optics

[greenseeking]

For a telescope with a convex lens with a short focal length as its ocular, the objective is a:

a. concave lens with a focal length that is very long
b. concave lens with a focal length that is vry short
c. convex lens with a focal length that is very long
d. convex lens with a focal length that is very short...

Answer is C-- Can anyone explain why the focal length has to be very long please?

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[milski]

The total magnification of the telescope is m=-Fo/Fe, where Fo is the focal length of the objective and Fe - the focal length of the eyepiece (ocular). It's obvious that if you want good magnification, you want to increase Fo and decrease Fe.

For derivation of the formula: http://www.tutorvista.com/content/physics/physics-iv/optics/astronomical-telescope.php

The diagram should make it fairly clear why it's calculated that way, but if you have question, I'll be happy to answer. Just did not feel like retyping the whole page.

 

[greenseeking]

The total magnification of the telescope is m=-Fo/Fe, where Fo is the focal length of the objective and Fe - the focal length of the eyepiece (ocular). It's obvious that if you want good magnification, you want to increase Fo and decrease Fe.

For derivation of the formula: http://www.tutorvista.com/content/physics/physics-iv/optics/astronomical-telescope.php

The diagram should make it fairly clear why it's calculated that way, but if you have question, I'll be happy to answer. Just did not feel like retyping the whole page.

wow thanks got it. but how were we supposed to figure out that m=-fo/fe??? I wouldn't have figured it out on the test...

 

[milski]

Well, that's the hard question, is not it. In theory you can stop for a moment and try to draw the ray-diagram of how a telescope works. That can be pretty time consuming. One way to shortcut things is to consider separately the two choices that you have. First, what is a concave lens as objective going to do? Not much, really, since no matter how far you are from it, it will always generate a smaller image than what you would have without it. So it must be convex.

Telescopes also tend to be big. If a shorter focal length of the objective was going to give you better magnification, most of them would be really tiny. And a huge telescope with a short focal length does not make much sense. So it must be a convex lens with long focal distance.

I don't know how much of that explanation is realistic and how much just a rationalization of the correct answer - I don't have the formula memorized but I did know the basic relation as an obscure fact.

 

[greenseeking]

Well, that's the hard question, is not it. In theory you can stop for a moment and try to draw the ray-diagram of how a telescope works. That can be pretty time consuming. One way to shortcut things is to consider separately the two choices that you have. First, what is a concave lens as objective going to do? Not much, really, since no matter how far you are from it, it will always generate a smaller image than what you would have without it. So it must be convex.

Telescopes also tend to be big. If a shorter focal length of the objective was going to give you better magnification, most of them would be really tiny. And a huge telescope with a short focal length does not make much sense. So it must be a convex lens with long focal distance.

I don't know how much of that explanation is realistic and how much just a rationalization of the correct answer - I don't have the formula memorized but I did know the basic relation as an obscure fact.

Wow awesome thanks a lot. I really appreciate your help!

 

[milski]

Wow awesome thanks a lot. I really appreciate your help!

No problem, you're welcome!