Calculator Inputs
Example Data Table
| Distance | Unit | Rotation | Faces | Path | Expected Result |
|---|---|---|---|---|---|
| 35.426 | km | 528 rev/s | 8 | Round trip | Near accepted light speed |
| 22 | mile | 31680 rpm | 8 | Round trip | Experimental estimate |
| 35426 | m | 528 rev/s | 8 | One way | Half round path estimate |
Formula Used
The calculator follows a rotating mirror timing model.
Angular step: θ = 2πm / N
Angular speed: ω = 2πf
Travel time: t = θ / ω
Speed of light estimate: c = path distance / t
For round trip mode, path distance equals 2L. For one way mode, path distance equals L.
Percent error: error = ((calculated c - accepted c) / accepted c) × 100
How to Use This Calculator
- Enter the distance between the rotating mirror and fixed mirror.
- Select the matching distance unit.
- Enter the mirror rotation rate.
- Choose the rotation unit used by your source data.
- Enter the number of mirror faces.
- Set the image shift order for the observed return beam.
- Select round trip or one way path mode.
- Press calculate to view the result above the form.
- Use the CSV or PDF buttons to save the output.
Michelson Method Article
Purpose of the Calculator
Albert A. Michelson improved the measurement of light speed. His method used rotating mirrors, long paths, and sharp observation. This calculator models that idea with adjustable inputs. It helps students test how distance, angular speed, and mirror geometry change the final speed estimate.
Rotating Mirror Idea
A beam travels from a rotating mirror to a distant reflector. It returns after a tiny time interval. During that interval, the rotating mirror turns through a small angle. When the return beam matches an observed position, the travel time can be inferred. The speed is then path length divided by travel time.
Important Inputs
Distance is the main scale factor. A longer path makes the tiny time delay easier to measure. Rotation rate sets how quickly the mirror angle changes. Mirror faces define the angular step between matching positions. The image shift order allows advanced trials where more than one angular step is involved.
Advanced Options
The calculator includes round trip and one way modes. Michelson style measurements usually use a reflected path, so round trip is common. You can also enter an accepted speed value. This gives percent error and a measured to accepted ratio. Uncertainty fields estimate how input errors affect the final answer.
Understanding the Result
The calculated value may differ from the accepted speed. Small changes in rotation rate can create large changes in the result. Distance errors also matter. Mirror face count should match the actual rotating mirror. Use consistent units before comparing trials. The tool converts common units automatically.
Classroom Use
This page is useful for lab reports and physics demonstrations. It can compare historical style data with modern values. It also shows why precise timing was difficult before electronic instruments. Export buttons let you save results for records, worksheets, and student notebooks.
Practical Note
This model is a simplified teaching calculator. Real experiments include alignment limits, air effects, bearing stability, mirror flatness, and observation uncertainty. Still, the core relationship remains clear. Light speed comes from distance divided by measured travel time.
FAQs
What does this calculator estimate?
It estimates the speed of light from rotating mirror data. It uses distance, mirror speed, mirror faces, and image shift order.
Is this based on Michelson’s experiment?
Yes. It models the rotating mirror idea used in Michelson style speed of light measurements. It is simplified for learning.
Why is round trip mode important?
The light beam often travels to a distant reflector and returns. That makes the path twice the mirror distance.
What is mirror face count?
It is the number of reflecting faces on the rotating mirror. More faces create a smaller angular step per face.
What is image shift order?
It represents how many angular face steps match the observed return beam. Most basic examples use one step.
Why can percent error be large?
Small errors in rotation rate, distance, or angle can strongly affect the final speed. Precision is very important.
Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.
Is the accepted speed editable?
Yes. You can enter any comparison value. The default is the modern accepted speed in meters per second.