# Homework Help: Focal Length problem for astronomy class

1. Mar 26, 2012

### Finnegan

1. The problem statement, all variables and given/known data
A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires an f/10 beam at its input. Compute the focal length of a 50mm diameter lens that, when inserted in the beam 150mm in front of the unmodified focal plane, produces the required beam.

2. Relevant equations
Focal ratio = focal length/diameter of entrance aperture. The notation f/10 means that the focal ratio is 10, not that the diameter is 10.

3. The attempt at a solution
I tried drawing some diagrams, which obviously can't be reproduced with ease here. I think the main problem might be that I'm not familiar enough with telescopes to know how one uses a spectrometer or an extra lens--must they go outside the telescope, thereby making the focal length longer, or can one or both be placed inside the telescope?

I also tried making up variables--saying, for instance, that the telescope's original focal length is 750 and its entrance diameter 100, which fits for f/7.5. But then I was stymied by the above fact: I don't know how a spectrometer works. I think if someone can give me information about the mechanics of the problem I should be able to make a better attempt.

Thanks.

2. Mar 27, 2012

### chemisttree

This isn't a question about the spectrometer. The only reason it was mentioned is to provide a rationale for the f10 requirement.

I will give you a hint: you need a lens with a negative focal length. These lenses are sometimes called barlows or Smythe lenses.

3. Mar 27, 2012

### Finnegan

Okay. I understand that the question doesn't focus on the spectrometer, but I'm still pretty sure that I need to understand how the setup would work in order to make any progress. If I could just get a text diagram of how the device would look, like so:

telescope lens--extra lens--focal plane--spectrometer

Or

extra lens--telescope lens--focal plane--spectrometer

As of right now, I don't know how the variables (focal length and lens diameter) have to vary, so I can't make any inferences.

4. Mar 29, 2012

### chemisttree

Does this sound like it is possible for the 50 mm lens to be placed in front of the objective? 150 mm in front of the unmodified focal plane.