I've been thinking about the doppler effect, where electromagnetic radiation experiences a redshift if the radiation source is relatively moving away from the observation point, and a blueshift if it's moving closer.
If I have a light source, a sensor which is stationary relative to the light source, and a mirror either moving towards or away from the light source while reflecting the light to the sensor — the sensor would pick up the electromagnetic waves as shifted, no? And thus photons (if they are being reflected) basically lose energy to or gain energy from an object (with which they interact) in accordance to the object's momentum relative to the vector of the wave?
I believe that should be the case as I know solar sails are "pushed" by light. Thus I assume light in a way should be able to be "pushed back" and gain energy (which causes the frequency shift).
I'm sorry if this is an obvious concept already explained by the doppler effect. I'm not formally learned in physics and didn't find this specific phenomenon explained in the texts I read.