For IB Physics HL, the diffraction grating equation is . It gives the angles at which constructive interference produces bright maxima when monochromatic light passes through a grating at normal incidence.
A diffraction grating contains many equally spaced slits. Waves from adjacent slits travel different distances to a point on the screen; this path difference is .
A bright maximum forms when the path difference equals a whole number of wavelengths:
| Symbol | Meaning |
|---|---|
| Order of the maximum: | |
| Wavelength of the incident light | |
| Distance between adjacent grating lines | |
| Angle between the diffracted maximum and the normal to the grating |
The central maximum is the zeroth order, , so . Positive and negative orders appear symmetrically on opposite sides of the normal. Increasing wavelength or order increases the diffraction angle, provided that the order is physically possible.
Since a grating contains many slits, its principal maxima are narrower and more intense than those from a double slit, allowing nearby wavelengths to be distinguished.
If a grating has lines per metre, its spacing is
For example, a grating has 600 lines per mm and is illuminated by light of wavelength 500 nm. First convert the line density:
Therefore,
For the second-order maximum, :
so .
The largest possible order must satisfy , because .
This is Additional Higher Level (AHL) content in C.3 Wave phenomena. In a calculation, show the conversion from lines per mm to lines per metre, calculate , and then substitute into the equation. A common misconception is that is the slit width; it is the centre-to-centre separation of adjacent lines. Also measure from the normal, not from the grating surface.
If asked to determine the highest order, calculate and take the greatest integer no larger than the result; do not round up. Check that your calculator is in degree mode before evaluating inverse sine.
