Can the colors of white light be separated through reflection alone? Can the colors of white light be separated through reflection alone? My answer to this is no since if we want to separate the colors, we use prism and when light passes through a prism, the dispersion of light is not produced by reflection. Is this correct?
 A: There's a difference between reflection and refraction.
Whereas the angle of reflection equals the angle of incidence and is wavelength-independent; the angle of refraction depends on the ratio of refractive indices of the incidence and transmitted media, which can have a wavelength dependence.
Of course if you allow reflection from ruled gratings or thin films, then interference effects can result in "rainbow-like" effects - consider reflection from a puddle covered by an oil film.
A: There is a definitional issue when you talk of reflection, refraction and diffraction. I will let others address those.
I am going to answer what I think was being asked which is whether one can produce a diffraction pattern with mirrors alone?
There is an experiment that is called Lloyds mirror where a light from a source is reflected off a conveniently placed mirror so that it interferes with unreflected light from the same source.  This generates an interference pattern at the intended target (you can look this up online).
This can account for changes in phase, but our perception of color depends on frequency. So how do we consider change in frequency? Generally there are two ways this can happen, either the mirror is less than 100% efficient, or the mirror is moving.
The less than 100% efficient mirror is kind of a weak answer, so that leaves the question of the moving mirror. The moving mirror changes frequency via the doppler effect.
The best way I can imagine this working is to shine light at an angle across a number of rotating reflecting cylinders each rotating at different velocities.
A quick search shows there is significant research and practical experiments regarding moving and/or rotating mirrors and its impact on light.
