Answer to Question #190275 in Physics for cia

Question

An inverted image is magnified by 2 when the object is placed 22 cm in front of a concave mirror. Determine the image distance and the focal length of the mirror.

1 / f = 1 / do + 1 / di where do = 22 cm and M = 2

Answer 1

Let's first find the image distance from the magnification equation:

$$M=-\dfrac{d_i}{d_o},$$ $$d_i=-Md_o=-(-2)\cdot22\ cm=44\ cm.$$

Finally, we can find the focal length of the mirror from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$f=\dfrac{1}{\dfrac{1}{d_o}+\dfrac{1}{d_i}},$$ $$f=\dfrac{1}{\dfrac{1}{22\ cm}+\dfrac{1}{44\ cm}}=14.66\ cm.$$