What is the focal length of the second lens in an afocal system?

[Lunar_Lander]

Homework Statement

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?

Homework Equations

Lens equations, f_s=(f₁*f₂)/(f₁+f₂).

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?

 

[Lunar_Lander]

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

 

[Redbelly98]

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.