Mass is energy at rest. Energy is mass in motion. The thoroughly proven equation E=MC2 is the expression of this mass/energy equivalency.
If you fire a hollow-point bullet 200 grains in weight, at 1000 feet per second, into a mud bank from a distance of ten feet, you will create a crater several inches in diameter. If you fire a hollow-point bullet the same weight at 2000 feet per second from the same distance into the same mud bank, you will create a crater significantly larger than the first one. It's the same with any mass at various speeds. Think of the damage a 1957 Chevy traveling at 60mph hitting a brick wall incurs. Then think of the damage traveling at 120 mph. Then think of two Chevys, each at 120 mph in a head-on collision. At increased speed, the mass in the mass/energy equivalency increases relative to the speed. It's a manifestation of relativity you can observe anytime. You can feel it in your hands when you clap them together. The harder you clap the more heat you feel.
It's not necessary to "understand" these phenomena. In truth, no one really does. But the theory can be deduced and proven by observation. In the case of mass/energy, the truth is in the result.
As for reflected light accelerating after the bounce; why should it? Does a rubber ball bounce back faster than it is thrown to the floor? No, it doesn't, because a portion its motion/energy is released as heat and sound, and some is used in the minuscule amount the floor is compressed in the impact. Otherwise the ball would keep on bouncing indefinitely. It is the same with light in that some of its energy is drained off as heat when it impacts a surface, and some is lost in refraction. Here again, the truth is in the result.
