1. Concave Mirror The center C of a concave mirror is outside the mirror.
Focal point F is also outside the mirror, half way between the center and the surface of the mirror.
The focal length f is half of the radius.

2. Significance of the focal point
All light rays that are parallel to the axis will pass (after extrapolating for convex mirror) through the focal point!
For a concave mirror, the light can pass through the focal point.

3. Image from a concave mirror: case 1
Step 1
Step 2
Step 3
Step 4

4. Image from a concave mirror: case 1

5. Properties of the Image
If we put an object outside of the center of a concave mirror, we find the image is
Real, in the sense that all light rays pass through the image.
Inverted, in the sense that the direction of the arrow has been changed.
The image is smaller!

6. Animation for case 1

7. Image for a concave mirror: case 2

8. If the object is in between the center and the focal point, the image is
Real
Inverted
Magnified in the sense that the image is bigger than the real object.
The direction of the light rays can be reversed and the result is still physically possible! (or the image and object interchanged)

9. Animation for case 2

10. Image from a concave mirror: case 3

11. Image from a concave mirror: case 3

12. Animation for case 3

13. Properties of the image
If the object is closer to the mirror than the focal point F, the image is
Virtual, it is behind the mirror
Upright, not inverted
Magnified
Can be used for shaving!

14. Summary

15. Java Applet

16. Some of the really-cool applications
Suppose you put a point source of light at F. All rays will be reflected back parallel to the axis of mirror: a neat way to construct a parallel beam!
Applications: flashlight! Headlight in the car.
Conversely, if one has parallel rays, all are reflected to pass through F. So all light energy is focused to one point!