Optimizing Telescope Lens Distance for Distant and Nearby Objects

[map7s]

A telescope has lenses with focal lengths f1 = +25.7 cm and f2 = +5.5 cm.
(a) What distance between the two lenses will allow the telescope to focus on an infinitely distant object and produce an infinitely distant image?
(b) What distance between the lenses will allow the telescope to focus on an object that is 5.0 m away and to produce an infinitely distant image?


I got the answer to the first part using the equation L=f obj +f eyp

however I do not know how to do the second part. I tried using the thin lens equation but I was not sure how to factor in the 5 m. (I did remember to convert to cm, so I know that that was not the problem.)

 

[robb_]

Since the light must pass through two lenses, you must apply the lens equation twice. Treat the image produced from the first lens as the object for the second lens. Be careful of the signs. (+ and -)

 

[map7s]

So

(1/25.7)-(1/500)=1/x

and then

(1/5.5)-(1/x) = 1/ d i

and then whatever answer you got, would you then add that to the sum of the two different foci (i.e. answer from part one)?

does that look right or did I mess up a sign?

 

[robb_]

I think you have over simplified slightly. The first equation looks okay. That will give you the image distance, that is the distance from the first lens to the first image. You do not know the distance between the lenses, so you do not know how far this image is from the second lens. Understand?

 

[map7s]

Oh, okay...I think that was what was messing me up...but I don't know how to set up an equation that solves for the distance between the lenses

if I know that d i is equal to infinity, then...? or does that even matter?

 

[robb_]

Draw a picture and note that the distance between the lenses is an unknown, a variable.

 

[map7s]

so when I did that, it kind of created two right triangles (or one obtuse triangle if you don't include the image/object in between)...

 

[robb_]

So, did you draw a ray trace of this system? I don't think that is needed but a good idea none the less.
Use the lens equation twice, noting that you do not know the separation by including appropriate variables in your equations. hope that helps.

 

[map7s]

Sorry...yes that did help A LOT. Thank you sooooo much!