (having a wavelength of 662 nanometers) light incident on a slit aperture (Aperture) that is 1260 nanometers wide. Because the slit diameter is less than the beam width of the incident light, wavefronts are diffracted as they pass through the slit. The diffraction pattern of the scattered waves is visible on a dark film screen behind the aperture, and is plotted as an intensity distribution beneath the screen. The diffraction minima are also calculated and constantly updated as the tutorial parameters are changed. To operate the tutorial, use the Wavelength slider to adjust the wavelength range of incident light between 400 and 700 nanometers. The Aperture slider can be employed to change the slit aperture size from 440 to 1260 nanometers. Note that the sliders are integrated so that reducing the wavelength will also automatically reduce the aperture size to ensure that diffraction still occurs.

One can observe single slit diffraction when the passing of light takes place via a single slit whose width (w) is on the order of the light’s wavelength. Furthermore, the diffraction pattern on the screen takes place at a distance L w away from the slit. Moreover, intensity happens to be a function of angle.

If the wavelength of light is much smaller than the aperture or slit width, a light wave simply travels onward in a straight line after passing through, as it would if no aperture were present (as presented in Figure 1). However, when the wavelength exceeds the size of the slit, diffraction of the light occurs, causing the formation of a diffraction pattern consisting of a bright central portion (the primary maximum), bounded on either side by a series of secondary maxima separated by dark regions (minima; see Figure 2). The maxima and minima are created by interference of diffracted light waves. Each successive bright band becomes less intense proceeding outward, away from the central maximum. The width of the central bright portion, and the spacing of the accompanying sidebands, depends on the size of the aperture (slit) and the wavelength of the light. This relationship can be described mathematically and demonstrates that the width of the central maximum decreases with decreasing wavelength and increasing aperture width, but can never be reduced to the size of a point light source.

Avocode logo. The intensity distribution of light diffracted by the single slit experiment is presented in Figures 1 and 2. It is assumed that both light beams in Figure 1 are composed of coherent, monochromatic waves emitted from a point source that is far enough away from the slit for the wavefronts to be considered linear and parallel. Light passing through aperture d on the right-hand side of the figure has a wavelength larger than the aperture and is diffracted, with the primary incident light beam landing at point P and the first secondary maximum occurring at point Q. As shown on the left-hand side of Figure 1, when the wavelength is much smaller than the aperture width (d), the wave simply travels through in a straight line, just as it would if it were a particle or no aperture were present. However, when the wavelength exceeds the size of the aperture, it is diffracted to produce a central peak containing most of the light intensity accompanied by secondary higher-order maxima and intensity minima governed according to the equation:

sin(q) = ml/d

where q is the angle between the central incident propagation direction and the first minimum of the diffraction pattern, and m indicates the sequential number of the higher-order maxima. The light intensity is maximum at q = zero degrees, and decreases to a minimum (where the intensity is zero) at angles dictated by the equation above. The experiment produces a bright central maximum, which is bounded on both sides by secondary maxima, with the intensity of each succeeding secondary maximum decreasing as the distance from the center increases. Figure 2 illustrates this point with a plot of beam intensity versus diffraction radius. Note that the minima occurring between secondary maxima are positioned in multiples of p.

Both the experiment described above, and the classical demonstration of diffraction using light passing between the fingers, utilize a narrow slit as an aperture to produce a diffraction pattern. All optical instruments, including microscopes, utilize circular lenses and apertures, as does the human eye itself. Circular apertures produce similar diffraction phenomena, although with circular symmetry (instead of linear geometry, as in the case of slits). Therefore the diffraction pattern of a point source of light, if highly magnified, is seen to consist of a central bright disk surrounded by a concentric series of diffraction rings (the secondary maxima and minima). When a lens, such as a microscope objective lens, is properly focused, the light intensity at the minima between the bright rings in the pattern is zero. No matter how perfect the lens is, the secondary diffraction maxima cannot be eliminated nor can the central spot be reduced to a single point of light (unless the lens could be made with an infinite diameter).

Contributing Authors

Matthew J. Parry-Hill, Thomas J. Fellers, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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Interference and Diffraction

Double-Slit Interference

Two overlapping transparencies on the overhead projector are used to simulate the interference from two coherent sources.

Equipment
  • Transparencies for double-slit simulation
  • Overhead projector
Description

The double-slit interference pattern is briefly described. Two transparencies consisting of concentric circles are overlapped on the overhead projector to show the pattern of constructive interference. The pattern is observed to spread out as the two simulated slits are brought closer together. As the slits are moved apart, the pattern bunches up.

Interference Simulation Using Polarized Light

A rotating polarizing transparency on the overhead projector is used to simulate the double-slit interference pattern.

Equipment
  • Polarizing sheets for a double-slit simulator
  • Polarizing sheet
  • Support frame
  • Overhead projector
DescriptionSingle

Two polarizing sheets are prepared with adjacent concentric rings, each with slightly different polarization orientation. When one of these sheets is placed on an overhead projector with a standard polarizing sheet overlayed, the rings appear as concentric circles. As the standard polarizing sheet is rotated, wave motion is simulated. When both polarizing sheets with concentric rings are overlapped and placed on the overhead projector, the double-slit interference pattern is observed. As the standard polarizer is placed between the two sheets and rotated, wave motion from two separate coherent sources is simulated . In this manner, the double-slit interference pattern is demonstrated. The same demonstration is included in the section tiltled Polarization.

Thin Film Interference: Oil Surfaces

Oil is dropped onto a water surface and the interference pattern is observed.

Equipment
  • Abalone shell
  • Oxidized copper plate
  • Flat glass tray filled with water
  • Puddle of water
  • Oil can

Single Slit Diffraction Simulator

Description

Thin film interference is briefly described and demonstrated using an abalone shell and a copper plate with an oxidized surface. In an experimental demonstration, oil is dropped onto a tray of warm water and rings of color are observed as the oil spreads. A similar experiment is done on a puddle of water outside on the sidewalk. A spreading pattern is observed as the skylight reflects from the thin film of oil on the water. (Some colors may not show well on certain monitors and projectors.)

Thin Film Interference: Soap Bubbles

The thin film interference of soap bubbles is demonstrated.

Equipment

Single Slit Diffraction Explained

  • Bottle of liquid soap
  • Ring for making bubbles
Description

Different colors are observed to be reflected from soap bubbles as the bubbles are created. As the bubbles fall, the colors change due to a changing thickness of the soap film. (Some colors may not show as well on certain monitors or projectors.)

Interference: Hologram

A hologram is demonstrated.

Equipment
  • Hologram with lighting system
  • Rotating platform
Description

A hologram with its lighting system is briefly described and shown. The lighting system is a light bulb with a reflecting mirror. The system is mounted on a rotating platform and viewed by the recording camera. As the platform is slowly rotated, a three dimensional moving image is observed.

Diffraction Of Light At A Single Slit

Single-Slit Diffraction: Laser

A single-slit together with a laser is used to demonstrate a diffraction pattern.

DiffractionEquipment
  • Laser
  • Variable width horizontal slit
  • Variable width vertical slit
  • Jack stand
  • Screen
Description

Single-slit diffraction is briefly described. As the laser beam is directed through a horizontally oriented slit, a diffraction pattern with vertical spread is observed on a distant screen. The pattern is shown to spread more as the width of the slit is narrowed and the pattern bunches up as the width of the slit is widened. The demonstration is then repeated with a vertically oriented slit, which produces a pattern with horizontal spread.

Single-Slit Diffraction: Line Filament

A single-slit together with a line filament light source is used to demonstrate a diffraction pattern.

Equipment

Diffraction Of Light At A Single Slit Experiment

  • Light bulb with vertical filament
  • Power supply
  • Connecting wires
  • Variable width vertical slit
  • Jack stand
Description

White light from a light bulb with a long vertical filament passes through a vertical slit to a recording camera. A diffraction pattern with a horizontal spread is observed for each color as the various wavelengths of light pass through the slit. Longer wavelength light is observed to spread more than the light of shorter wavelength. As the slit is narrowed, the spreading of the pattern is observed to increase. As the slit is widened, the pattern is observed to bunch up.

Diffraction: Various Objects

Diffraction Of Light At A Single Slit Process

Various objects together with a laser are used to form diffraction patterns.

Equipment
  • Laser
  • Wire mesh screen
  • Piece of cloth
  • Bird feather
  • Diffraction grating
  • CD
  • Stands and clamps
  • Screen
Description

Diffraction Of Light At A Single Slit Rate

In a series of separate experiments, a laser beam passes through various objects and a diffraction pattern for each object is formed on a screen. It is demonstrated that the pattern changes with orientation of the object but remains unchanged when the object is moved vertically or horizontally. A similar demonstration is done by reflecting laser light from a CD.