special relativity - Expression for the (relativistic) mass of the photon

I started learning a bit ahead from an old physics book, and they were discussing the photoelectric effect and after that Planck's hypotheses and energy quantas.

The book said that the mass of a microscopic oscillator (what is that?) is not continuous, but discrete and the difference between states is an energy quanta:

$\varepsilon = h\nu = E_k - E_i$

And since $E = mc^2$ then the (relativistic) mass of the photon is

$m = \frac{h\nu}{c^2}$

How did they deduce that?

Answer

This is probably related to the derivation of de-Broglie wavelength... Since photon has wave-particle duality,

We could equate Planck's quantum theory (wave nature) which gives the expression for energy of a wave of frequency $\nu$, ($E=h\nu$) with Einstein's mass-energy equivalence (particle nature) which gives relativistic energy for photon ($E=mc^2$)

$$mc^2=h\nu$$

The resultant mass gives the relativistic mass for a moving photon (since photon has zero rest mass)