Diffraction Grating Calculator
Calculate diffraction angles using the grating equation d sin θ = mλ. Determine the angular positions of interference maxima for spectroscopy and optical analysis applications.
This free online diffraction grating calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
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Results
Diffraction Angle
19.23°
How to Use This Calculator
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Fill in all required input fields for the Diffraction Grating Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
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Explore parameter sensitivity
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When to Use This Calculator
- •Use the Diffraction Grating Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
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About Diffraction Grating Calculator
The Diffraction Grating Calculator determines the angles at which constructive interference produces bright maxima when light passes through a periodic array of slits. Diffraction gratings are the workhorses of spectroscopy — they separate white light into its component wavelengths far more effectively than prisms. With thousands of slits per millimeter, gratings produce sharp, well-defined spectral lines. This technology enables astronomers to determine stellar compositions, chemists to identify substances, and engineers to characterize laser sources with extraordinary precision.
The Math Behind It
Formula Reference
Grating Equation
d sin θ = mλ
Variables: d = slit spacing, θ = diffraction angle, m = order, λ = wavelength
Worked Examples
Example 1: Green Light, First Order
d = 1.67 μm (600 lines/mm), λ = 550 nm, m = 1
First-order maximum at 19.22°.
Example 2: Hydrogen Alpha Line
d = 1.67 μm, λ = 656.3 nm, m = 2
Second-order Hα line appears at 51.82°.
Common Mistakes & Tips
- !Confusing lines per mm with slit spacing — d = 1/(lines per mm) in mm, then convert to μm.
- !Forgetting that sin θ cannot exceed 1, limiting the maximum observable order.
- !Not converting wavelength from nm to μm to match slit spacing units.
- !Ignoring that higher orders may overlap with different wavelengths from adjacent orders.
Related Concepts
Frequently Asked Questions
Why are gratings better than prisms for spectroscopy?
Gratings provide higher resolving power (proportional to number of slits), work across all wavelengths uniformly, and produce linear dispersion. Prisms have higher efficiency for small wavelength ranges but non-linear dispersion.
Why do CDs show rainbow colors?
The spiral track on a CD acts as a reflection diffraction grating with spacing ~1.6 μm. White light diffracts at different angles for each wavelength, producing the characteristic rainbow pattern.
What limits the number of orders visible?
The condition sin θ ≤ 1 limits the maximum order to m_max = d/λ. For d = 1.67 μm and λ = 500 nm, m_max = 3.34, so only orders 0, ±1, ±2, ±3 are visible.
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