Question

A real image is four times as far from a lens as is theobject.
What is the object distance, measured in focal lengths? ____from the lens

Answer 1

Answer:

1.25 focal lengths

Explanation:

The lens equation states that:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$

where

f is the focal length

p is the object distance

q is the image distance

In this problem, the image is 4 times as far from the lens as is the object: this means that

$q=4p$

If we substitute this into the lens equation and we rearrange it, we get

$\frac{1}{f}=\frac{1}{p}+\frac{1}{4p}=\frac{4+1}{4p}=\frac{5}{4p}\\p=\frac{5}{4}f=1.25 f$

so, the object distance measured in focal lengths is

1.25 focal lenghts