Free · Physics models
Oblique-Incidence Diffraction Grating Orders
Compute principal diffraction angles for five positive grating orders, with wavelength, line-density and angle units.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A 500 nm wavelength and 100 lines/mm grating at normal incidence have first-order angle about 2.866° and fifth-order angle about 14.478°.
sin θm + sin α = m λ N; θm = asin(m λ N − sin α).
Worked example
Enter these known values and leave the other values blank.
- Wavelength
- 500 nm
- Grating line density
- 100 lines / mm
- Angle of incidence
- 0 deg
- First order
- 2.866 deg
- Second order
- 5.739 deg
- Third order
- 8.627 deg
- Fourth order
- 11.537 deg
- Fifth order
- 14.478 deg
Assumptions and limitations
- Angles use the stated sign convention sin θ + sin α = mλN. The inverse sine selects the principal transmitted angle between −90° and +90°.
- Grating density is lines per selected length, not slit width. Wavelength and density are positive; incidence is strictly between −90° and +90°.
- An order exists only when its inverse-sine argument lies between −1 and +1. Higher orders may remain unavailable while lower orders are physical.
- This ideal scalar grating equation does not predict intensity, blaze efficiency, polarization, resolution or finite-aperture broadening.
- Enter known quantities and leave the unknown blank. Editable quantities support inverse solutions and locks; inconsistent locked quantities are reported. Unit selectors convert the quantity independently of its display.
Common questions
Why can a higher diffraction order be missing?
Its inverse-sine argument can exceed one in magnitude. That order has no propagating angle even when lower orders exist.
Is grating density the slit spacing?
Density counts lines per length. Spacing is its reciprocal after using a consistent length unit.
How do I use the inverse calculation?
Clear the quantity you want to find and enter the remaining known values in their selected units. The model can only solve branches with enough independent information.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.