Question

A concave mirror has a radius of curvature of 24.0cm. Determine the object position for which the resulting image is upright and larger than the object by a factor of 3.00. Is the image real of virtual?

Answer 1

Answer on Question #52215-Physics-Optics

A concave mirror has a radius of curvature of $24.0\mathrm{cm}$. Determine the object position for which the resulting image is upright and larger than the object by a factor of 3.00. Is the image real of virtual?

Solution

In this case the image is virtual. $R = 24.0\mathrm{cm}$.

$$\left| \frac {v}{u} \right| = 3.$$

$v = -3u$ where $u$ is object distance and $v$ is image distance.

The negative sign arises because image distance is behind mirror (virtual).

Using mirror formula

$$\frac {1}{u} + \frac {1}{v} = \frac {2}{R}$$

with $v = -3u$

$$\frac {1}{u} - \frac {1}{3 u} = \frac {2}{24}.$$ $$\frac {2}{3 u} = \frac {1}{12}.$$ $$u = \frac {24}{3} = 8 \mathrm{~cm}.$$

Answer: 8 cm; virtual.

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