Doesn't this statement signify that the delay is accumalated over time, which means light slows down gradually through a medium?
A delay being accumulated over time does not mean that the speed is changing.
Imagine two cars, white and black, traveling at 60mph on the highway. The black car exits the highway at 60mph and gets stuck at a traffic light. It gets stuck at every traffic light for the next 10 miles before getting back on the highway.
Its velocity upon exiting the highway immediately dropped to an average 30mph (or whatever) and remained at that (average) speed the whole time it was on side streets. The delay accumulated (if it had stayed off the highway for 100 miles, the delay would be much greater.)
When incident light hits glass at a perpendicular angle, it does not refract but it still slows down.
You have cause and effect reversed. The slowing down is the
cause of the refraction (well, simplistically, anyway). Thus, there can be slowing without refracting, though there cannot be refracting without slowing.
So the first color of light you see when you are ascending from deep scuba diving is red?
No, the FIRST colour (after black, that is) you see will be blue. However, underwater is almost entirely blue. As you ascend, you will see more and more red (red is the LAST colour you'll see), which is why it will LOOK very red. Your brain will filter out most of the blue, as will a picture from a camera.
This is a tricky subject, involving subjective observation and other factors. I'll go into it further if you wish.