Replace two slits with thousands and the bright fringes become narrow, brilliant lines at precise angles. That sharpness makes a diffraction grating the instrument of choice for measuring wavelength.
A diffraction grating has many equally spaced slits. Maxima occur at angles given by d sinθ = nλ, where d is the slit spacing, θ the angle from the straight-through direction and n the order (0, 1, 2, ...). Because so many slits interfere, the maxima are much sharper and brighter than double-slit fringes, allowing a precise measurement of wavelength.
Set the wavelength and the grating spacing and watch the orders appear at the angles given by d sinθ = nλ, with the highest visible order limited by sinθ ≤ 1.
One relation handles every order.
| Relation | Use |
|---|---|
| d sinθ = nλ | positions of the maxima |
| d = 1 / N | slit spacing from N lines per metre |
| n ≤ d / λ | highest order visible (sinθ ≤ 1) |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The diffraction grating equation is:
In the grating equation, the symbol n represents the:
Compared with a double slit, a diffraction grating produces maxima that are:
A grating ruled with 300 lines per millimetre has a slit spacing d of:
The grating equation gives both the angles and a limit on how many orders exist.
Use sinθ, not tanθ or cosθ, in d sinθ = nλ. The spacing d is the distance between adjacent slits, found from d = 1/N when N is the number of lines per metre, so more lines per millimetre means a smaller d and wider-spread orders. There is a maximum order, set by sinθ ≤ 1, so n cannot exceed d/λ.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
Light of wavelength 6.0 × 10⁻⁷ m falls on a grating with slit spacing d = 2.0 × 10⁻⁶ m. The angle of the first-order maximum is:
For light of wavelength 6.0 × 10⁻⁷ m on a grating with d = 2.0 × 10⁻⁶ m, the highest order that can be observed is:
A diffraction grating is preferred over a double slit for measuring a wavelength because its maxima are:
This skill is now lit gold on your star map. You have finished the lessons of Topic 8; the Paper 1 set awaits.