Chapter 44: Problem 22

Question: An illuminated arrow forms a real inverted image of itself at a distance $d~=~40~{\rm cm}$, measured along the optic axis of a lens (Fig 32 Chap 44). The image is just half the size of the object. What kind of lens must produce this object. How far from the object must the lens be placed. What is the focal length of the lens.

Solution: The lens must be convex. Now since m = -I/O, we have that m=-0.5 and d = O+I = O(1-m) = 3 O/2, hence $O~=~80/3~{\rm cm}$, and $I~=~40/3~{\rm cm}$. We have that

$${1\over O}+{1\over I}~=~{1\over f}$$

which gives $f~=~80/9~{\rm cm}$.