A camera has a lens that has an adjustable film distance used for focusing purposes.When the object being photographed is at a very large distance,the distance from the lens to the film is 50.0 mm.What would be the lens-to-film distance for an in-focus object 2.00 m from the camera?
A) 66.7 mm
B) 40.0 mm
C) 51.3 mm
D) 48.8 mm

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 from the lens (2.00 m in this case), and di is the image distance from the lens (what we are solving for). 
When the object is at a very large distance, we can assume that the object distance is effectively at infinity, so 1/do is essentially 0. 
Thus: 
1/f = 0 + 1/di 
Solving for di: 
di = f = 50.0 mm 
Now we can use the same equation with the new object distance: 
1/f = 1/do + 1/di 
1/f = 1/2000 + 1/di 
Solving for di: 
di = 51.3 mm 
Therefore, the lens-to-film distance for an in-focus object 2.00 m from the camera is 51.3 mm, which is choice C.

A Camera Has a Lens That Has an Adjustable Film