Answer to Question #287066 in Optics for monkey

Question

An object 6 cm tall is placed 9 cm in front of a concave mirror that has a focal length of 18cm. Round your answers to 2 decimal places.  

Answer 1

(a) We can find the image distance from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$d_i=\dfrac{1}{\dfrac{1}{f}-\dfrac{1}{d_o}},$$ $$d_i=\dfrac{1}{\dfrac{1}{18\ cm}-\dfrac{1}{9\ cm}}=-18\ cm.$$

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

(b) We can find the image height from the magnification equation:

$$\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o},$$ $$h_i=-\dfrac{h_od_i}{d_o}=-\dfrac{6\ cm\times(-18\ cm)}{9\ cm}=12\ cm.$$

The sign plus means that the image is upright.