Question

A magnitude, inverted image is located to a distance of 32.0 com concave mirror with a focal length of 12.0 cm . Determine the object distance and tell whether the image is real or virtual

Answer 1

The mirror equation is the following (see https://byjus.com/physics/mirror-equation/):

$$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$$

where $f = 12.0cm$ is the focal length, $v = 32.0cm$ is the distance to the image, $u$ is the distance to the object. Thus, obtain:

$$u = \dfrac{vf}{v-f} = \dfrac{32.0cm\cdot 12.0cm}{12.0cm-32.0cm} = -19.2cm$$

Since $v>0$, the image is located behind the mirror and thus is a virtual one.

Answer. -19.2cm, virtual.