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Textbook representation for light passing through a convex lens

This image is a representation for light passing through a convex lens. It shows light entering from air to glass. When the light enters the glass we can see that it bends towards the normal. Now when the ray of light leaves the glass and enters the air again, we see no refraction.

What I expect:

The ray of light should bend away from normal once it exits the glass because it is going from an optically denser medium to a rarer medium.

Is it just a bad representation or the bend is negligible or I am getting something wrong?

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    $\begingroup$ Your image is using the "thin lens approximation"; note that the "corners" on the light rays are not quite on either surface of the glass. Useful search terms: lens maker's equation, plano-convex lens, or even plano-concave lens. $\endgroup$
    – rob
    Aug 12, 2021 at 19:52
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    $\begingroup$ That diagram is very poorly drawn. It does not represent reality. $\endgroup$ Aug 12, 2021 at 19:55
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    $\begingroup$ Thanks for the help, so to get a rough idea of how a lens forms an image, we choose not to draw that stuff, making it clumsy, but it does get considered when we formulte the lens equation $\endgroup$ Aug 12, 2021 at 20:09
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    $\begingroup$ Where is that diagram from? Unless there's a specific reason not to, please always cite your sources. $\endgroup$
    – ACuriousMind
    Aug 13, 2021 at 8:01
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    $\begingroup$ @ACuriousMind see google.com/… and try reverse image searching, that diagram is near identical to probably hundreds of other pictures that show the same thing (bending in the middle). $\endgroup$
    – Krupip
    Aug 13, 2021 at 20:05

4 Answers 4

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They technically should "bend" because of refraction, and a more accurate drawing would be this:

Enter image description here

But drawings like the one that you show usually just tell you the net effect of the lens, i.e. treating the lens as a black box and not a series of interfaces.

In the derivation of the thin lens equation, however, both curved surfaces, refractive indices, and radii of curvature are taken into account.

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You are right. The drawing shown in your question is quite poor.

Here is a much better drawing, which correctly shows the refraction of rays on both convex surfaces. The rays bend towards the normal when entering the glass. And they bend away from the normal when exiting the glass.

enter image description here
(image from Toppr - Convex Lens)

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    $\begingroup$ But doesn't the top and bottom of the lens introduce a lot of distortions/aberrations? $\endgroup$ Aug 13, 2021 at 7:17
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    $\begingroup$ I don't think the drawing is poor. It's an easy and fast way to reach a qualitative result. It's a model after all. $\endgroup$ Aug 13, 2021 at 7:30
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    $\begingroup$ I agree with @infinitezero - the original drawing is good for what it's intended for. I'm guilty of cluttering my own diagrams with extraneous details, but even I wouldn't draw the rays passing through a lens accurately - especially as I'm often illustrating achromats $\endgroup$
    – Chris H
    Aug 13, 2021 at 7:55
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    $\begingroup$ @PeterMortensen most certainly there is focus blur, both lateral and longitudinal, for any spherical lens. But here I think the OP will be satisfied with the paraxial, monochromatic approximations. $\endgroup$ Aug 13, 2021 at 15:00
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That diagram shows what's called the "thin lens" approximation.

In real life, lenses have thickness, and light rays get refracted both when entering and exiting the material. But in practice, this thickness tends to be very small compared to the lenses' focal length. Ignoring it makes the equations much simpler.

So in introductory discussions of optics, physicists tend to use the "thin lens" approximation: pretend that the lens has no thickness, and is just a plane that magically changes the angle of any light that touches it. This makes it easier to discuss the most important properties of lenses (the way they focus or un-focus light to make images) without getting bogged down by smaller details.

That's what's happening in this image: the diagram-maker is pretending that light only gets refracted once, when it passes through the magic plane, instead of twice, when it enters and exits the glass.

(Of course, like any approximation, the thin lens approximation isn't perfect. Ignoring the actual details of the lens material means you can't predict things like chromatic aberration. So this approximation is mainly used to get an intuition for how lenses work, and isn't actually used in, say, manufacturing real lenses for cameras.)

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You can think of a convex-convex lens as (approximately) one prism on top of another. The light rays bend at both air interfaces.

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