The equation you mentioned, E=mc^2, is actually the famous mass-energy equivalence equation derived by Albert Einstein in his theory of relativity. However, this equation specifically applies to objects with mass. For photons, which are particles of light, they do not possess rest mass. Therefore, the equation E=mc^2 cannot be directly applied to photons.
Instead, the energy of a photon is determined by a different equation, known as the energy-frequency relationship for photons:
E = hf
In this equation, E represents the energy of the photon, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), and f is the frequency of the photon.
The relationship between frequency (f) and velocity (v) for photons is given by the equation:
c = λf
Where c is the speed of light (approximately 3 x 10^8 meters per second) and λ is the wavelength of the photon.
By substituting λf for c in the energy-frequency equation, we can write:
E = hf = (hc) / λ
Therefore, the energy of a photon is inversely proportional to its wavelength. Photons with higher frequencies (shorter wavelengths) have higher energies, while photons with lower frequencies (longer wavelengths) have lower energies.
In summary, the energy of a photon is determined by its frequency and is given by the equation E = hf, where h is Planck's constant. The mass-energy equivalence equation, E=mc^2, applies to objects with mass and cannot be directly used to calculate the energy of a photon.