Does light have mass or not? We know light is made of photons and so it should not have mass, but light is a form of energy (light has energy) and has velocity ($c$), so according to $E=mc^2$, light should have mass... So what is correct?
 A: This the complete Einstein equation:
\begin{equation}
E^2=m^2c^4+p^2c^2
\end{equation}
Photons don't have mass but they still carry energy due to their momentum.
A: The value $E/c^2$ has sometimes been called relativistic mass, but we make an effort nowadays to discourage that term because it refers to a frame-dependent quantity, and it's more helpful to focus on the invariant mass. A free particle has energy-momentum relation $E^2=m_0^2c^4+p^2c^2$ (see here for a generalization to a non-free particle, but we'll overlook that for now), with $m_0$ a symbol we have to use for invariant mass, instead of the preferred $m$, if someone's already claimed $m$ for $E/c^2$ in the discussion. I'll stick with $m_0$ for now, since we're already "in this deep".
With that preamble out of the way, a photon in the vacuum has $m_0=0,\,E=|p|c>0$. The photon has zero invariant mass, and no rest frame. This makes "rest mass", another term that's been used for invariant mass, unnecessarily confusing! (It's less of a problem for particles with $m_0>0$, which do have a rest frame; indeed, light in a medium with refractive index greater than $1$ has been modelled in terms of $m_0>0$ photons.) But any photon, regardless of the context, has a frame-dependent $E/c^2>0$, which was discussed above.
A: 
Does light have mass or not

Light is the word we use for classical electromagnetic radiation at optical frequencies.
Electromagnetic radiation is emergent from a large number of photons. The figure in this experiment is a clear proof that the addition of photons, elementary particles of zero mass and energy equal to $hν$ where   $ν$ is the frequency of the classical electromagnetic wave arising from the confluence of very many photons .
Photons are described by four vectors in the special theory of relativity . The addition of the four vectors of two non collinear photons has an invariant mass even if each individual photon has zero mass,

thus the built up light will have an invariant mass, within the formalism of special relativity.
Experimental proof is the decay of the pi0 to two gamma. The added four vectors of the two gamma have the invariant mass of the pi0. (Related )
A: When the value of mass is given as mc^2=hf, or m=hf/c^2, this is the equivalent newtonian mass, which appears in momentum for example.
Under Special relativity, it has no mass.
