In a simple telescope (converging lenses, long focal length objective and short focal length eyepiece), why is the distance between the objective and the eyepiece approximately equal to the sum of their focal lengths?
Sorry if this sounds like it is straight off a homework question, but well, it is. However, it really got me thinking about it.
I’m not looking for just a quick answer so I can get my points. I really want to understand why it works out this way. It seems logical enough, but I don’t know the real reason why the distance between is equal to the sum of the focal lengths. Can someone explain why this is? Maybe a diagram/drawing? Thanks.
I know the equation for lenses in contact with one another, but is there an equation for lenses that are apart like in this case?
It’s simple, really. The first lens (objective) creates a virtual image of distant objects at its focus, and the second lens (eyepiece) is placed to magnify that virtual image by putting it at its focus.
So that’s really all there is to it? Let me see if I’ve got thsi straight. If you go down the telescope, here’s what happens. The big objective lense gathers light and eventually focuses it to a sharp point. Then the light leaves this point invetered and the rays are going away from each other to make an enlarged image. Then a short distance away, they hit the eyepiece, where they are re-bent to be straight and focused again.
It’s close. The “sharp point” focus is only valid for a point source of light like a distant star or a laser. The more general description is that the light from each individual point on the object is focused to a separate point in the middle of the telescope, forming an inverted image there.
(By the way, I was wrong before – it’s a “real” image, not a “virtual” image. It can be projected onto a piece of paper at the focal point.)
The second lens doesn’t quite “straighten out” the light; it just bends it in the manner of a typical magnifying glass. What you see is then a virtual (I got it right this time) image that’s a larger version of the first real image.
Since the eyepiece magnifier doesn’t invert anything, the final view is indeed reversed in all directions, just as if it had been rotated 180 degrees. More complex optics, typically mirrors and/or prisms, can re-invert the image to make it match the real-world orientation; that’s how fancy binoculars and so-called “terrestrial” telescopes work. (Many reflector telescopes have a “diagonal” mirror that reverses the image in one direction, and some refractors also include an optional “star diagonal” to make it easier to observe things high overhead and which incidentally does the same single-axis reversal.)