Single Slit Diffraction Calculator
Find the angle, screen offset, and fringe spacing for minima in single slit diffraction.
What it does
A single slit spreads light into a pattern of bright and dark bands. The dark bands, called minima, appear where light from different parts of the slit cancels. Their positions depend on the wavelength, the slit width, and the distance to the screen.
The condition for a minimum is a sin(theta) = m lambda, where a is the slit width, theta is the angle from the center line, m is a nonzero integer, and lambda is the wavelength. The first minimum uses m = 1. Higher orders sit farther out on each side.
The default example uses helium-neon laser light at 632.8 nm, a slit 0.1 mm wide, and a screen 2 m away. The first minimum occurs at sin(theta) = 0.006328, or 0.363 degrees. The linear offset on the screen is 12.66 mm, and the next minimum is another 12.66 mm farther out.
For small angles, sin(theta) is close to tan(theta), so the offset is roughly L x lambda / a. This calculator uses the exact sine relation for the angle and the tangent for the screen position. The spacing output uses the standard lambda L / a expression.
The pattern is only as clean as the setup. A wide or uneven slit, a nearby screen, a broad light source, or a nonuniform beam will blur the minima. The formula predicts the ideal far-field pattern, not every laboratory image.
How to use
- Pick metric or imperial units for the slit and screen.
- Enter the light wavelength in nanometers.
- Enter the slit width in millimeters or mils.
- Enter the distance from the slit to the screen.
- Choose the minimum order, starting with 1.
- Read the angle and the offset from the center of the pattern.
Formula
- a
- Slit width in meters.
- theta
- Angle from the center line.
- m
- Minimum order, a positive integer.
- lambda
- Wavelength in meters.
- L
- Distance from the slit to the screen.
- y
- Linear offset on the screen.
The order must satisfy m lambda < a, otherwise no minimum exists at that order. The angle is found with the inverse sine. The screen offset uses the tangent, and the spacing uses the small-angle form lambda L / a. For the usual narrow-angle setup these agree closely. The slit is treated as one uniform rectangular opening.
Worked example
Example: 632.8 nm, 0.1 mm slit, 2 m screen
The default metric values and first order are already filled in the form.
- Convert the wavelength: 632.8 nm = 6.328 x 10^-7 m.
- Convert the slit width: 0.1 mm = 1.0 x 10^-4 m.
- For m = 1, sin(theta) = 6.328 x 10^-7 / 1.0 x 10^-4 = 0.006328.
- The angle is asin(0.006328) = 0.006328 rad, or 0.363 degrees.
- Screen offset: y = 2 x tan(0.006328) = 0.01266 m, shown as 12.66 mm.
- Spacing: lambda L / a = 6.328 x 10^-7 x 2 / 1.0 x 10^-4 = 0.01266 m, also 12.66 mm.
- The imperial mirror uses 3.937 mil and 6.56 ft and returns 0.498 in for the offset.
Reference table
| Slit width | Angle | Screen offset | Spacing |
|---|---|---|---|
| 0.05 mm | 0.725 degrees | 25.31 mm | 25.31 mm |
| 0.10 mm | 0.363 degrees | 12.66 mm | 12.66 mm |
| 0.20 mm | 0.181 degrees | 6.33 mm | 6.33 mm |
Limits
- The formula describes far-field Fraunhofer diffraction, not a pattern measured too close to the slit.
- The slit is assumed uniform and much wider than the wavelength, with a plane wave hitting it.
- The spacing expression is a small-angle approximation, while the offset uses the tangent.
- A broad source, lens aberrations, or a nonuniform beam can shift and blur the minima.
Common mistakes
- Entering the wavelength in millimeters while the field expects nanometers.
- Forgetting to convert slit width and screen distance to compatible units before comparing results.
- Measuring to a bright fringe and calling it a minimum.
- Using the double slit formula and expecting evenly spaced bright fringes.
- Choosing an order where m times the wavelength exceeds the slit width.
Try it yourself
Quick checks. Answers sit tucked under each question.
500 nm light passes a 0.05 mm slit onto a screen 3 m away. Where is the second minimum?
sin(theta) = 2 x 5.00 x 10^-7 / 5.0 x 10^-5 = 0.0200. The angle is 1.146 degrees, the offset is 60.01 mm, and the spacing is 30.00 mm.
With 632.8 nm light and a 0.1 mm slit, what is the first minimum on a 1 m screen?
The angle stays 0.363 degrees. The offset is 6.33 mm and the spacing is 6.33 mm.
450 nm light passes a 0.02 mm slit onto a screen 2 m away. What is the first minimum offset?
sin(theta) = 4.50 x 10^-7 / 2.0 x 10^-5 = 0.0225. The angle is 1.289 degrees, the offset is 45.01 mm, and the spacing is 45.00 mm.
Questions
What is a single slit diffraction minimum?
A dark band where light from different parts of the slit arrives out of phase and cancels. The condition is a sin(theta) = m lambda.
What is the difference between a minimum and a maximum?
A minimum is a dark band with near-zero intensity. A maximum is a bright band. The simple formula in this tool locates minima.
Why does a wider slit make a narrower pattern?
The angle depends on lambda divided by slit width. A larger slit width makes the same wavelength bend through a smaller angle.
Can I use this for a double slit?
No. A double slit adds interference between two openings and produces a different pattern. This calculator models one slit.
Does the wavelength depend on the screen material?
The wavelength in air is what matters for the geometry. If the path is in another medium, use the wavelength in that medium.
Why is the spacing equal to the offset in the example?
For the first minimum and a small angle, the offset is one spacing from the center. At larger angles the exact tangent makes the two differ slightly.
Sources
- OpenStax University Physics, single slit diffraction
- LibreTexts College Physics, single slit diffraction