1. Millions of light rays reflect from objects and enter our eyes – that’s how we see them!
When we study the formation of images, we will isolate just a few useful rays: or

2. i = r i = incident angle r = reflected angle Reflection
measured from the normal
r = reflected angle
A line  to the surface at the point of incidence
i = r
Law of reflection

3. Plane (flat) mirrors object mirror image To locate the image:
1) Draw 2 different rays leaving the same point.
2) Draw their reflections.
3) Extend the reflections behind the mirror.
4) The point where they meet locates the image.

4. There are two different types of images:
Real image Light rays actually meet at that point
Virtual image Light rays only appear to emanate from that point
Which type do you get from a plane mirror ?
For all plane mirrors:
Image is upright
Image is same size as object
object’s distance from mirror (do) = image’s distance from mirror (di)
Right and left are reversed

5. do di

6. How tall a mirror do you need to be able to see your entire body?
Does it matter how far away from the mirror you stand?

7. When mirror surfaces are curved instead of flat, strange things happen……

8. Spherical Mirrors
concave side
convex side

9. Concave Spherical Mirrors
principle axis
(axis of symmetry) C R
C = Center of Curvature
R = Radius of Curvature
Parallel Rays (distant object):
F = focal point C
f = focal length F f
f = ½ R
Concave mirror

10. Convex Spherical Mirrors
Parallel Rays (distant object): C
Since it’s behind the mirror F
f = -½ R
Convex mirror f

11. Locating Images: Ray Tracing
The use of 3 specific rays drawn from the top of the object to find location, size, and orientation of the image
For a Concave Mirror:
Ray #1: Parallel to the axis Relects through F
Ray #2: Through F Reflects parallel to axis
Ray #3: Through C Reflects back on itself

17. Object is in front of C: Image is always real, smaller, and inverted C
Results: Ray Tracing for concave mirrors (in each case, draw in the 3 rays for practice)
Object is in front of C: Image is always real, smaller, and inverted C F
Object between C and F: Image is always real, larger, and inverted C F
Object between F and mirror: Image is always virtual, larger and upright C F
Ex: Makeup mirror

18. For a Convex Mirror:
Ray #1: Parallel to the axis / Relects as if it came from F
Ray #2: Heads toward F / Reflects parallel to axis
Ray #3: Heads toward C / Reflects back on itself

19. Wherever the object is: Image is always virtual, smaller and upright
Results: Ray Tracing for convex mirrors (draw in the 3 rays for practice)
Wherever the object is: Image is always virtual, smaller and upright C F
Ex: Car side mirrors
Convex mirrors widen the field of view
“Objects in mirror are closer than they appear”
Web Link: Ray tracing

20. The Mirror Equation works for both concave and convex mirrors:do C F f do OR
f = mirror’s focal length (+ for concave, - for convex )
do = distance between object and mirror
di = distance between image and mirror
+ for in front of mirror (real)
- for behind mirror (virtual)
The Mirror Equation

21. What about the size of the image ??
ho = height of object
The Magnification Equation
hi = height of image
m = magnification = hi /ho
m is - if the image is inverted
m is + if the image is upright
m>1 if the image is larger than object
m<1 if the image is smaller than object

22. Ex:
15 cm
80 cm
The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the cat.

23. Ex:
15 cm
80 cm
The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the dog.