How this calculation works
A diffraction grating directs monochromatic light into a set of permitted angular orders. The grating period and wavelength determine which orders can propagate; the screen distance then maps an angle to a position. This page calculates a chosen order and lists the first nonnegative orders that satisfy the propagation condition. Corresponding negative orders are symmetric for the stated normal-incidence geometry.
d = 1/line density; sinθm = mλ/d; xm = L tanθmA worked example
At 600 lines/mm, the period is 0.00166667 mm. With 500 nm light, the first-order sine is 0.3 and its angle is 17.4576 degrees. A screen 1000 mm away intercepts that ray about 314.485 mm from the centre. The largest nonnegative propagating order for these values is three. Order four would require sine 1.2 and is rejected rather than producing an invalid inverse-trigonometric result.
Good to know
The model assumes normal incidence and equal grating period. A tilted grating requires an incident-angle term and cannot be represented by merely changing screen distance. Blaze efficiency, finite aperture, line defects, slit envelopes and spectral resolving power are excluded. An allowed order may be very weak in a real grating even though its geometric angle is well defined.
Reference: OpenStax — diffraction gratings (opens in a new tab) ↗
What this calculation answers
A diffraction grating directs monochromatic light into a set of permitted angular orders. The grating period and wavelength determine which orders can propagate; the screen distance then maps an angle to a position.
This page calculates a chosen order and lists the first nonnegative orders that satisfy the propagation condition. Corresponding negative orders are symmetric for the stated normal-incidence geometry.
The Double slit fringes with finite slit envelope calculator combines interference fringes with a finite-slit envelope. A permitted grating order is likewise a geometric direction, not a guarantee of high efficiency.
Use the right input conventions
Line density is entered in lines per millimetre, not the spacing between lines. Wavelength uses nanometres and is converted to millimetres before comparison with the grating period. The selected order must be a whole nonnegative integer.
A selected order must have mλ/d strictly below one to meet a parallel screen at a finite distance. An exactly grazing order can be listed as a mathematical boundary but has no finite screen intercept.
Interpret the result
Increasing line density reduces grating spacing and increases the angle of a fixed order. It can also remove higher orders entirely when the required sine exceeds one. This is a propagation limit, different from an efficiency or brightness prediction.
The order table is capped at fifty nonnegative orders for a bounded result size. The separately reported largest mathematical order can be larger; the cap does not mean those other orders are forbidden.
Work through the example
At 600 lines/mm, the period is 0.00166667 mm. With 500 nm light, the first-order sine is 0.3 and its angle is 17.4576 degrees. A screen 1000 mm away intercepts that ray about 314.485 mm from the centre.
The largest nonnegative propagating order for these values is three. Order four would require sine 1.2 and is rejected rather than producing an invalid inverse-trigonometric result.
Where the model stops
The model assumes normal incidence and equal grating period. A tilted grating requires an incident-angle term and cannot be represented by merely changing screen distance.
Blaze efficiency, finite aperture, line defects, slit envelopes and spectral resolving power are excluded. An allowed order may be very weak in a real grating even though its geometric angle is well defined.
A few questions, answered
Why can the next order disappear?
Its required mλ/d exceeds one, so no real propagation angle satisfies the grating equation.
What changes in the comparison?
Reduce line density and inspect smaller order angles and additional permitted orders.