Interference Fringe Spacing Calculator

Calculator Inputs

Use the responsive form below. It displays in three columns on large screens, two on smaller screens, and one on mobile.

Wavelength

Vacuum or air wavelength before medium correction.

Slit separation d

Center-to-center distance between coherent slits.

Slit width a (optional envelope)

Set zero to ignore the diffraction envelope.

Screen distance L

Distance from slit plane to screen plane.

Screen width for counting fringes

Used for the graph span and fringe-count estimate.

Refractive index n

Effective wavelength becomes λ₀ / n.

Incidence angle i (degrees)

Adds central-fringe shift from oblique incidence.

Screen tilt α (degrees)

Projected fringe spacing increases with tilt.

Fringe order m

Used for specific bright and dark fringe positions.

Visibility factor V

Zero flattens the graph. One gives full contrast.

Output unit

Controls the displayed length unit in results.

Decimal precision

Choose between 2 and 10 decimal places.

Reset

Example Data Table

These sample cases illustrate how spacing changes with medium, tilt, and geometry.

Wavelength	Slit separation d	Slit width a	Screen distance L	n	Tilt	Fringe spacing	Bright position
632.8 nm	0.25 mm	0.04 mm	2 m	1	0°	5.0624 mm	15.1872 mm
532 nm	0.2 mm	0.03 mm	1.5 m	1.33	5°	3.0115 mm	-7.0669 mm
650 nm	0.15 mm	0.05 mm	1.8 m	1	10°	7.9203 mm	0.2670 mm

Formula Used

1) Effective wavelength in the medium
λ_eff = λ₀ / n

2) Basic fringe spacing
β = (λ_eff L) / d

3) Tilt-adjusted spacing on a rotated screen
β_tilt = β / cos(α)

4) Central shift for oblique incidence
x₀ = -L sin(i)

5) Bright and dark fringe positions
x_m,bright = x₀ + mβ_tilt
x_m,dark = x₀ + (m + 0.5)β_tilt

6) Central diffraction-envelope width, when slit width is supplied
W_env = 2λ_effL / a

7) Normalized plotted intensity
I(x) = 0.5[1 + V cos(2π(x - x₀) / β_tilt)] · sinc²(πa(x - x₀) / (Lλ_eff))

How to Use This Calculator

Enter the light wavelength and choose its unit.
Provide slit separation d and optional slit width a.
Set the screen distance L and optional screen width.
Enter the refractive index for the propagation medium.
Add any incidence angle or screen tilt if the setup is not perfectly aligned.
Pick a fringe order m to find a specific bright and dark location.
Choose visibility factor and output unit.
Press the calculate button to show results above the form and generate the graph.

Frequently Asked Questions

1) What does fringe spacing mean?

Fringe spacing is the distance between adjacent bright fringes or adjacent dark fringes on the screen. In a standard two-slit setup, it depends on wavelength, screen distance, and slit separation.

2) Why does increasing wavelength increase spacing?

The spacing formula is proportional to wavelength. A larger wavelength increases the path-difference scale required for adjacent interference maxima, so the fringes spread farther apart on the screen.

3) Why does larger slit separation reduce spacing?

Fringe spacing is inversely proportional to slit separation. When the slits are farther apart, a smaller screen displacement creates the needed path difference, so the fringes become tighter.

4) What does refractive index change here?

A higher refractive index reduces the effective wavelength in the medium. Because the spacing uses that effective wavelength, the fringe spacing shrinks when the medium becomes optically denser.

5) Why is incidence angle included?

Oblique incidence shifts the whole fringe pattern sideways. It usually changes the central fringe position more than the spacing itself, which is why the calculator reports both shift and fringe locations.

6) What does the screen tilt option do?

Tilting the screen changes the projected distance measured along the screen surface. This stretches the apparent fringe spacing by a cosine factor, making the observed separation larger.

7) Why include slit width if spacing already uses d?

Slit width mainly shapes the diffraction envelope that modulates the interference pattern. It does not set the main spacing, but it affects intensity distribution and the number of visible fringes inside the central envelope.

8) What do the CSV and PDF buttons export?

They export the calculated result table shown after submission. CSV is useful for spreadsheets or logs, while PDF is convenient for reports, class notes, and quick documentation.