How do you find the position and magnification of a convex mirror?
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, andd_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.