Question

A concave mirror has a focal length of 0.29 m. If an object produces a real image 0.40 m from the mirror, where is it located?

Answer 1

In order to calculate the object's position, we can use the formula below:

$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$

Where f is the focal length, do is the object distance and di is the image distance.

So, using f = 0.29 and di = 0.4, let's solve for do:

$\begin{gathered} \frac{1}{0.29}=\frac{1}{d_o}+\frac{1}{0.4}\\ \\ \frac{1}{d_o}=\frac{1}{0.29}-\frac{1}{0.4}\\ \\ \frac{1}{d_o}=3.448-2.5\\ \\ \frac{1}{d_o}=0.948\\ \\ d_o=\frac{1}{0.948}\\ \\ d_o=1.055\text{ m} \end{gathered}$

Therefore the object's position is 1.055 meters.