Strange Refraction from Glasses

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I recently got a stronger prescription for my glasses, and I now notice something strange. If I look at an object, say my computer screen through the left edge of the left lens, the left side of the screen will be red, while the right side will be blue. This happens for any object the is somewhat bright. Obviously the light is refracting in the lens, but I don't understand why the left side is red, and the right side is blue.

I've attached a picture that I hope makes this comprehensible.
 

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Haven't seen the pic yet, but it is probably a case of chromatic aberration.
This is due to the different refractive strength of the glass for different colours.
 
This is because of dispersion. Lights of different wavelengths, which make up white light, have got different refractive indices, and so bends at different angles when being refracted into the glass. But the lights of various wavelengths from neighbouring points also break up, and these all join up so that the resulting emergent ray is again white. Only the rays in the sides don’t have matching wavelengths to mix up with and so you see this effect only on the sides. Notice that one side would be violet and the other side red.

Drawing a diagram would help a lot in understanding. Unfortunately, I am horrible at making picture files.
 
Strong prescriptions have large differences in thickness from the edge to the center of the lens, and therefor they will act as a prism, dispersing light of different frequencies by different amounts. Generally, well-figured lenses perform very well when you are looking through the optical center, but the performance degrades toward the edges. I have a pair of progressive lenses in my regular glasses, and though they are pretty good performers when looking through the centers (vertical zone from the OC down through the bottom area that is corrected for close vision), when I turn my head, I see axial shear (scissoring) in vertical lines like window frames, door frames, etc. My next lenses will be plain bifocals, not progressives for just this reason.