Question

An object 25.4-centimeters high is located 91.5 centimeters from a concave mirror, focal length 15 centimeters.

Answer 1

A) 17.9 cm

We have:

$f=+15 cm$ is the focal length of the mirror (for concave mirror, the focal length is positive)

$p=91.5 cm$ is the distance between the object and the mirror

$q=?$ is the distance between the image and the mirror

We can then use the mirror equation to find q:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\\\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{15 cm}-\frac{1}{91.5 cm}=0.056 cm^{-1}\\q=\frac{1}{0.056 cm^{-1}}=17.9 cm$

B) -5.0 cm

The height of the image can be determined by using the magnification equation:

$\frac{q}{p}=-\frac{h_i}{h_o}$

where

$h_i = ?$ is the heigth of the image

$h_o = 25.4 cm$ is the height of the object

Substituting and re-arranging the formula, we find

$h_i = -h_o \frac{q}{p}=-(25.4 cm)\frac{17.9 cm}{91.5 cm}=-5.0 cm$

And the negative sign means the image is inverted.