How do I determine the distance between two lenses in a telephoto lens system?

[creative_wind]

Homework Statement

A simple camera telephoto lens consists of two lenses. The objective lens has a focal length f1 = +36.0 cm. Precisely 33.0 cm behind this lens is a concave lens with a focal length f2 = -10.0 cm. The object to be photographed is 3.67 m in front of the objective lens.

(a) How far behind the concave lens should the film be placed?

(b) What is the lateral magnification (ratio of image height to object height) of this lens combination?

Homework Equations

1/f=1/d_i + 1/d_o

M=-d_i/d_o

The Attempt at a Solution

My understanding is that the d_i1 (the objective lens) is the d_o2 (for the second/concave lens). Calculating d_i1 gives me 0.399 m which is greater than the distance between the two lenses, so that would mean d_o2 on the same side that the film would be on. I tried using 0.399m - 0.33 m = 0.069m = d_o2 to calculate d_i2 anyways, but that answer is wrong. I'm stuck as to what value to use for d_o2. As for part b) I know to find the magnification of each lens and then multiply the two magnification values to get the final magnification. I just need to figure out part a). Thanks so much for any help!

 

[tiny-tim]

My understanding is that the d_i1 (the objective lens) is the d_o2 (for the second/concave lens). Calculating d_i1 gives me 0.399 m which is greater than the distance between the two lenses, so that would mean d_o2 on the same side that the film would be on. I tried using 0.399m - 0.33 m = 0.069m = d_o2 to calculate d_i2 anyways, but that answer is wrong. I'm stuck as to what value to use for d_o2. As for part b) I know to find the magnification of each lens and then multiply the two magnification values to get the final magnification. I just need to figure out part a). Thanks so much for any help!

Hi creative_wind!

You really need to show us what you did if we're going to see where the mistake is.

I'll guess … did you remember to make the 1/f for the second lens negative?

 

[creative_wind]

Okay so as I wrote above I was using 0.399 m -0.33 m = 0.069 m. It should be 0.33 m - 0.399 m = -0.069 m, which gives me the correct answer. I can't say I really understand the concept of locating the position of the image of the first lens since it never really forms (hits second lens first) but at least I understand how to answer the question and could do it on an exam now. Thanks for your help!

 

[tiny-tim]

… don't talk to me about reality …

I can't say I really understand the concept of locating the position of the image of the first lens since it never really forms …

You're really into reality aren't you?

Forget reality!

phsyics is reality … maths (including geometry) isn't …

and this is a geometrical trick …

the rays behave as if they did come from the virtual image …

just like the image in an ordinary flat mirror, which saves you the effort of having to draw incidence and reflection angles carefully!