Diffraction-grating and double-slit maxima
For equally spaced coherent apertures, constructive interference occurs where the path difference between neighboring rays is an integer number of wavelengths. The same angular condition describes double-slit bright fringes and principal diffraction-grating maxima.
The equation does not describe a single-slit central-maximum width or complete intensity pattern. It assumes monochromatic coherent light and far-field geometry.
How to calculate an interference angle
- Enter wavelength: Provide a positive wavelength in nanometers.
- Enter spacing: Provide center-to-center slit or grating spacing in meters.
- Enter order: Use zero or a positive whole number.
- Calculate and check: Verify that the order exists and that far-field, coherent-light assumptions apply.
Formula and variables
A real solution exists only when |mλ/d| ≤ 1. The calculator accepts non-negative orders and reports the corresponding positive angle.
d sin θ = mλ; θ = sin⁻¹(mλ/d)- d — Slit or grating spacing
- Center-to-center spacing of adjacent apertures (m)
- θ — Interference angle
- Angle from the central axis (degrees)
- m — Order
- Non-negative integer identifying the maximum
- λ — Wavelength
- Light wavelength (nm)
First-order grating maximum
Light of wavelength 500 nm reaches a grating with 2.0 µm spacing.
- Wavelength
- 500 nm
- Spacing
- 2.0 × 10⁻⁶ m
- Order
- 1
- sin θ = (1 × 500 × 10⁻⁹)/(2.0 × 10⁻⁶)
- θ = sin⁻¹(0.25)
Result: The first-order maximum is approximately 14.48°.
An equivalent maximum appears at −14.48° in a symmetric ideal arrangement.
Understanding your results
Check whether the order can exist
Higher order increases angle until mλ exceeds d and no propagating maximum exists.
- Order zero is the central maximum at 0°.
- Positive and negative orders appear symmetrically in the ideal model.
- More slits sharpen principal maxima but do not change this angular condition.
Assumptions
- Light is monochromatic and coherent across the apertures.
- Spacing is uniform and the observation is in the far field.
- The medium wavelength is the entered wavelength.
Limitations
- Does not calculate intensity, fringe width, envelope modulation, resolving power, or screen position.
- Does not model single-slit minima as a distinct physical case.
- Does not include refractive-index conversion, finite coherence, imperfections, or near-field diffraction.
Common mistakes
- Entering grating line density instead of converting it to spacing.
- Mixing nanometers and meters.
- Using a non-integer order.
- Applying the result to single-slit bright maxima.
Practical use cases
Diffraction-grating analysis
Estimate spectral-line angles for known grating spacing.
Double-slit education
Check ideal bright-fringe angles before converting them to screen positions.
Frequently asked questions
Why can some orders not exist?
The sine magnitude cannot exceed one, so orders with |mλ| greater than d have no real far-field angle.
Does this calculate single-slit diffraction?
Not completely. The same-looking equation describes single-slit minima, not its bright maxima or full intensity distribution.
How do I convert lines per millimeter to spacing?
Convert line density to lines per meter and take its reciprocal to obtain d in meters.
Sources and review
- Diffraction Gratings — OpenStax, University Physics Volume 3. Accessed 2026-07-13.
Reviewed 2026-07-13.