1. Curved Mirror Equations

2. Curved Mirror Equation
We can describe images produced by mirrors not only using our eyes or using ray diagram drawings, but also by using math.
1/f = 1/di + 1/do
f is the focal length
di is the distance between the image and the mirror
do is the distance between the object and the mirror
By convention, all virtual distances are negative

3. Curved Mirror Equation Example
A concave mirror with a 20 cm focal length has a candle placed in front of it 30 cm from vertex. Find the image position (di).
do =
f =

4. Another Curved Mirror Equation Example
A candle is placed 30 cm in front of a concave mirror that has a center of curvature of 15 cm. Find di.
do =
f =

5. Magnification Equation
M = hi/ho = - di/do
m= magnification
hi = the image height
ho = the object height
We can use this magnification equation to determine if the image is bigger or smaller than the object
By convention, inverted images have a negative value

6. Magnification Example
A concave mirror with a 20 cm focal length has a candle placed in front of it 35 cm from vertex. Find the image position (di) and then find the magnification.
do =
f =

7. Magnification equation can be rearranged to determine the height of the image:

8. Height of Image Example
A candle is placed 30 cm in front of a concave mirror that has a center of curvature of 15 cm. If the candle is 35 cm tall, how tall is the image?
do =
f =
di =
ho =
M =

9. Negative Signs
In optics, the negative sign is used to indicate virtual distances (image and focal point) as well as inverted heights.
Sometimes you may need to insert the negative sign yourself.

11. Negative Signs Example
Given a convex mirror with focal length 20 cm, a candle is placed 5.0 cm away from the vertex. Find the image position (di) and the magnification.

12. Helpful hints Draw the diagram first so you get the big picture
Write down the knowns given in the question
Write down what you need to determine and figure out which equations will help!