The relationship between wavelength and frequency is derived from fundamental wave physics and has deep connections to quantum mechanics and relativity.
Derivation of the Wave Equation
The relationship c = λν comes from the definition of wave speed as distance traveled per unit time. For a wave, the distance traveled in one period (T) is one wavelength (λ), so the speed is λ/T. Since frequency is the inverse of period (ν = 1/T), we get c = λν. This relationship applies to all types of waves, not just electromagnetic waves.
Quantum Mechanical Interpretation
In quantum mechanics, light is described as particles called photons, each with energy E = hν. The wavelength is related to the photon's momentum through the de Broglie wavelength: λ = h/p, where p is momentum. This connects the wave and particle descriptions of light, showing that wavelength and frequency are fundamental properties of the quantum nature of electromagnetic radiation.
Relativistic Considerations
The speed of light is a fundamental constant in Einstein's theory of relativity. According to special relativity, the speed of light in vacuum is the same for all observers, regardless of their relative motion. This means that while wavelength and frequency may change due to the Doppler effect when the source and observer are moving relative to each other, their product (c = λν) remains constant.
Dispersion and Medium Effects
When light travels through a medium other than vacuum, its speed decreases, and the relationship between wavelength and frequency becomes more complex. The refractive index of the medium affects the wavelength, while the frequency remains constant. This is why the calculator assumes vacuum conditions for simplicity, but users should be aware of medium effects in practical applications.