How are wavelength, frequency, and energy related for light?

For light, which is a form of electromagnetic radiation, wavelength, frequency, and energy are fundamentally linked through the wave-particle nature of light.1

Mathematical Relationships

The relationship between frequency ($\nu$) and wavelength ($\lambda$) is governed by the speed of light ($c$):
$$\nu =\frac{c}{\lambda }$$
This equation shows that frequency and wavelength are inversely proportional; as the wavelength of light increases, its frequency decreases, and vice versa.234

The energy ($E$) of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This is expressed as:1
$$E=h\nu =\frac{hc}{\lambda }$$
In this formula, $h$ represents Planck’s constant. Consequently, light with a higher frequency (and shorter wavelength) carries more energy, while light with a lower frequency (and longer wavelength) carries less energy. These relationships are consistent across the entire electromagnetic spectrum, from radio waves to gamma rays.531