2. To recap: Real/virtual images Upright/inverted
q: image distance, p: object distance
Magnification: M = -q/p
For mirrors: f = R/2

3. Paraxial rays
principal axis
f = R/2
centre of curvature R

4. Mirror equation
Orange triangle similar to green triangle

5. Combining …
Mirror equation
f = R/2

6. Sign Conventions for Mirrors
p > 0 if object is in front of the mirror (real object)
p < 0 if object is in back of mirror (virtual object)
q > 0 if image is in front of mirror (real image)
q < 0 if image is in back of mirror (virtual image)
If M > 0 image is upright
If M < 0 image is inverted
Both f and R > 0 if centre of curvature is in front of mirror (concave mirror)
Both f and R < 0 if centre of curvature is in back of mirror (convex mirror)

7. Ray tracing

9. Three situations for spherical mirrors:
Concave: p > f
Concave: p < f
Convex: p anywhere

10. Concave mirror: p > f

11. Concave: p < f

12. Convex mirror

13. Spherical Mirrors concave: p > f real concave: p < f virtual
convex
sign conventions

14. 2000 Q6
a) Draw a ray diagram showing the formation of a
magnified image in a concave spherical mirror.
b) A shaving or make-up mirror of this type has a
radius of curvature of 30 cm. What is the
magnification of the image when the face is
10 cm from the centre of the mirror?

15. A 1-cm high object is positioned 12 cm in front of a spherical concave mirror having a radius of curvature of 8 cm. Completely describe the resulting image.

16. Design a spherical mirror which will form an
upright half-sized image of an object if that
object is 100 cm from the vertex. Where
will the image be located?

17. A concave spherical mirror of 20-cm radius is
to be used to project an image of a candle
onto a wall 110 cm away. Where will the
candle have to be placed and what will the
image look like?