(1) A virtual image -7 cm tall and 17 cm away from a mirror is created by an object 7 cm away from a mirror. How tall is the object? What kind of mirror created the image? What is its focal length?

Question

(2) If a 1.75 m tall man is looking at a plane mirror from an eye which is 15 cm from the top of their head, what is the minimum length that the mirror must be so that he can just barely see his whole body in the mirror? How far up from the ground must the mirror be placed?

Answer 1

(1) |(object size)/(image size)|
= |(object distance)/(image distance)|
(use absolute values above)

object size/7 = 7/17

object size = 49/17 = 2 15/17

1/f = -1/17 + 1/7
f = 17*7/(7-17) = -11.9 cm
A convex mirror formed the image.
The minus sign is in front of 1/17 because it is a virtual image

Answer 2

Draw an image diagram with three vertical lines spaced equal distances apart. (The separation distance does not matter, as long as they are equal). The three vertical lines represent the man, the mirror and the virtual image. The man and image will have equal height, at the left and the right. Mark a spot near the top of the left-most line representing his eye, 1.60 m up from the bottom.

A ray from his toes that gets reflected reaches his eye will strike the mirror 0.8 m from the floor. A ray from the top of his head that gets reflected will strike the mirror 1.675 m from the floor. There must be mirror between these to points to be able to see the entire body length. Drawing the figure will show you why and what the two answers are.