Answer to Question #211033 in Physics for Festus

Question

An object 5cm in height is placed 10cm from a curved mirror and produces an image of 6.5cm height. Where is the image located and what type of mirror is this?

Answer 1

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

$$\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o},$$ $$d_i=-d_o\dfrac{h_i}{h_o},$$ $$d_i=-10\ cm\cdot\dfrac{6.5\ cm}{5\ cm}=-13\ cm.$$

The sign minus means that the image is virtual and located behind the mirror.

(b) Let's find the focal length of the mirror from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$f=\dfrac{1}{\dfrac{1}{d_o}+\dfrac{1}{d_i}},$$ $$f=\dfrac{1}{\dfrac{1}{10\ cm}+\dfrac{1}{-13\ cm}}=43.3\ cm.$$

The focal length is positive for concave mirrors. Therefore, it is a concave mirror.