Suppose a binary star system has relatively a dim red star (such as a red giant or red dwarf) and a very bright blue star. From standing on a planet much closer to the red star, would it be possible to look up into the sky and see something like this:
where the lighter-coloured part is reflected light from the blue star.
There are really two questions here: (1) would the red star reflect light from the blue one at all, given that its surface is made of slightly ionised hydrogen gas (in contrast to planets like Jupiter, which are mostly not ionised); and (2) would the amount of light reflected be enough not to be overwhelmed by the light from the red star?
I'm also interested in whether the colour difference between the emitted red light and reflected bluish light would be enough to be detected by the human eye. (We can assume the human is wearing very dark glasses.)
A bonus question: if star-reflected starlight of this kind does exist, are there cases where it can be detected from Earth, spectroscopically?