This document contains lecture notes on optics, including mirrors and lenses. Key points include: - Spherical mirrors can be convex or concave, and the location and properties of images formed by each type are explained using ray tracing diagrams. - Convex mirrors form virtual, upright, smaller images closer to the mirror than the object. Concave mirrors can form real or virtual images depending on the object location. - Lenses use refraction rather than reflection, and convex lenses converge rays while concave lenses diverge them.

1. Homework Notes
• If you are struggling with the homework, start
working on it early enough that you can come to
office hours if needed.
• You can go to the help room even when one of us
is not there, at least for the first half of the
course.
• Do not email me Wednesday night with
homework questions.

2. Chapter 3: Mirrors and Lenses

3. Chapter 3: Mirrors and Lenses
• Mirrors
– Spherical mirrors
– Ray tracing
• Convex mirrors
– Image formation
– Applications
• Concave mirrors
– Image formation
– Applications
• Lenses
– Refraction
– Converging rays
– Diverging rays

4. Reflection Review
• Recall our ray tracing of a flat mirror
• Recall that there are “special” rays that are
sufficient for locating the image

5. Clicker Question
• Which shows the correct location, orientation,
and size for the image?
A)
D) E)
C)B)

6. Spherical Mirrors

7. What is the normal to a curved surface
and how is it used to find rays?
• To find the normal to a curved
surface at a point where a ray hits
that surface (and will be reflected
or refracted)
– First draw a tangent line to the curve
(or tangent plane to the surface)
– The normal is perpendicular to that
line or plane and going through the
point
– Once you have drawn the normal you
can draw the reflected or refracted
ray

8. Ray Tracing & Spherical Mirrors
Radius of Curvature: The radius of the sphere the mirror is “cut from”
Center of Curvature (C): The center of the sphere the mirror is cut from
Focal Point (F): The point where rays from a distance appear to converge
For a spherical mirror, the focal point is halfway between the surface
and the center of curvature
Paraxial Ray: A ray coming on to the mirror parallel to the axis
CF
radius of curvature
paraxial rays

9. Convex vs. Concave
Convex Concave
• Spherical mirrors are drawn in two dimensions, so you have
to imagine the 3D mirror this line represents
• Both convex and concave mirrors obey the same law of
reflection, but they make different kinds of images

10. Sources of Paraxial Rays
• The rays coming from a distance source can be
considered approximately paraxial when they
reach a mirror
Convex mirror
• The rays from a nearby source, such as a candle
or bare light bulb, cannot be considered paraxial

11. Special Rays: Convex Mirror
CF
axis
Ray 1 Rule:
All rays incident parallel to the axis are reflected so that they
appear to be coming from the focal point, F.

12. Special Rays: Convex Mirror
CF
axis
Ray 2 Rule:
All rays that (when extended) pass through C are reflected back on
themselves

13. Special Rays: Convex Mirror
CF
axis
Ray 3 Rule:
All rays that (when extended) pass through F are reflected back
parallel to the axis.

14. Locating an Image: Convex Mirror
CF
axis
Image properties:
•virtual (behind the mirror)
•right-side up
•closer to the mirror than the object
•smaller than the object.

15. Compare to Flat Mirror
Image properties:
•virtual (behind the mirror)
•upside down
•the same distance from the mirror as
the object
•the same size as the object

16. Clicker Question
• The image formed in a convex mirror is smaller
than the object. This would make a convex mirror
useful for which application?
A.Makeup or shaving mirror
B. Wide-angle mirror, such as on a car or a blind
intersection
C. A mirror in a clothing store dressing room

17. Convex Mirrors
• Because the image is smaller than the object,
convex mirrors reflect from wider angles than flat
mirrors.

18. Concave Mirrors
C Faxis
Ray 1 Rule:
All rays incident parallel to the axis are reflected so that they pass
through the focal point, F.

19. C Faxis
Concave Mirrors
Ray 2 Rule:
All rays that pass through C are reflected back on themselves

20. Concave Mirrors
C Faxis
Ray 3 Rule:
All rays that pass through F are reflected back parallel to the axis.

21. Image Formation: Concave Mirrors
C F
Image properties:
•real (in front of the mirror)
•upside down
•farther from the mirror than the object
•larger than the object.
Object location:
Between the center of curvature and the
focal point

22. Concave Mirrors
C F
Image properties:
•virtual (behind the mirror)
•right-side up
•farther from the mirror than the object
•larger than the object.
Object location:
Between the surface and the focal point

23. Concave Mirrors
C F
Object location:
Past the center of curvature

24. Concave Mirrors: Clicker Question
C F
Object location:
Past the center of curvature
Is the image
A.Real and magnified
B.Real and reduced
C.Virtual and magnified
D.Virtual and reduced

25. Clicker Question
• The inside of a spoon bowl is a concave surface
with a radius of curvature of a couple of inches
(depending on the spoon). If you hold it about a
foot from your face, what will your face look like?
A.Normal size, upside down
B. Normal size, right side up
C. Smaller, upside down
D.Smaller, right side up

26. Concave Mirrors: Application
Because rays coming in parallel, as from a very distant source, are
all reflected to the focal point, a receiver placed there will pick up
the waves received over the large area of the dish, instead of just
the small area of the receiver itself.

27. Concave Mirrors: Application
• What if we put a light source at the
focal point of a concave mirror?
• All the rays emitted by the light go
through the focal point, and are
therefore reflected parallel to the
axis of the mirror.

28. Spherical Lenses
What if we don’t want to have to
look at a reflection to magnify or
reduce an image?
We can use refractive optics
instead (lenses)

29. Convex Glass Surface
CF
axis
A concave surface is called “converging” because parallel rays
converge towards one another

30. Convex Glass Surface
C Faxis
The surface is converging for both air to glass rays and glass to air
rays

31. C Faxis
A concave surface is called “diverging” because parallel rays
diverge away from one another
Concave Glass Surface

32. CF axis
Again, the surface is diverging for both air to glass rays and glass to
air rays
Concave Glass Surface