# A convex spherical mirror, whose focal length has a magnitude of 15.0 \ cm, is to form an image...

## Question:

A convex spherical mirror, whose focal length has a magnitude of {eq}15.0 \ cm {/eq}, is to form an image {eq}10.0 \ cm {/eq} behind the mirror.

a) Where should the object be placed?

b) What is the magnification of the mirror?

## Convex Mirror:

Convex mirror produces an image behind the mirror making its image distance to be negative. Also, in convex mirror, the focal length and radius of curvature is negative since it is behind the mirror.

The formula for getting the focal length and magnification are the following:

{eq}\frac{1}{f} = \frac{1}{s} + \frac{1}{s'} {/eq}

{eq}m = \frac{-s'}{s} {/eq}

Given:

f = -15 cm

s' = -10 cm

Solution:

Part A.

In Convex Mirror, the focal point is behind the mirror. Thus, it has negative focal length and radius of curvature.And since the image formed is also behind the mirror, it is also negative.

Using the formula for getting the focal length, we can solve for the object distance s.

{eq}\frac{1}{f} = \frac{1}{s} + \frac{1}{s'} \\ \frac{1}{s} = \frac{1}{f} - \frac{1}{s'} \\ \frac{1}{s} = \frac{1}{-15 \ cm} - \frac{1}{-10 \ cm} \\ s = 30 \ cm {/eq}

Part B.

Magnification is given by the formula:

{eq}m = \frac{-s'}{s} \\ m = \frac{-(-10 \ cm)}{30 \ cm} \\ m = 0.33 {/eq}