Answer to Question #167593 in Physics for gayle

Question

A 20 cm inverted image is formed in a concave mirror with a focal length of 15 cm. If the object is placed 25 cm away from the mirror (a) What is the height of the object? (b) How far is the image from the mirror? (c) Describe the image. 

Answer 1

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

$$\dfrac{1}{d_0}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$d_i=\dfrac{1}{\dfrac{1}{f}-\dfrac{1}{d_0}}=\dfrac{1}{\dfrac{1}{15\ cm}-\dfrac{1}{25\ cm}}=37.5\ cm.$$

Then, we can find the height of the object from the magnification equation:

$$\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o},$$ $$h_o=-\dfrac{h_id_o}{d_i}=-\dfrac{(-20\ cm)\cdot25\ cm}{37.5\ cm}=13.3\ cm.$$

The image is inverted, enlarged and real.