Lesson summary
8.4.1 The Diffraction Grating — AS PHYSICS 9702 notes: Use the diffraction grating equation d sin θ = nλ and describe the experiment to find a wavelength.Structure — a large number of very thin, equally spaced parallel slits cut into a glass plate.Action — it diffracts monochroma…
- What the symbols mean
- Lines per unit length
- Calculation
- Separation
- Highest order
- Vernier scale
Section 1 of 9The diffraction grating
The diffraction grating
Structure
- Structure a large number of very thin, equally spaced parallel slits cut into a glass plate.
Action
- Action it diffracts monochromatic light into bright and dark fringes.
Maxima
- Maxima regions of constructive interference are regions of maximum intensity.
Section 2 of 9The grating equation
Equation
- Equation d sin θ = nλ.What the symbols mean: d = grating spacing (m) · θ = angle of the nth-order maximum · n = order number (0, 1, 2 …) · λ = wavelength (m)
- d is the spacing between adjacent slits in m.
- θ is the angle from the centre to the nth order maximum.
- n is the order of the maximum, n = 0, 1, 2, 3 …
- λ is the wavelength in m.
Angle
- θ is measured from the centre, not between two orders.
Section 3 of 9Slit spacing
Lines per unit length
- Lines per unit length gratings are described by N, the number of lines per mm or per m.
Calculation
- Calculation d = 1/N.
Units
- Units if N is in lines per mm then d is in mm, and if N is in lines per m then d is in m.
Section 4 of 9Angular separation and highest order
Angles
- Angles rearrange to sin θ = nλ/d and take the inverse sine.
Spread
- Spread higher orders appear at greater angles.
Separation
- Separation the angular separation between two orders is θ2 − θ1.
Highest order
- Highest order set θ = 90°, so sin θ = 1 and n = d/λ.
- If n is a decimal, round it down to the highest visible order, for example 2.7 gives n = 2.
Section 5 of 9Determining the wavelength of light
1
Shine monochromatic light through the grating onto a screen at a measured distance D.
2
Measure the distance h from the central maximum to the nth order maximum.
3
Obtain the angle from tan θ = h/D, so θ = tan−1(h/D).
4
Substitute θ, n and d into λ = d sin θ / n.
5
Repeat for other orders and average.
Section 6 of 9Improving the experiment
Repeats
- Repeats take multiple measurements of h, between 3 and 8, and find the average.
Vernier scale
- Vernier scale use it to record h to reduce percentage uncertainty.
Across fringes
- Across fringes measure across all fringes and divide by the number of fringes.
Distance
- Distance increase the grating-to-screen distance D to increase the fringe separation.
Darkened room
- Darkened room it makes the fringes clearer.
More lines per mm
- More lines per mm use a grating with more lines per mm so h is larger and the percentage uncertainty is lower.
Section 7 of 9More from the specification
More from the specification
Structure and Diffraction Grating Equation
- A transmission diffraction grating consists of thousands of closely spaced parallel slits separated by slit spacing d (in metres);
- constructive interference produces sharp diffraction maxima according to d sin(θ) = n λ.
Calculating Grating Spacing (d)
- If a grating consists of N lines per millimetre, the slit spacing d is determined in SI terms by d = (1 × 10-3 m) / N.
Determining Highest-Order Maxima Visible
- The highest-order visible diffraction fringe (nmax) is determined by setting the maximum diffraction angle taken as θ = 90° (sin(θ) = 1),
- giving nmax = integer part of (d / λ).
Diffraction Pattern Characteristics and Wavelength Resolution — Compared to double-slit interference, a diffraction grating produces narrow, intensely bright principal fringes on an observation screen,
- allowing the constituent wavelengths of multi-frequency light sources to be resolved with high precision.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Diffraction grating | Plate with many equally spaced parallel slits that diffracts light into sharp maxima. |
| Slit spacing | Distance d between adjacent slits, d = 1/N. |
| Order of maximum | Integer n in d sin θ = nλ. |
| Grating equation | d sin θ = nλ. |
| Highest order | Largest whole number n with nλ ≤ d. |
Section 9 of 9Exam technique
1
Using the angle between two orders as θ — θ is from the centre line.
2
Forgetting to convert lines per mm to a spacing in m.
3
Giving the highest order as a decimal — round it down.
4
Confusing d with the slit width — d is the spacing between adjacent slits.