Thin lenses: A thin converging lens is found to form an image of a distant building 24 cm from the lens. If an insect is now placed 16 cm from this lens, how far FROM THE INSECT will its image be formed?

Question

Quizplus · Accepted Answer

We can use the thin lens equation: 
1/f = 1/do + 1/di 
Where f is the focal length of the lens, do is the object distance (distance of the building from the lens), and di is the image distance. Since the building is at a very far distance, we can assume that do is essentially infinity and thus 1/do is approximately 0. 
So we have: 
1/f = 0 + 1/di 
Rearranging, we get: 
di = f 
Since we are given that the image of the building is formed 24 cm from the lens, we know that the focal length of the lens is also 24 cm. 
Now we can use the thin lens equation again, but with the insect as the object distance: 
1/24 = 1/16 + 1/di 
Solving for di, we get: 
di = 32 cm 
So the image of the insect will be formed 32 cm from the lens, which is 16 cm past the insect.

Thin Lenses: a Thin Converging Lens Is Found to Form