Find the Relation Between the Focal Length and the Object Distance

Question

There is a specific case where for a single converging lens the object distance equals the image distance. Find the relation between the focal length and the obect distance in this case. 

 

Answer 1

The key equation is the lens equation:

 

1/p + 1/q =  1/f    where p is the object distance, q is the image distance and f is focal length.

 

Since the image distance is equal to the object distance we can write

 

2/p  =   1/f

 

so  f =  p/2