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Diffraction Grating Resolving Power & Angles Calculator

Diffraction gratings are the core dispersive elements in spectrometers, monochromators, and laser tuning systems.

Number of grating ruling lines per millimeter (e.g. 300, 600, 1200, 1800).

Spectral diffraction order integer (typically 1, 2, or 3).

Spectral wavelength.

Width of grating illuminated by incoming collimated beam.

Calculated Result
30,000

Chromatic Resolving Power (R)

Diffraction Angle (θ)

17.46°

Min Resolvable Wavelength (Δλ)

0.0167 nm

Illuminated Rulings (N)

30,000

Calculation Breakdown

  1. Step 1: Diffraction Angle at Normal Incidencesin(θ) = m·λ / d = 1·(500 nm) / 1666.7 nm => θ = 17.46°
  2. Step 2: Rayleigh Resolving CriterionR = m · N = 1 · 30000 = 30,000
  3. Step 3: Minimum Spectral ResolutionΔλ = λ / R = 500 nm / 30,000 = 0.0167 nm

What Is the Diffraction Grating Resolving Power & Angles Calculator?

A diffraction grating is an optical component with a periodic surface pattern that splits and diffracts light into several beams traveling in different directions.

How Does the Diffraction Grating Resolving Power & Angles Calculator Work?

Computes grating period d = 1 / groove density.

Applies grating equation sin(θ) = m·λ / d to determine angular deflection.

Computes theoretical chromatic resolving power R = m · N.

Evaluates minimum resolvable wavelength difference Δλ = λ / R.

Diffraction Grating Resolving Power & Angles Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

d·sin(θ) = m·λ, R = λ / Δλ = m·N, N = (groove density) · W

Standard grating equation at normal incidence and Rayleigh chromatic resolving power criterion.

How to Use the Diffraction Grating Resolving Power & Angles Calculator

  1. Enter groove density and diffraction order.
  2. Provide wavelength and illuminated grating width.

Step-by-Step Example Calculation

Visible Spectrometer Monochromator

Input Values:

grooveDensity:600
order:1
wavelength:500
gratingWidth:50
Worked Steps: 600 lines/mm grating across 50 mm width illuminating 30,000 grooves.

Understanding Your Result

Primary output displays resolving power R.

Summary reports diffraction angle in degrees and minimum detectable Δλ.

Factors That Affect the Result

  • Total number of illuminated grooves N.
  • Diffraction order m.

When Should You Use This Calculator?

  • Optical spectrometer design, astronomical spectroscopy, and laser wavelength meters.

Assumptions & Limitations

  • Assumes normal beam incidence and plane transmission/reflection grating.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard wave optics diffraction formula.

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