What is Babinet's principle?

Babinet's principle states that the diffraction pattern of an opaque body is identical to that of a hole of the same shape, except for the overall forward beam intensity. A hair produces the same pattern as a slit of equal width.

Which laser should I use?

Any visible laser works. Red He-Ne (632.8 nm) or red diode (650 nm) lasers are most common. Green (532 nm) lasers produce slightly tighter patterns.

How accurate is this method?

With careful measurements, accuracy of ±5 µm is typical. Using multiple orders and averaging improves precision. Systematic errors from non-perpendicular alignment are the main concern.

Why can't I see the pattern clearly?

Ensure the room is dark, the hair is taut and perpendicular to the beam, and the screen is far enough away (30+ cm) for the fringes to spread adequately.

How does hair color affect the measurement?

Hair color does not affect the diffraction-based measurement because the technique depends on the diameter, not the optical properties. However, lighter/finer hairs tend to be thinner.

Can I measure other thin objects this way?

Yes, any thin opaque filament (wire, fiber, thread) can be measured using the same technique, as long as its diameter is comparable to the laser wavelength (tens to hundreds of micrometers).

Hair Diffraction Calculator

Measure hair diameter using laser diffraction (Babinet's principle). Calculate fringe positions, pattern width, and classify hair type from diffraction data.

Laser Wavelength (nm)

Screen Distance (mm)

First Minimum Position (mm)

Known Hair Diameter (µm, optional)

Number of Orders to Show

Hair Diameter

31.6 µm

Calculated from the first minimum position using Babinet's principle

Hair Diameter (mm)

0.0316 mm

Diameter in millimeters

Central Maximum Width

20.000 mm

Width of the bright central band on the screen

Pattern Total Width

100.48 mm

Total width across 5 diffraction orders

Wavelength

632.8 nm

Laser wavelength used

Screen Distance

500 mm

Distance from hair to screen

Hair thickness classification

Very Fine (30µm)Medium (85µm)Coarse (180µm)

Order (m)	Angle (°)	Position (mm)
1	1.1458	10.000
2	2.2920	20.012
3	3.4391	30.048
4	4.5876	40.121
5	5.7380	50.242

Hair Type Reference

Type	Diameter Range	1st Min Angle (°)	1st Min Pos (mm)
Fine/Blond	50–70 µm	0.6043	5.27
Medium	70–100 µm	0.4266	3.72
Coarse/Dark	100–120 µm	0.3296	2.88
Very Fine	30–50 µm	0.9065	7.91
Wire-like	120–180 µm	0.2417	2.11

Planning notes, formulas, and examples

About the Hair Diffraction Calculator

The hair diffraction experiment is a classic physics laboratory exercise that elegantly demonstrates wave optics while providing a practical measurement of hair thickness. By shining a laser beam at a single strand of hair and observing the resulting diffraction pattern on a distant screen, students can determine the hair's diameter to within a few micrometers — all without a microscope.

The technique exploits Babinet's principle, which states that the diffraction pattern from an opaque obstacle (like a hair) is identical to that from an aperture of the same size. Therefore, a hair of diameter d produces the same single-slit diffraction pattern as a slit of width d, with dark minima at angles satisfying d·sin(θ) = mλ. By measuring the distance from the central bright spot to the first dark fringe and knowing the screen distance and laser wavelength, the hair diameter can be calculated precisely.

This calculator works in two modes: calculate the hair diameter from a measured first minimum position, or predict the diffraction pattern from a known hair diameter. It includes an order table showing all visible minima, a hair thickness classification guide, and a reference table comparing different hair types — making it the perfect companion for the classic physics lab experiment.

When This Page Helps

This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows.

How to Use the Inputs

Select a laser wavelength preset or enter a custom value.
Enter the distance from the hair to the observation screen.
Measure the distance from the central maximum to the first dark fringe and enter it.
Alternatively, enter a known hair diameter to predict the pattern.
View the calculated hair diameter and thickness classification.
Check the order table for positions of higher-order fringes.

Formula used

Babinet's principle + single slit: d·sin(θ) = mλ, so d = mλ/sin(θ). For small angles: d ≈ mλL/y, where L is screen distance and y is fringe position.

Example Calculation

Result: ≈ 31.6 µm (very fine hair)

With a He-Ne laser (632.8 nm) and screen at 500 mm, the first minimum at 10 mm gives sin(θ) = 10/√(10²+500²) ≈ 0.02, so d = 632.8e-6/0.02 ≈ 0.0316 mm = 31.6 µm.

Tips & Best Practices

Check that all inputs use the same scale and assumptions before trusting the result.
Compare the answer with the worked example or a rough estimate to catch entry mistakes.

When To Use This Calculator

Measure hair diameter using laser diffraction (Babinet Use it when you need a repeatable calculation in the physics / optics category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

Babinet's principle states that the diffraction pattern of an opaque body is identical to that of a hole of the same shape, except for the overall forward beam intensity. A hair produces the same pattern as a slit of equal width.