Question

what is the focal length of a convex mirror that produces an image that appears 15.0 cm behind the mirror when the object is 27.5 cm from the mirror?

Answer 1

We can find the focal length of a convex mirror from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$f=\dfrac{1}{\dfrac{1}{d_o}+\dfrac{1}{d_i}},$$ $$f=\dfrac{1}{\dfrac{1}{27.5\ cm}+\dfrac{1}{-15\ cm}}=-33\ cm.$$

By the sign convention for spherical mirrors, the focal length is negative for convex mirrors. The sign minus simply denotes that this is convex mirror. Therefore, the focal length of a convex mirror is 33 cm.