PhysicsOpticsUniversity
University Curriculum

Diffraction Grating Minima Condition Calculator

This equation determines the angular positions of the minima in a multiple-slit diffraction pattern.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Diffraction Angle

Formula first

Overview

In a diffraction grating with N slits, the intensity pattern is characterized by sharp principal maxima and smaller secondary minima. This formula identifies the angles at which destructive interference occurs between the slits, effectively defining the dark regions between the principal maxima. The variable m represents an integer order, while N is the total number of slits in the grating.

Symbols

Variables

d = Grating Spacing, = Diffraction Angle, m = Order Number, N = Number of Slits, = Wavelength

Grating Spacing
Diffraction Angle
rad
Order Number
dimensionless
Number of Slits
dimensionless
Wavelength

Apply it well

When To Use

When to use: Use this when calculating the angular position of the dark fringes (minima) in the diffraction pattern produced by a grating with a finite number of slits.

Why it matters: It allows for the precise characterization of the intensity distribution of light passing through a grating, which is essential for designing spectrometers and analyzing spectral resolution.

Avoid these traps

Common Mistakes

  • Confusing the minima condition for a grating with the single-slit diffraction minima condition.
  • Forgetting to include the N-dependent term, which is only relevant for finite-slit gratings.
  • Using degrees instead of radians when calculating the sine function in a calculator.

One free problem

Practice Problem

A diffraction grating has 500 slits (N=500) and a spacing d of 2.0 micrometers. For the first order (m=1) minimum, what is the angle theta in radians for light with a wavelength of 500 nm (5e-7 m)?

Grating Spacing0.000002 m
Order Number1 dimensionless
Number of Slits500 dimensionless
Wavelength5e-7 m

Solve for: theta

Hint: Calculate the right side of the equation first, then take the arcsin.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Hecht, E. (2017). Optics (5th ed.). Pearson.
  2. Young, H. D., & Freedman, R. A. (2020). University Physics with Modern Physics (15th ed.). Pearson.
  3. Hecht, Eugene. Optics. 5th ed., Pearson, 2017.
  4. NIST CODATA
  5. IUPAC Gold Book
  6. Wikipedia: Diffraction Grating
  7. Jenkins, Francis A., and Harvey E. White. Fundamentals of Optics. 4th ed., McGraw-Hill, 1976.
  8. NIST Digital Library of Mathematical Functions, Section 25.11, Diffraction Gratings.