# How do you find the position and magnification of a convex mirror?

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Assume the reflected object is #3.00# cm high and is placed #20.0# cm from the convex mirror with focal length of #8.00# cm.

Assume the reflected object is

##### 2 Answers

See below.

Position:

Magnification:

#### Explanation:

Since we are given that the height of the object is

Consider the following two formulas:

Lensmaker's Formula:

#1/f=1/d_(obj)+1/d_(img)# Magnification Equation:

#M=h_(img)/h_(obj)=-d_(img)/d_(obj)#

To determine the image's position, we can solve for

Taking the reciprocal of both sides, we get:

Now, we can substitute the given values of

Using this value, we can find the magnification of the convex mirror:

See below.

#### Explanation:

You will need to calculate the distance between the mirror and the image first, which can be done using the mirror equation:

#1/f=1/d_(o)+1/d_i# where

#f# is the focal length,#d_o# is the distance between the mirror and the object, and#d_i# is the distance between the mirror and the image.

We can solve for

Note that because this is a convex mirror, the focal length must be negative.

Given that

#d_i=(-1/8-1/20)^-1#

#=(-7/40)^-1#

#=-40/7cm#

The magnification of a curved mirror can be expressed by the following equation:

#m=-d_i/d_(o)#

Thus we have:

#m=(-(-40/7))/20#

#m=40/140=2/7#

This answer makes sense, as a convex mirror will always produce an image which is reduced, upright, and virtual.