Calculate Double-Slit Diffraction

Online calculator and formulas for principal maxima in double-slit diffraction

Double-Slit Calculator (JavaScript)

Principal maxima condition

Principal maxima for double slits satisfy: d·sin(θ) = m·λ. Use this to calculate angle θ or slit distance d.

m = 0, 1, 2, 3, ...
Result

Example calculations

Example 1: Angle of first principal maximum

Given: d = 0.50 mm, λ = 550 nm, m = 1

\[sin(θ)=\frac{m·λ}{d}=\frac{1·550\,nm}{0.50\,mm}=0.0011\]

Result: θ ≈ 0.06°

Example 2: Determine slit distance

Given: θ = 0.06°, λ = 550 nm, m = 1

\[d=\frac{m·λ}{sin(θ)}\]

Result: d ≈ 0.50 mm

Example 3: Effect of d

A larger slit distance causes smaller interference angles.

Rule of thumb: The larger d, the closer the maxima.

Double-slit formulas

In double-slit interference, principal maxima occur when the path difference between both slits is an integer multiple of the wavelength.

Principal maxima
\[d·sin(θ)=m·λ\]
Angle
\[θ=arcsin\left(\frac{m·λ}{d}\right)\]
Slit distance
\[d=\frac{m·λ}{sin(θ)}\]
Validity range
\[\left|\frac{m·λ}{d}\right|\le1\]
Note
This formula gives the position of principal maxima. The full intensity pattern can additionally be modulated by a single-slit envelope.

Description

What is Double-Slit Interference?

The double-slit experiment is one of the most iconic demonstrations in wave physics. Two narrow, parallel slits act as coherent light sources according to the Huygens-Fresnel principle. The light emerging from both slits overlaps—a phenomenon called interference—which produces a characteristic pattern of alternating bright and dark fringes. This pattern is compelling proof that light behaves as a wave.

Condition for Constructive Interference (Bright Fringes)

Two light waves reinforce each other constructively (creating bright fringes) when their phase difference is an integer multiple of the wavelength. The path difference between rays from the two slits must satisfy:

\[d·sin(θ)=m·λ \qquad m = 0, 1, 2, \dots\]
  • d – slit separation (distance between the two slits)
  • θ – deflection angle from the straight-ahead direction
  • m – order of the maximum (m = 0 is the central maximum in the middle)
  • λ – wavelength of light

Unlike the single slit (where m = 1, 2, 3... describe the minima), the double-slit formula describes the maxima, including m = 0 at the center. The intensity is additionally modulated by the single-slit diffraction envelope.

Key Differences
Single Slit Double Slit
PhenomenonDiffractionInterference + Diffraction
Maxima at–d·sin(θ) = m·λ (m = 0, ±1, ±2, ...)
Minima ata·sin(θ) = m·λ (m = 1, 2, ...)Modulation by single-slit envelope
PatternBroad central maximum with many weak secondary maximaClosely spaced maxima, modulated by diffraction envelope
Applications
  • Wavelength determination by measuring interference fringe spacing
  • Demonstration of the wave nature of light and matter waves
  • Foundation for diffraction gratings and optical spectrometers
  • Understanding interference phenomena in nature (iridescence, soap bubbles)
Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?