A convex mirror has a focal length of −27 cm. What is the object distance if the image distance is −16 cm?
The following formula relates object distance, image distance, and focal length for convex mirrors:
1/(focal length) = 1/(object distance) + 1/(image distance)
1/fo = 1/do + 1/di
The image distance being negative means that it is a virtual upright image located behind the mirror.
1/(-27 cm) = 1/do + 1/(-16)
-.037 cm^-1 = 1/do + (-.0625 cm)
.0255 cm^-1 = 1/do
39.22 cm = do
What this means is that an object placed 39.22 cm in front of the convex mirror with a focal length of -27 cm will possess a virtual image, 16 cm behind the mirror.