Why do the raptors(methane burning engines) burn pink(at 0:53)?
Like Yasar has explained, it depends on the temperature faced by the hydrocarbon (whatever it is, they are all C-H combos) in presence of oxygen.
If the stochiometric mix is perfect, you will only ever see a blue flame, like that you see of a bunsen burner (when you swivel the air duct)....and get the commensurate temperature and (higher) electron excitation in the C, H and O atoms involved to give a combined register of blue (specifically the conversion of C + O2 to CO2 directly, since I believe H + O2 -> H2O is largely colourless)
If the mix is instead fuel rich (and not stochiometrically balanced) as is the case with most rockets (given premium of the oxidizer compared to the fuel), you will instead see some amount of fuel expelled out the nozzle unburnt or only partially burned (C + O --> CO)....somewhat similar to a bunsen burner when you keep the air duct closed.
The CO + O2 ---> CO2 happens further down the (intense velocity) ejecta plume along with some further C + O---> CO. These combine to give a yellower flame given the lower electron excitations involved. As to why lower energy released by the electron shifts cause lower frequencies in the light emitted, needs a look into electron structure physics and chemistry and Planck's E=hf (and associated series of light emission in the atom w.r.t balmer series, which is the visible part our eyes are capable of picking up).
So pink is a transition colour depending on these dynamics of the plume and fuel-rich combustion (blue closer to the nozzle, and more red and yellow tinge further down added to give purples and pinks where there are both happening).
You see similar phenomena happen with afterburners too depending on flame temperature....since again its a hydrocarbon.
When you have only full hydrogen and oxygen combusting (say hydrolox rather than kerolox or metholox), water vapour does its own thing with opaque droplet refraction shielding the near-transparent combustion colour (as non visible light is activated mostly in the electron excitations here).
Camera filters can further add a skew to the colour too sometimes.
