Formula Used
The calculator uses standard photon relations in vacuum. The speed of light is c = 299,792,458 m/s. Planck’s constant is h = 6.62607015 × 10^-34 J·s.
c = λff = c / λE = hfE = hc / λwavenumber = 1 / λp = h / λλ medium = λ vacuum / n
Here, λ is wavelength, f is frequency, E is photon energy, p is photon momentum, and n is refractive index.
How to Use This Calculator
- Select the known quantity: wavelength, frequency, photon energy, or wavenumber.
- Enter the known value in the input box.
- Choose the matching unit for that known value.
- Enter a refractive index when medium wavelength is needed.
- Select the number of significant figures for scientific notation.
- Click Calculate to view the result above the form.
- Use Download CSV or Download PDF for reports.
Example Data Table
| Example |
Wavelength |
Frequency |
Energy |
Band |
Color |
| Violet light |
405 nm |
7.402 × 10^14 Hz |
3.061 eV |
Visible |
Violet |
| Green laser |
532 nm |
5.635 × 10^14 Hz |
2.331 eV |
Visible |
Green |
| Red laser |
650 nm |
4.612 × 10^14 Hz |
1.907 eV |
Visible |
Red |
| Infrared source |
1550 nm |
1.934 × 10^14 Hz |
0.800 eV |
Infrared |
Not visible |
Understanding Wavelength and Photon Energy
Why These Values Matter
Light can be described as a wave and as photons. Wavelength tells how far one wave cycle travels. Frequency tells how many cycles pass each second. Photon energy tells how much energy each photon carries. These values are linked. When wavelength becomes shorter, frequency becomes higher. Energy also becomes higher.
Useful Physics Connections
The main relation is simple. Light speed equals wavelength multiplied by frequency. This relation works in vacuum with the accepted speed of light. Photon energy then comes from Planck’s equation. Multiply Planck’s constant by frequency. You can also divide Planck’s constant times light speed by wavelength. Both paths give the same photon energy.
Wavelength and Color
Visible light covers only a narrow part of the spectrum. Violet light has shorter wavelengths. Red light has longer wavelengths. Ultraviolet sits below visible violet. Infrared sits above visible red. This calculator estimates the spectral band and visible color from vacuum wavelength. It helps students connect numbers with physical meaning.
Advanced Output
The calculator also gives angular frequency, period, wavenumber, photon momentum, and molar photon energy. These outputs are useful in optics, spectroscopy, chemistry, and quantum physics. Wavenumber is common in spectroscopy. Photon momentum is useful when studying radiation pressure. Molar photon energy helps compare photon energy with chemical energy scales.
Medium Correction
Light changes wavelength inside a material. Frequency stays fixed at a boundary. The wavelength in a medium equals vacuum wavelength divided by refractive index. Glass, water, and other materials have refractive indexes above one. This calculator includes that correction. Use vacuum wavelength for photon energy. Use medium wavelength for propagation inside the selected material.
FAQs
1. What does this calculator convert?
It converts between wavelength, frequency, photon energy, and wavenumber. It also estimates period, angular frequency, photon momentum, spectral band, and visible color.
2. Which wavelength is used for photon energy?
Photon energy uses vacuum wavelength. Frequency and photon energy do not change when light enters a medium. The medium wavelength is shown separately.
3. What is the formula for photon energy?
The main formula is E = hf. Since f = c / λ, energy can also be written as E = hc / λ.
4. Can I enter energy in electron volts?
Yes. You can enter energy in joules, eV, keV, or MeV. The result also shows both joules and electron volts.
5. What does wavenumber mean?
Wavenumber is the reciprocal of wavelength. It is often written in m^-1 or cm^-1 and is common in spectroscopy.
6. Why is refractive index included?
Refractive index adjusts wavelength inside a material. It does not change the photon frequency or energy in this calculator.
7. Is the visible color exact?
No. It is an approximate range-based label. Real perceived color also depends on intensity, observer response, and display conditions.
8. Can I export the results?
Yes. Use Download CSV for spreadsheet data. Use Download PDF after calculation to save a clean report.