What is the effect of the expansion of the universe on light?
It causes redshift.
The expansion of the Universe can be imagined as a pie with raisins in the oven. As time goes by the pie is growing and the raisins (the galaxies) are receding from each other. But what's really happening is that the pasta (the space itself) is growing, and not the galaxies are moving. The galaxies are standing, and they are getting further from each other, by the space what's separating them is growing.
When light travels in a Universe like this, it's wavelength is getting longer just like any other distance. That causes the redshift, and that's called the cosmological redshift.