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For compound lenses, the image formed by first lens acts as the imaginaryobject for the second lens.

In telescopes, the objective lens projects an image on its focal point which works as the object for the eyepiece. Per the property of convex lenses, the eyepiece magnifies the image. If the focal length of the eyepiece is smaller we'll get a higher magnification.

Now if the focal length of the objective lens is increased, it'll again project a small image on its focal point. So for two objective lenses with different focal length, it seems the image size should about the same.

So why does the magnification change?

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It's like leverage. The longer the distance from the objective lens to the virtual image, the larger the virtual image.

Imagine there's a piece of frosted glass at the focal point. It will show the virtual image.

Now the eyepiece looks at that virtual image with a magnifying glass. That also makes it look bigger.

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  • $\begingroup$ any reference for this? $\endgroup$
    – Amit Kumar Gupta
    Commented May 3, 2013 at 2:56
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    $\begingroup$ @articlestack: Wikipedia $\endgroup$
    – Mike Dunlavey
    Commented May 3, 2013 at 11:41
  • $\begingroup$ So in simple words, it is because of angular magnification. When focal length of objective lens increases, angle subtended by the objective lens gets decreased. Hens magnification gets increased. Am I correct? $\endgroup$
    – Amit Kumar Gupta
    Commented May 4, 2013 at 13:27
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    $\begingroup$ @articlestack: Suppose you have two stars, where the angular distance between them is .01 radian. Then if you have an objective lens that focuses them to an image plane, how big is the image of the two stars? It will be .01 times the focal length, right? 10cm -> .1cm, 100cm->1cm, 1000cm -> 10cm. So then if you look at that image plane with a keplerian eyepiece (magnifying glass), you're examining a small piece of a bigger image. $\endgroup$
    – Mike Dunlavey
    Commented May 4, 2013 at 18:34
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It is easy to understand that the higher the focal length is the narrower the angle of the image from the objective lens or mirror to the eyepiece. So the narrower the angle (higher focal length that is) the deeper the image can go into the eyepiece without losing focus. The lower the focal length is the shorter the depth of focus. It means that you have less play with your focuser with shorter focal length than longer focal length. In fact you can still get same magnification for both focal lengths but the one with shorter focal length will run out of its focus long before the one with a longer focal length. This is why you notice the expansion of the "star" as it goes out of focus in either direction. The longer focal length is more forgiving with the depth of focus thus giving you more play with your focuser. The longer focal length affords you to move more forward toward the objective lens or mirror to get larger image while still in focus than with shorter focal length which expands the image beyond the field of your eyepiece in use. It has a lot to do with the eyepiece ability to eat the whole image in one gulp.

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