# Homework Help: A system of two lenses

1. Oct 14, 2011

### Lunar_Lander

1. The problem statement, all variables and given/known data

An object at a distance a1 in front of a convex lens with the focal length f1 is imaged at a distance b1. A second lens at the distance d from the first lens with the focal length f2 is then imaging this Image with the image distance b2.

a) Give the image distance b1 as a function of f1 and a1, as well as the image distance b2 as function of d, a1, f1 and f2.

b) What is the focal length of a System of two lenses which distance d approaches zero?

c) Which focal length must the second lens in b) have to compensate the action of the first lens? How is such a lens called?

2. Relevant equations
Lens equations, fs=(f1*f2)/(f1+f2).

3. The attempt at a solution
For b) I have found the equation given above. How can I figure out c)? I think it is an afocal system, is that correct? For that, the focal length must be f2=d-f1?

2. Oct 15, 2011

### Lunar_Lander

For clarification, here is a picture of the system I am asking about.

#### Attached Files:

• ###### Lens System.png
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3. Oct 15, 2011

### Redbelly98

Staff Emeritus
If I interpret the question in part (c) correctly, the image formed by lens #2 must be located at the original object. The usual equation relating object, image, and focal length can be used to work out what f2 must be to achieve this.

I'm not sure what the name is for such a lens, sorry.