Hair Diffraction Calculator
Estimate hair width from laser diffraction fringe spacing using wavelength, wall distance, and dark fringe position.
Measure Hair Width with a Laser
A single hair acts like a thin slit in a classic diffraction experiment. Shine a laser through a strand and a pattern of bright and dark fringes appears on a wall. By measuring fringe spacing, laser wavelength, and distance to the wall, you can estimate hair width without a microscope.
Diffraction Formula for a Hair
For the \(n\)th dark fringe, destructive interference gives:
$$w = \frac{n \lambda}{\sin \theta}$$When the wall is far compared to hair width, the small-angle approximation applies:
$$\sin \theta \approx \frac{x}{D}$$So hair width \(w\) is approximately \(n \lambda D / x\), where \(x\) is distance from the central bright spot to the dark fringe, \(D\) is wall distance, and \(\lambda\) is laser wavelength.
Classroom Experiment Tips
Use a red laser pointer (often 650 nm), tape a hair vertically, and measure in meters and millimeters. Measuring the second or third dark fringe instead of the first reduces relative error. Human hair is typically 50 to 120 micrometers wide.
Related tools: Diffraction Calculator and Energy to Wavelength Calculator.
Frequently Asked Questions
Why does a hair create a diffraction pattern?
The hair blocks part of the wavefront. Light bending around the edges interferes, producing alternating bright and dark bands on the screen.
What wavelength should I use?
Read the value printed on your laser, often 650 nm for red pointers or 532 nm for green. Enter it in nanometers for convenience.
Which dark fringe should I measure?
The first dark fringe is easiest to find, but the second or third fringe often gives a more accurate width because measurement error is a smaller fraction of the distance.
What is fringe order n?
It counts which dark band you measure: n = 1 for the first dark fringe on either side of center, n = 2 for the second, and so on.
How accurate is this method?
With careful distance measurements and a stable setup, results within a few percent of micrometer caliper readings are typical in classroom conditions.
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