A convex mirror has a focal length of −27 cm. What is the object distance if the image distance is −16 cm?

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The following formula relates object distance, image distance, and focal length for convex mirrors:

1/(focal length) = 1/(object distance) + 1/(image distance)

or

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.

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