chukhung, I don’t think anyone uses lasers to shape the lens, but that doesn’t mean they can’t. I know that lens capsule surgery (“secondary cataract”) is done with a laser.
l’il Dickie, I will say it again: no one does RK with lasers. Sure, it’s been tried, and sure, it probably worked as well as a keratome (that is to say, poorly), but laser surgery is an unnecessarily expensive way to achieve those poor results. Hell, the only reason RK still exists is that you can do it with a knife at a fraction of the cost of laser surgery. It is therefore incorrect to call it a laser surgery, and it’s unlikley that any doctor would call it that.
Isn’t it the differing thickness of the lens that is important, not the curvature per se? Sunglasses, ski goggles, windshields, etc., are all curved, many curve a lot more than corrective lenses. But they do not act as lenses because they have constant thickness (at least approximately).
PBear,
Maybe he was talking about the lingering bluriness that can occur after you come out of the water?
If you have, say, a pair of ski goggles in air, then light will be refracted going into the glass, but immediately unrefracted again by the same amount coming out, so there’s almost no net effect. If it’s air on both sides of the glass, then the only way to make the amount of refraction not cancel is to give the two sides different curvature, which means that the lens will be of varying thickness.
On the other hand, if you have different materials on the different sides of the glass, then even if it’s the same curvature, the amount of refraction will be different, so it won’t cancel out. Another way to think of it is to consider the lens to not be the glass, but the water on the other side of it. Since the lens is curved, the water will have different “thickness”, so it can act like a lens.
Surprisingly, curved surfaces of uniform thickness do have optical power – that is, they act as lenses. In order to eliminate the lensing, you actually have to have nonuniform thickness.
Of course, in most cases, with roughly uniform thickness the lensing is far too small to notice.
That depends on how one defines “uniform thickness”. I was assuming that “uniform thickness” meant that lines parallel to the axis of the “lens” would all pass through the same amount of material, and in this case, there is no net optical power. For instance, the space between these two parentheses )).
If, on the other hand, “uniform thickness” means that lines perpendicular to the surface all pass through the same amount of material, then a uniform-thickness lens still focuses.
You’re usually very accurate, Chronos, but I’m afraid you’re slightly in error here. The “Lensmasker’s formula” that you can use to calculate the paraxial power of lenses has three terms. If the lens looks the way you have described and pictured it, the first two terms cancel out, but the third term remains. Granted, that’s generally a pretty weak term, but a lens in which the front and rear surfaces have the same radius of curvature still has some residual power. So does a lens in which the front and rear surfaces are concentric. You actually have to have slightly different front and back radii of curvature to have a truly zer-power lens.
Of course, the kicker is that such a lens is only zero power for rays that are parallel to the optical axis. Rays that are at an angle to the optical axis end up being deviated. And even rays parallel to the optical axis are displaced. It’s hard to make a “do nothing” lens that acts as if it’s not there. Sinclair Optics had a design challenge to produce such a lens a few years ago.
You’re the optics guy, so I’ll take your word for it, but I don’t remember the third term you’re referring to. I take it that it’s due to light rays being displaced to a different portion of the lens? Might that have been omitted from the formula in an undergrad book?
On the contrary, it’s easy; all you need is air!
But seriously, it’s difficult to make anything different from the surrounding medium which nonetheless leaves light paths unchanged. Even a flat piece of glass will displace rays, with the effect of screwing up depth perception (ever notice that bulletproof glass looks a lot thinner than it actually is?).
So, did anyone actually succeed at Sinclair’s challenge? It would be interesting to see the results.
They did, but only after long arguments about what “doing nothing” meant, and over what ranges. The results are published somewhere, but I can’t remember exactly where.
The requirement for zero power is that n(R1-R2) + (n-1)t = 0, where R1 and R2 are the radii of curvature of the two surfaces and t is the thickness, and n is the refractive index. In the limit as t goes to zero you have the two radii getting closer and closer, but as long as the thickness is finite you’ve got to have them slightly unequal.
The lensmaker’s formula is power = (n-1)((1/R1)-(1/R2)+((n-1)/n)(t/R1R2)). You can find it in any good intro to optics text – Hecht, Jenkins and White, Rossi, Smith’s Modern Optical Engineering, Hecht’s Schaum’s Outline book on Optics…
Does anybody know anything about these “certain features of the lens and cornea”? My further searches on google didn’t help much. (Maybe if I could read Dutch…)
SCUBA divers, yeah, but submariners? Maybe some submarines, but I was under the impression that the submarines occupied by those who call themselves submariners (namely military submarines) aren’t pressurized to a significant amount beyond atmospheric. If they were, there would be no worries about crush depths, and that full blow thing they do where they shoot out of the water from some depth would injure or kill everyone onboard from nitrogen narcosis.
The rest of the thread is quite interesting, although no one has mentioned the speed of light yet.
Nametag, you appear more informed on the topic than I. I just looked up some of the terms you used on a medical website because I sure didn’t know them. All I know is that my mom had RK done about 8 years ago. At the time, she talked to her doctor about the options. He used a scalpel, but said that some people were starting to use lasers. This was pre-LASIK and -LASEK and apparently a number of other procedures, I guess. Anyway, at the time, laser RK was new, but he recommended scalpel because he had been doing it for years and had lots of experience, whereas the laser guys were new at what they were doing. (Even experienced eye surgeons were new to the equipment.) I guess things have changed since then.
Doesn’t that vary by frequency? I know that my glasses (which are actually high-refractive-index plastic) refract light differently at their outer corners depending on what frequency (i.e colour) it is… higher frequencies (greens, blues) appear to be refracted less.
