# Convex lenses

#### Nano

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

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

3. 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

Homework Helper
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

Homework Helper
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!

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving