Transmission grating and holder
Provide parallel equally spaced grooves with density 300 lines per millimetre; hold the grating perpendicular to the incident beam.
Physics / Diffraction grating wavelength
FREE TO EXPLOREEXPERIMENT 11 · PHYSICS LABORATORY
Wavelength of light using a diffraction grating
Determine the wavelength of monochromatic light from the angles of successive diffraction orders produced by a transmission grating at normal incidence. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
HALF-SEPARATION ANGLE Θ—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
This deterministic model assumes a perfectly aligned transmission grating, monochromatic parallel illumination and exact groove spacing. It computes peak positions and rounds the reduced angle to 0.01°. It does not predict intensity, blaze efficiency, missing orders, slit profiles, spectral overlap, aperture clipping or telescope resolution. Availability of orders 1 to 5 in this lesson does not guarantee their practical visibility in every apparatus. The ordinary fit omits angle-dependent vertical weights and shared grating-calibration uncertainty. The generator uses wavelength 550 nm and density 300 lines/mm, giving d = 10⁻³/300 m. For orders 1 to 5, theta = arcsin(m lambda/d) is rounded to 0.01 degrees. The stored y value is sin(theta_deg × pi/180), x is the integer order and the estimated wavelength is fitted gradient times d. The fifth-order sine is 0.825, so it is geometrically permitted. The reference wavelength is a chosen teaching parameter rather than an identification of a particular atomic emission line. The displayed raw angle represents half a symmetric left/right separation; independent telescope readings are not generated.
Know your apparatus.
Monochromatic source and collimator
Send a narrow, approximately parallel beam of one wavelength toward the grating.
Spectrometer telescope and angular scale
Centre left and right images of the same spectral line and determine their angular separation.
Levelled rotating table
Keep the grating vertical and permit alignment of its normal with the incoming beam.
FOLLOW THE METHOD
A reason behind every step.
Determine the wavelength of monochromatic light from the angles of successive diffraction orders produced by a transmission grating at normal incidence. Suggested independent settings: 1, 2, 3, 4, 5 order.
Prepare and align
Focus the eyepiece crosshairs, focus the telescope for a distant image and adjust the collimator for a sharp narrow slit. Level the grating and set its normal along the incident beam.
Why this step matters
The simple grating equation used here assumes normal incidence and a collimated beam.
Record the spacing
Read the specified groove density and convert 300 lines/mm into d = 10⁻³/300 m. Identify the central undeviated image as order zero.
Why this step matters
Correct spacing and an unambiguous zero prevent unit and order errors.
Choose a diffraction order
Select a positive order from 1 to 5 in the virtual apparatus. In a physical spectrometer locate the same monochromatic line in the corresponding orders on both sides.
Why this step matters
Pairing different orders or spectral lines produces an invalid half-separation.
Measure and record the angle
Centre the left and right images and compute half their angular separation after accounting for any scale wrap. The simulator returns this reduced angle directly, rounded to 0.01°. Record it before changing order.
Why this step matters
A common angular zero offset cancels in a symmetric pair; the raw virtual angle is not the full left-to-right separation.
Collect the order series
Take readings for orders 1, 2, 3, 4 and 5. Calculate sin(theta) using the degree setting or convert each angle into radians first. Fit sin(theta) = s m + b.
Why this step matters
Using the sine transformation preserves the exact angular relation across the full range.
Calculate and assess wavelength
Multiply the slope by grating spacing, then convert metres to nanometres by multiplying by 10⁹. Check an individual row with lambda = d sin(theta)/m and discuss calibration, alignment and model omissions.
Why this step matters
The graph result and a manual row calculation provide independent arithmetic checks.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
d sin θ = kλ; sin θ = mk + b; λ = md
| # | Diffraction order k (order) | Half-separation angle θ (°) | Diffraction order k | sin θ | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING