|MadSci Network: Physics|
Excellent question, my friend! Your glasses are different from your windshield, in that your windshield is basically a FLAT piece of glass. The inner and outer surfaces of your car's windshield are basically parallel to one another, even where the glass curves pretty strongly. This is deliberate. (The NHSTA and DOT mandate it.) Your glasses are different. Depending upon your prescription, the inner and outer surfaces of your lenses are probably convergent / divergent to some degree. They refract light differently. Please bear with me as I try to illustrate this… Think of standing knee deep in a clear, still pond and trying to reach in and grab a fish you see by your ankle near the bottom. (The classic example involves trying to spear the fish. I'll try to be a little more sensitive.) Can you grab that fish? Maybe, but you'll probably miss, because you are probably watching a "virtual" fish! Light travels at different speeds through different media. It changes direction at the intersection of two different things like air and water. (It "bends") Try this: Draw a line. This is the surface of the pond water. Now draw a fish underneath… Now, add a light ray coming from the sun, entering the water, bouncing off the fish, and going into your eye…(REMEMBER: Light changes directions a bit when it hits the interface between two different media!) See where the arrow points? That's where you are "looking", and where you will try to grab the fish. It's not where the fish is! The light "bent" between the air and water, saving the fish! (I think fish understand this intuitively.) Which, you ask, has what to do with windshields and eyeglasses? (After all, fish understand neither of these…) When light hits glass it "bends" in a similar fashion. If you'll note, I tried (badly) above to make the "bend" angles about the same for the light ray entering and leaving the water. Light actually behaves this way. If it hits a perpendicular glass surface it "bends", as above, but gets "bent" back by the same amount when it leaves the glass and hits the air again. (Assuming parallel front and rear surfaces, as in your windshield.) As far as you are concerned, the light travels straight through the glass, so you "see" things where they "are". I don't know about your particular glasses, but mine are quite different from a windshield. If I pinch the middle of my eyeglass lens between my thumb and forefinger, then drag my pinched fingers outward to the edge of the lens, I can easily tell the edges are thicker than the center. [I'm myopic, or, "nearsighted", like many semi-nerds.] (Aside: I cleaned my fingers first, because I don't like dirty glasses. I also don't like bird "stuff" which lands on my car windshield. I'm pretty sure fish don't like it landing on the surface of their ponds, either, because they usually eat "stuff" they see fall on the surface of the pond…YUK!) Anyway… Assuming light "bends" a certain amount when it hits the interface between two media, and that the angle of "bend" at exit is opposite of that of entry into the medium we should be able to figure out…nothing at all! Unless, of course, we realize that light "rays" are actually light "wave" fronts. Our one line ray… Becomes a wave-front of many rays… See how the "fat" lines (wave-fronts, or, "sum" of many independently directed rays) follow each other in parallel lines? Can you also see how they hit the surface differently? (The line closer to the surface has crossed more deeply into the "water" than the next wave's "ray-line".) Just like ocean waves hitting a big rock on the beach, there's a discreet time between the arrival of one wave and the next. If the ocean waves are really big you can time them on your wristwatch. (Fish don't need wristwatches, as they already understand about rocks and big waves.) Can you see how the waves above are "breaking" on the surface of the water as they arrive over time? The first [leftmost] wave is more underwater than the next [middle] wave. It's also more "bent". Why? Light travels at different speeds in different media, right? Speed involves time. In other words, the first ray that hits the surface bends a certain amount. Then comes the second, which bends the same, but not as quickly as the first, because it's travelling behind that wave. (I tried to draw the above rays with the first one shorter, so you could see the top one got there first. Actually, you should pretend the rays all come from the same point and hit the same point. Similarly, my "waves" should not be shorter / longer above, or below, the surface line. This is just meant to enhance the visual effect…kind of like a funky vector-diagram.) I imagine you want to slap me with a fish at this point, so, I'll try to bring things into focus: Your windshield acts just like the pond. It "bends" (refracts) light. Your glasses do the same. The difference is time. If the surfaces of your windshield are parallel, the ray / wave transit time is basically equal for all incident rays / waves. The surfaces of your eyeglasses are most deliberately NOT like this, though. (Remember the "pinch" experiment I described before?) Eyeglasses are intentionally thicker and thinner in certain places. All else equal, this means light waves have to spend more time transiting the thicker parts than they do the thinner parts. Assuming equal entry and exit angles, this means… it might sound "fishy"…light which goes through a thicker part of a lens will appear to be "bent" [refracted] more to your eye. That's exactly what your eye doctor wants, and what your windshield manufacturer fears. (If you have a Physics text you should look under "Snell's Law", or, "index of refraction". If you happen to have Physics for Science and Engineering [Marion and Hornyak. CBS College Publishing / Saunders College Publishing, 1982. ISBN 0-03-062831-8] as I do, you should look at page 1074 for Snell, then work back to page 1066 for a good overview of all of this. Better have your "calcul-us-ator" handy, though!) I briefly wondered if auto manufacturers could make "prescription" windshields. Don't think so! To do the job the "glass would have to be really thick, flexible, moveable on many axes, and, probably, computer controlled. Why? My glasses pretty much sit in one place on my nose. If they don't, I don't see as well. Windshields stay fixed. Drivers do not, by ANY means. You'd have to have some means for a windshield-controlling computer to know where the driver was looking and adjust the glass accordingly. It probably wouldn't work out, even then, though…as drivers would soon learn… their passengers either had different prescriptions, or perspectives: if we can't see out the front window…that's where our senses tell us we're "going" as we ride…we tend to get motion sickness more easily. Arguably, cleaning up the tragic results of this scenario could easily outweigh the benefits of drivers not having to wear vision correction! Hope this has helped you in some way. (If only to fall asleep!) If you'd like more detailed information - all the nasty math and physics stuff- please e-mail me at email@example.com. I really enjoyed working on this! Your MadSci, -Matt (firstname.lastname@example.org, or, email@example.com) P.S. - My thanks to Mason Rogers, CPI Corp. (St. Louis, MO) for his help with this. He mapped out this answer on a single page. It's not his fault I'm so long winded! (He, too, harmed no fish while helping answer this.)
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