Question

A 10.0 cm object is 5.0 cm from a concave mirror that has a focal length of 12 cm. What is the distance between the image and the mirror?

Answer 1

Let's use the mirror equation to solve the problem:

`(1)/(f)= (1)/(d_o)+ (1)/(d_i)`
where f is the focal length of the mirror,
`d_o` the distance of the object from the mirror, and
`d_i` the distance of the image from the mirror.
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for
`d_i` by using the numbers given in the text of the problem:

`(1)/(12 cm)= (1)/(5 cm)+ (1)/(d_i)`

`(1)/(d_i)= -(7)/(60 cm)`

`d_i = -8.6 cm`
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.

Answer 2

The answer is -8.6 cm