Question

Find the location of the image if an object 2 cm in height is 5.0 cm in front of a concave mirror of focal length 10.0 cm. How large is the image ?

Answer 1

Find the location of the image if an object $2\mathrm{cm}$ in height is $5.0\mathrm{cm}$ in front of a concave mirror of focal length $10.0\mathrm{cm}$. How large is the image?

Mirror magnification:

$$m = \frac {h _ {i}}{h _ {o}} = - \frac {d _ {i}}{d _ {o}} \rightarrow h _ {i} = - h _ {o} \frac {d _ {i}}{d _ {o}}$$

Where $d$ – distance, $h$ – height. Indexes $i$ and $o$ corresponds to the image and object respectively.

Mirror equation:

$$\frac {1}{d _ {o}} + \frac {1}{d _ {i}} = \frac {1}{f} \rightarrow d _ {i} = \frac {1}{\frac {1}{f} - \frac {1}{d _ {o}}} = \frac {f d _ {o}}{d _ {o} - f}$$

Thus:

$$h _ {i} = - h _ {o} \frac {\frac {f d _ {o}}{d _ {o} - f}}{d _ {o}} = h _ {o} \frac {f}{f - d _ {o}}$$ $$h _ {i} = 0. 0 2 * \frac {0 . 1 m}{0 . 1 m - 0 . 0 5 m} = 0. 0 4 m$$

Answer: $h_i = 0.04m$