optics
I am myopic ~ -2.75 sph +1cyl. When I went snorkeling they tell you not to wear glasses behind the goggles. Surprisingly, underwater, things remain in focus with goggles on even without prescription lenses, while things outside the water at an equal distance would be blurry. Why is this the case?
Thank you.
The thing is that paper fibers are really transparent (unless the paper has been painted some color, of course). The only reason paper blocks light is that its fibers are all "immersed" in air.
Try to imagine what you would see with a very potent microscope: various clear tubes going in all directions. What happens to a ray of light entering this maze of "transparent tubes"? It gets refracted each time it enters and each time it leaves each tube. The final result is that light might scatter in any direction, but it's more probable to leave by the same surface it entered, that means: back to you. That makes paper white.
Now, if you fill all this space with a fluid (by soaking paper in said fluid) and this fluid has a refractive index similar to the fibers, the light will not "feel" so much when it passes from fluid to fiber. The end result is that light will not scatter that much, and the paper becomes more transparent. The better the matching between the refractive indexes the more transparent the paper will be.
What you are noticing is that oil has a refractive index that is more similar to that of the fibers than water has. Still, water is closer to target than air, so paper gets a bit transparent with water too.
P.S. This is also related to your other question ("wet is dark"). If the object is thick (imagine a pile of paper, or sand). Wetting it will enable light to penetrate more. Less of it will be reflected back to you, making the object look darker.
This is a real effect, but it doesn't have anything to do with coma or any of the optical aberrations. It is caused by the fact that the effective focal length shortens as you tilt a lens. When your eyesight gets worse, you need a stronger focal length lens in your eyeglasses, and tilting the lenses has this effect. The problem with doing this all of the time is that it introduces distortions such as the coma you've pointed out in your question.
This presentation and this journal paper show the the effective focal length of a tilted lens from ray tracing simulations and from theory respectively. From the paper, the focal length for the tangential focal point (up and down as you look through your glasses) and the sagittal focal point (left and right as you look forward) are given from the paper by
$$
\begin{align}
f_{tan}&=f_0\frac{n-1}{n}\frac{\cos\theta\sqrt{n^2-\sin^2\theta}}
{\sqrt{n^2-\sin^2\theta}-\cos\theta}\\
f_{sag}&=f_0(n-1)\frac{1}{\sqrt{n^2-\sin^2\theta}-\cos\theta}
\end{align}
$$
where $n$ is the index of refraction of the material and $f_0$ is the original focal length. I've plotted $f/f_0$ for both of these in the figure below for an index of refraction of 1.5. I believe that this is special to a lens which has equal radii of curvature on both sides (bi-convex or bi-concave), but the results for other types of lenses will have similar outcomes.
Best Answer
the assertion that corrective lenses are not needed underwater is incorrect. diving masks with corrective lenses built-in have been in use for decades. the reason you yourself experience this effect is probably contained in Chris' and Martin's comments above.