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I understand that light entering a parallel block of glass at a non-90 degree angle will cause dispersion of colours within the block but that these will be refracted by the same degree upon exit so there will be no overall dispersion and will appear white. But in that case, why don't concave (or convex) lenses disperse?

Additionally, with a block of parallel glass, if it were sufficiently thick and wide, although different frequencies would eventually "catch up" to each other and merge upon exit, this would occur only after a distance equal to the distance they were dispersed inside the glass right? So the human eye, if positioned close enough to the exit side of the glass, would be able to see a rainbow correct?

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2 Answers 2

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They do. It's called chromatic aberration - each different frequency has a slightly different focus point, blurring the image by different amounts for the different colors. Modern lenses of high quality have multiple elements added specifically to address the issue of chromatic aberration.

What happens with flat glass can be explained by thinking of it in terms of the wave fronts instead of the ray paths, because that is closer to the physical optics. For a person looking directly through the glass, it messes up the phase relationship between waves of a different color, but our eyes aren't sensitive to that, anyway. A spherical wave front on one side will be spherical on the other, for all colors (same for flat). All of the spherical wave fronts that share a center on one side of the glass will have a center that is on the same line on the other side. Because of this, if you look through the glass at an angle you'll observe a small chromatic aberration.

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  • $\begingroup$ "All spherical wave fronts that share a center on one side of the glass will also share a center on the opposite side." — this is wrong. The output waves' centers are shifted just as the geometric-optical rays are. It's easy to see if you use beams instead of rays/spherical-waves. The result is shown experimentally in this answer. $\endgroup$
    – Ruslan
    Nov 19, 2021 at 20:12
  • $\begingroup$ @Ruslan Thanks. I was a bit iffy (hence the "take it with a grain of salt" bit), but I've corrected the answer now. Although there is an important difference. In your experiment you're looking at a source in the medium. With a pane of glass the ray paths bend and then unbend. The effect is probably still there, though, so I won't undo the correction. $\endgroup$ Nov 19, 2021 at 21:16
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Sean E. Lake's answer is right: convex lenses disperse light like prisms and that effect is known as chromatic aberration - which is easily noticeably by zooming in in the corners of photographs taken with cheap cameras.

I would add to his answer the reasons why usual convex lenses disperse light much less than a prisma does. For example, it's difficult to project an spectrum using a pair of common eyeglasses, a magnifier or even a photography objective.

The first reason is that lenses are usually thin, and therefore their sides are nearly parallel - at least compared with a prism. Dispersion is very related to angle between faces, and lens faces are just a few degrees apart while in a prism they could be at 60º.

The second reason doesn't hold for simple lenses (like eyeglasses or magnifiers) but holds for more complex systems equivalent to a convex lens (like photography objectives): lenses are combined in a way that most of their chromatic aberration get cancelled.

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    $\begingroup$ As an example with eyeglasses, I believe it is possible in many cases to tilt them to an extreme angle to the sun and cause a thin rainbow to be projected under them. $\endgroup$
    – Darren
    Jun 23, 2017 at 22:49
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    $\begingroup$ Although possible, we are more likely to get a rainbow using the edge of the eyeglasses - which is in fact a prism - than using the lens itself. $\endgroup$
    – Pere
    Jun 24, 2017 at 6:56
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    $\begingroup$ It's also easily noticed by wearing corrective lenses and looking through any part but the dead center. $\endgroup$ Jun 24, 2017 at 21:40
  • $\begingroup$ It depends on how strong the correction is - and probably on the kind of material, too. With a few dioptres I can't notice any kind of chromatic aberration in my eyeglasses. $\endgroup$
    – Pere
    Jun 24, 2017 at 22:41
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    $\begingroup$ @Pere Look to the edge of the glasses - the closer the object is to the edge, the higher the chromatic aberration. It essentially makes one edge of the observed object red-yellowish, and the other edge bluish (of course, it's not really the edge, the whole object's image is shifted depending on colour, but it's easiest to see on the edge). It depends a lot on the thickness of the glass (or plastic), and overall quality of the lens, but it should be very slightly visible even on good and weak glasses. $\endgroup$
    – Luaan
    Aug 13, 2019 at 6:28

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