Solving for p: Finding Distance from Convex Lens

[Nano]

Homework Statement

Given only the distance between the object and its image (p +q), how is it possible to find p, the distance of the object from the convex lens?

Homework Equations

1/p + 1/q = 1/f
in this case, p + q =40
also, the image is smaller than the original, so p > 2f

The Attempt at a Solution

I don't understand how to find p if q and f are unknown. I tried solving for q as q=40-p, but that didn't take me anywhere.

 

[Delphi51]

You need more information than you gave in part 1.
How did you know the image is smaller than the original - do you know what fraction it is?

 

[Nano]

It said if was 1/2 the size of the original. But how does that information help?

 

[Nano]

Ahh, I think I get it. It has something to do with the similar triangles formed by the object/image and a light ray passing through the center of the convex lens, right?

 

[Delphi51]

Yes, or you can use the formula relating the object and image heights to their distances from the lens to get a 2nd equation relating p and q.

 

[Nano]

Ok, thank you for your help!