1. Reflection & Mirrors

2. Law of Reflection θi = θr
The angle of incidence = the angle of reflection
We like smooth surfaces because the normal is easy to identify and is perfectly vertical…if the surface isn’t smooth, it gets a little more complex.

3. Law of reflection still applies!!
Specular Reflection
Parallel light rays reflected parallel
Because reflected rays are scattered from a rough surface, they cannot be seen…this is why materials with rough surfaces cannot be used as mirrors.
Diffuse Reflection
parallel light rays NOT reflected parallel – instead are scattered off a rough surface

4. Question???
Can you see light that isn’t directed toward your eyes?

5. Answer
No…
What you see are the reflected rays. If none of the reflected rays are directed straight toward your eye, then you see no light.
Again, this is why we don’t see a reflection in a piece of paper…the incident rays go in parallel, but then are scattered all over. Our eyes cannot produce an image from the scattered reflected rays.

6. Plane Mirrors
Flat, smooth surface from which light is reflected by specular reflection.
Object – source of light (either luminous or illuminated)
Image – brain always processes information as if light has traveled in a straight path, so we don’t see the object…we see the image.
Look at figure 17-5 on page 461

7. di = -do hi = ho Plane Mirrors Image Position Image Height
The object is always on the positive side of the mirror.
The image formed with a plane mirror is on the opposite side of the mirror.
We call this a virtual image, and its distance is negative.
di = -do
hi = ho

8. Curved Mirrors
Convex Concave

9. Variables
Object distance- distance from the object to the mirror do di
Image distance- distance from the image to the mirror ho
Object height- how tall the object is hi
Image height- how tall the image is
Real Image:
Formed when actual reflected or refracted rays converge; can be projected onto a screen
Virtual Image:
Formed when the extended (dotted) lines converge to form the image

10. Concave Mirror – Edges curve toward observer
Principal Axis
Center of Curvature
Focal Pt. (f)
Focal length
Radius of Curvature (2xFocal Length)
Focal Point – point where incident light rays that are parallel to the principal axis converge after reflecting from the mirror.

11. Convex Mirror – Edges curve away from observer
Focal Length
Focal Pt. (f)
Principal Axis
Center of Curvature
Radius of Curvature = 2f

12. Graphical Method of Finding the Image
-Ray Diagrams-
Determine properties of an image formed by a curved mirror.
Typically Given
Type of mirror
Focal Length & Center (or radius) of curvature
-Object Height
Object distance
What are we looking for??
Is the image real, or virtual?
Is the image smaller, larger, or same size?
Is the image erect or inverted?
How far is the image from the mirror? (di)

13. Step 1: Draw the principle axis
Step 2: Represent the kind of mirror being used.

14. Step 3: Show focal pt. and center of curvature
C = 2f ho f C do
Step 4: Show Object

15. Convex Mirror
f =
do =
ho = f C
Ray 1: For a convex mirror, a ray entering towards the focal point will reflect parallel to the principle axis

16. Convex Mirror
f =
do =
ho = f C
Ray 2: For a convex mirror, a ray entering parallel to the principle axis will reflect in a direction that makes it appear to come from the focal point.

17. Convex Mirror
f =
do =
ho = f C
Ray 3: For a convex mirror, a ray entering towards the center of curvature will reflect back upon itself, appearing to have come from the center of curvature.

18. Convex Mirror
f =
do =
ho = f C
Draw in the image of the object. The head of the image is located where either solid lines or dotted lines converge. The bottom of the image is located on the principle axis.

19. Convex Mirror
f =
do =
ho = f C
For each drawing, complete each of the following:
di = cm
hi = 1.5 cm
Smaller
Erect
Virtual
Measure the image distance (di)
Measure the image height (hi)
Bigger or Smaller?
Erect or Inverted?
Real or Virtual?

20. Mathematical Method for Locating the Image
Magnification

21. Practice!!
Given the following information, use ray diagrams to locate the image. Then calculate the image location and size using the mathematical method.
Type of Mirror
Focal Length
Object Distance
Object Height
Convex
-7.0 cm
3.0 cm
5.0 cm
-3.0 cm
8.0 cm
2.0 cm
Concave
12.0 cm
6.5 cm
3.5 cm

22. Important Reminders
Use only one sheet of plain white paper for each drawing
You must use at least two colors on each drawing- but it might be best to use light pencil first and trace over the lines later.
The dotted lines are always an extension of the reflected ray, not the ray that is incident on the mirror.

23. Ray Diagrams
for Thin Lenses

24. How lenses are different from mirrors...
Thin lenses are not “spherical” in shape.
Therefore there is no Center of Curvature
Our drawings use lenses that have two curved surfaces

25. How lenses are different from mirrors...
With two curved surfaces,
In a sense you have two focal points, on each side of the lens.
As long as each has the same amount of curve, the focal length will be equal on both sides. f f

26. How lenses are different from mirrors...
The biggest and most important difference:
Refraction, not reflection is occurring.
The solid lines on your drawings will be the ones passing through the lens to the right side of your drawing.

27. How to represent lenses on your drawing
Converging Lens
Diverging Lens

28. A quick example
Ray 1
Ray 2
Ray 3 f f
di =
hi =
Smaller
Inverted
Real

29. Ray Diagram Calculations
Each drawing will require five (5) quick calculations based on the given information and your measurements.
These are the calculations you will make:
Image distance
Magnification using image height and object height
Magnification using image distance and object distance
Percent Error : Measured image distance vs. calculated image distance
Percent Error : Magnification (using measured hi and given ho) vs. Magnification (calculated di and measured do)

30. Equations:
The same equations work for spherical mirrors and symmetrical thin lenses.
This equation relates focal length, object distance, and image distance.
Use this equation to calculate di.

31. Magnification can be calculated two ways:
Equations:
Magnification can be calculated two ways:
Compare hi to ho
Based on a measurement of image height
Compare di to do
Based on a calculated image distance

32. Percent Error Just how well did you draw the ray diagrams?
Percent Error : Measured image distance vs. calculated image distance
Percent Error : Magnification (using measured hi and given ho) vs. Magnification (calculated di and measured do)

33. Ray diagram Equations Calculate di using:
2. Calculate Magnification using:
Calculated!
3. Calculate Magnification using:
4. Calculate Percent Error
5. Calculate Percent Error

34. f = +4.5 cm
do = 10.9 cm
ho = 1.5 cm f f
Calculations: (On Back of your Drawings)
di = cm 1
hi = cm
Smaller
Inverted 2
Real 3 4 5

35. Convex Mirror f = -7.0 cm do = 3.0 cm ho = 5.0 cm f = -3.0 cm
Drawing #
Type of Mirror/Lens
Focal length, Object distance, Object Height 1
Convex Mirror
f = -7.0 cm
do = 3.0 cm
ho = 5.0 cm 2
f = -3.0 cm
do = 8.0 cm
ho = 2.0 cm 3
f = -6.0 cm
do = 6.0 cm
ho = 2.5 cm 4
Concave Mirror
f = 5.0 cm
do = 12.0 cm 5
f = 6.5 cm
do = 2.0 cm
ho = 3.5 cm 6
f = 4.0 cm
do = 4.0 cm

36. 7
Converging Lens
f = 10.0 cm
do = 4.0 cm
ho = 2.0 cm 8
f = 7.5 cm
do = 7.5 cm
ho = 3.0 cm 9
f = 6.0 cm
do = 11.0 cm
ho = 4.5 cm 10
do = 12.0 cm 11
Diverging Lens
f = -5.0 cm
do = 8.0 cm
ho = 3.5 cm 12
f = cm
do = 5.0 cm

37. Example Exercise
When an object is placed 75 cm away from a concave mirror, an image is produced that is real and twice the size of the object. What must be the focal length of the mirror?

38. Equations for Mirrors and Lenses

39. When an object is placed 75 cm away from a concave mirror, an image is produced that is real and twice the size of the object. What must be the focal length of the mirror?

40. Lens Activity Which lenses will allow a real image to be formed
How does the side that light is incident upon change the focal length?

41. Lens Makers Equations
Important Rules for the side light is incident upon:
R is positive when C is on the side of the lens that light emerges
R is negative when C is on the side of the lens on which light is incident

42. Lens Makers Equations
As long as there is air surrounding the lens, then nenv= 1, so the equation looks like this:
If the focal length is measured in meters, then 1/f has a unit of diopters (D), and this represents the power of the lens

43. Lens Makers Equations
As long as there is air surrounding the lens, then nenv= 1, so the equation looks like this:
The radius of curvature for the curved surface that light is incident upon
The radius of curvature for the surface that light is exiting through

44. Using the Lens Makers Equation
An optometrist prescribes a corrective lens with a power of +1.5 diopters. The lens maker will start with a glass blank that has an index of refraction of 1.6 and a convex front surface whose radius of curvature is 20cm. To what radius of curvature should the other surface be ground?

45. Quiz topics Mirrors and Lenses Human Vision Nearsighted vs. Farsighted
Retina
Lens Makers’ Equations