Question

What is the the focal length of a convex mirror which produces an image 1/5 the size of an object located 17 cm from the mirror?
−2.4cm
3.2cm
−4.2cm
5.3cm

Answer 1

Answer on Question#52729 - Physics - Optics

What is the focal length of a convex mirror which produces an image 1/5 the size of an object located 17 cm from the mirror?

-2.4cm

3.2cm

-4.2cm

5.3cm

Solution:

The magnification of the convex mirror is given by

$$M = - \frac {f}{a - f},$$

where $f$ – is the focal length of the mirror, and $a$ – is the object distance. Since $M = \frac{1}{5}$ and $a = 17$ cm, we obtain

$$f = - \frac {M \cdot a}{1 - M} = - \frac {\frac {1}{5} 17 \mathrm{~cm}}{1 - \frac {1}{5}} = - 4.2 \mathrm{~cm}$$

Answer: -4.2 cm.

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