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** Up:** Paraxial Optics
** Previous:** Example 13.1: Concave mirrors

*Question:* How far must an object be
placed in front of a convex mirror
of radius of curvature cm in order to ensure that the
size of the image is ten times less than the
size of the object? How far behind the
mirror is the image located?

*Answer:* The focal length of a convex mirror is *minus*
half of its radius of curvature (taking the sign convention for
the focal lengths of convex mirrors into account). Thus, cm.
If the image is ten times smaller than the object then the magnification
is
. We can be sure that , as opposed to , because
we know that images formed in convex mirrors are always virtual and
upright.
According to Eq. (352), the image distance
is given by

where is the object distance. This can be combined with Eq. (358)
to give

Thus, the object must be placed cm in front of the mirror.
The image distance is given by

Thus, the image is located cm behind the mirror.

** Next:** Example 13.3: Converging lenses
** Up:** Paraxial Optics
** Previous:** Example 13.1: Concave mirrors
Richard Fitzpatrick
2007-07-14