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Hair-Width Diffraction Estimate — result sheet
Estimate the first diffraction minimum angle and screen displacement for light diffracted by an opaque hair-sized obstacle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: d sin θ = mλ; θ = asin(mλ/d); first-minimum displacement y = L tan θ and central-width estimate = 2y.
A hair can act as a narrow opaque obstacle whose diffraction pattern is closely related to the complementary single-slit geometry. The calculator uses the entered diameter as the characteristic width and reports the angle and screen position of a selected minimum.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Light wavelength — nm; minimum 1.0E-6; maximum 1000000000
- Hair diameter — µm; minimum 1.0E-6; maximum 1000000
- Minimum order m — minimum 1; maximum 1000
- Screen distance — m; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Light wavelength | 650 |
| Hair diameter | 70 |
| Minimum order m | 1 |
| Screen distance | 1 |
First-minimum angle about 0.53° and central-width estimate about 18.6 mm
Assumptions and limits
- The hair is approximated by a straight obstacle with a uniform diameter and the light is monochromatic.
- The screen is far enough away for the simple diffraction geometry to be useful, but the exact tangent is retained for the reported displacement.
- Alignment, hair shape, coherence, surface scattering, camera response, and Babinet-complement details are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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