Diffraction Gratings (HL) (HL IB Physics)

• A diffraction grating is a piece of optical equipment that also creates a diffraction pattern when light is passed through it
• Diffraction gratings diffract::
  • Monochromatic light into bright and dark fringes
  • White light into its different wavelength components

A laser beam is diffracted through a diffraction grating

• A diffraction grating consists of a large number of very thin, equally spaced parallel slits carved into a glass plate

A diffraction grating consists of many parallel equally spaced slits cut into the glass plate

When you look closely at a diffraction grating you can see the curved shape of the slits

The Diffraction Grating Equation

• Diffraction gratings are useful because they create a sharper pattern than a double slit

  • This means their bright fringes are narrower and brighter while their dark regions are wider and darker

A diffraction grating is used to produce narrow bright fringes when laser light is diffracted through it

• Just like for single and double-slit diffraction the regions where constructive interference occurs are also the regions of maximum intensity
• Their location can be calculated using the diffraction grating equation

• Where:
  • n is the order of the maxima, the number of the maxima away from the central (n = 0)
  • d is the distance between the slits on the grating (m)
  • θ is the angle of diffraction of the light of order n from the normal as it leaves the diffraction grating (°)
  • λ is the wavelength of the light from the source (m)

Number of Slits

• Increasing the number of slits increases the number and intensity of the maxima in the intensity pattern
  • This is because more slits means more diffraction and more constructive interference

The combined diffraction and interference patterns, called the intensity pattern, for light interfering through different numbers of slits. The maximum intensity increases as the number of slits increases, so the intensity in each graph is relative to that number of slits only

Slit Spacing

• Diffraction gratings come in different sizes
  • The sizes are determined by the number of lines per millimetre (lines / mm) or lines per m
  • This is represented by the symbol N
• d can be calculated from N using the equation
  • If N is given in terms of lines per mm then d will be in mm
  • If N is given in terms of lines per m then d will be in m

Diffraction gratings come in different sizes according to the number of lines per mm

Angular Separation

• The angular separation of each maxima is calculated by rearranging the grating equation to make θ the subject
• The angle θ is taken from the centre meaning the higher orders of n are at greater angles of diffraction

Angular separation increases as the order of maxima increases

• The angular separation between two angles is found by subtracting the smaller angle from the larger one
• The angular separation between the first and second maxima at n₁ and n₂ is θ₂ – θ₁

Orders of Maxima

• The maximum angle of diffraction with which maxima can be seen is when the beam is at right angles to the diffraction grating
  • This means θ = 90^o and sin θ = 1

• The highest order of maxima visible is therefore calculated by the equation:

• Since n is an integer number of maxima, if the value obtained is a decimal it must be rounded down to determine the highest-order visible
  • E.g If n is calculated as 2.7 then n = 2 is the highest-order visible

The Diffraction of White Light

• A source of white light diffracted through a diffraction grating will produce the following diffraction pattern:
  • It is different to that produced by a double or single slit
  • The first-order spectrum n = 1 is used for analysis
• The central maximum is a very thin bright strip because each wavelength interferes here constructively
  • It is surrounded by wide dark destructive interference fringes
• All other maxima are composed of a spectrum
• Separate diffraction patterns can be observed for each wavelength of light
  • The shortest wavelength (violet / blue) would appear nearest to the central maximum because it is diffracted the least
  • The longest wavelength (red) would appear furthest from the central maximum because it is diffracted the most
• The colours look blurry and further away from the central maximum, the fringe spacing gets so small that the spectra eventually merge without any space between them
  • As the maxima move further away from the central maximum, the wavelengths of blue observed decrease and the wavelengths of red observed increase

The diffraction pattern of white light diffracted through a diffraction grating