The polished/unpolished debate has been around for a while. I think of it as a further extension of the narrow angle/wide angle LED decision. You are right that an unpolished edge will act a s a sort of a diffractor of the beam to some degree and with many of us, that isn’t a bad thing. I personally opted to ‘kind-of-polish’ my edges (sanded them with 400 grit, then buffed them a bit with brasso & a cloth). Your diagram shows the LED basically pointing straight into the plexi, so I’m going to reiterate my explanations of the beamwidth vs orientation opinions to help you understand why some people might prefer polished vs. unpolished (and hence additional diffusion or not).
In theory, IR that strikes the surface of your plexi at 40 degrees will reflect almost totally; in practice, the closer it is to 90, the higher the percentage that escapes, & the closer to 0 (straight in), the more it is lost to attenuation AND escape. Remember, plexi isn’t perfectly clear, and the farther the IR travels through it the less you have left, which only really becomes a problem with big displays & thick plexi. Also, the thicker your plexi, the the more distance between each time the ray hits your top surface (for example, if you trace a single ray at 40 degrees through a 1/2” thick plexi, it hits the top surface again roughly every 1.2”, and travels a total of about 1.5” through plexi on it’s journey down and back up)
So the two schools of thought are:
1. choose a rather narrow beamwidth LED, and angle it towards the edge at something between 30-50 degrees...theoretically 40 would be perfect. If you have a 10 degree ‘half angle’ of beam, then 40 degree angle of approach means 90% of your IR will hit the surface between 30-50 degrees. With narrow LEDS and thick plexi, it is possible to accidentally create light & dark ‘bands’ or hot/cold spots on your surface, particularly close to the edges, as done this way you are illuminating only one of the two surfaces with each device. In practice, this usually isn’t a problem, but a small amount of dispersion from unpolished edges can help prevent it.
2. use wide beamwidth LEDs and point them straight in. Done this way, with a 110 degree beam width, you will have greater losses to attenuation (as some IR is simply cast at too narrow of an angle to refract well or is cast at the other edge), but you are then hitting both the top and bottom surface with a decent amount of IR. So you end up getting twice the surface coverage from each device (every .6” in the above example), removing the need to think about angling your LEDs, and reducing the incidence of cold spots.
What you should definitely NOT do, is point narrow beam LEDs straight into the edge, particularly if it’s polished!