Reflection Grating Calculator Form
Plotly Graph
The graph shows diffraction angle versus wavelength for the current order, line density, and incidence angle.
Example Data Table
This example uses 600 lines/mm, 500 nm wavelength, and 20° incidence angle to show how diffraction angle changes with order.
| Line Density (lines/mm) | Order m | Wavelength (nm) | Incidence Angle α (deg) | Diffraction Angle β (deg) |
|---|---|---|---|---|
| 600 | 1 | 500.00 | 20.00 | -2.408286 |
| 600 | 2 | 500.00 | 20.00 | 14.950228 |
| 600 | 3 | 500.00 | 20.00 | 33.916206 |
| 600 | 4 | 500.00 | 20.00 | 59.090512 |
Formula Used
The reflection grating equation used in this calculator is:
Here, m is the diffraction order, λ is wavelength, d is groove spacing, α is the incidence angle, and β is the diffraction angle.
Groove spacing and line density are linked by:
Angular dispersion is calculated with:
Resolving power is estimated with:
In this expression, N is the number of illuminated grooves, found from illuminated width × line density.
How to Use This Calculator
- Select what you want to solve.
- Enter the grating line density in lines per millimeter.
- Enter the diffraction order as a positive integer.
- Enter the incidence angle and any other required value.
- Provide illuminated width to estimate resolving power.
- Click Calculate Now to display the result above the form.
- Review the graph, verification table, and derived optical metrics.
- Use the CSV or PDF buttons to export the current result.
FAQs
1. What is a reflection grating?
A reflection grating is an optical surface with many closely spaced grooves. It reflects light and separates wavelengths by diffraction, producing different output angles for different colors and orders.
2. What does diffraction order mean?
Diffraction order, written as m, identifies which constructive interference path is being observed. First order is usually brightest and easiest to use, while higher orders can improve dispersion but may overlap.
3. Why can some inputs return no real angle?
The grating equation may produce a sine value outside the range from -1 to 1. When that happens, the chosen wavelength, order, and geometry cannot form a real diffracted beam.
4. What is groove spacing?
Groove spacing is the distance between adjacent grating grooves. It is the inverse of groove density. Smaller spacing means more grooves per millimeter and usually stronger angular separation.
5. What is Littrow angle?
Littrow angle is the special case where the incidence and diffraction angles are equal. In that setup, the grating equation becomes mλ = 2d sinθ, which is common in spectrometer design.
6. What does resolving power tell me?
Resolving power estimates how well a grating can separate nearby wavelengths. A larger illuminated groove count and a higher diffraction order generally increase the ability to distinguish close spectral lines.
7. What is angular dispersion?
Angular dispersion measures how quickly diffraction angle changes with wavelength. A larger value means small wavelength changes produce larger angle changes, which helps spectral separation and instrument sensitivity.
8. Can I use this calculator for lab and design work?
Yes. It is useful for homework, lab setup checks, and first-pass design work. Final instrument design should still consider blaze angle, polarization, efficiency curves, coatings, and mechanical tolerances.