1. Preview Section 1 Characteristics of Light Section 2 Flat Mirrors
Section 3 Curved Mirrors
Section 4 Color and Polarization

2. What do you think? What are electromagnetic waves?
Are there different types of electromagnetic waves?
If so, what are they?
How are they similar?
How are they different?
Do all electromagnetic waves travel at the same speed?
If so, what is it?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Students may have ideas about electromagnetic waves from previous science classes. Some students may think that all electromagnetic waves are visible light waves.

3. Electromagnetic (EM) Waves
Visible light can be separated into a spectrum.
Red through violet
Visible light is very small part of a larger spectrum, the electromagnetic wave spectrum.
All EM waves travel at the same speed, the speed of light (c).
In a vacuum, v = c = 3.00  108 m/s (186,000 miles/s).

4. Electromagnetic (EM) Waves
Electromagnetic waves consist of electric and magnetic fields.
The fields are mutually perpendicular.
The Visual Concepts video clip on the next slide demonstrates the perpendicular fields. Like other waves, EM waves are produced by vibrating objects. In this case, vibrating charged particles produce the waves.

5. Electromagnetic Waves
Click below to watch the Visual Concept.
Visual Concept

6. Have students note the frequency and wavelength ranges for each of the 7 different types of waves.

7. Classroom Practice Problems
The middle of the visible spectrum is green light. Calculate the wavelength for green light if the frequency is 5.5 x 1014 Hz.
Answer: 5.4 x 10-7 m or mm
The middle of the audible spectrum is 1.0 x 104 Hz ( Hz). Calculate the wavelength of this sound in air if the temperature is 25°C.
Answer: m or 35 mm
By what factor are the sound waves farther apart than the light waves?
times
Simply use v = f or c = f.

8. Waves and Rays
Huygen’s principle states that each point on a wave front acts as a source for new waves.
The diagram shows five points on the initial front sending out waves. These waves are part of the new front.
Plane waves are simply the leading edge of an infinite number of spherical waves.

9. Illumination Illumination is measured in lumens (lm).
Illumination depends on the brightness of the source and the distance from the source.
Predict the relationship between illumination and distance.
It is an inverse square relationship.
The relationship between illumination and brightness is inverse square because the light spreads out spherically. Because the area of a sphere is 4r2, the area increases as the square of the distance. The same amount of light is spread out over a greater area. Ask students what happens when you double and triple the distance. (If you double the distance, the illumination is 1/4 as much; tripling makes it 1/9 as much.)

10. Now what do you think? What are electromagnetic waves?
Are there different types of electromagnetic waves?
If so, what are they?
How are they similar?
How are they different?
Do all electromagnetic waves travel at the same speed?
If so, what is it?
EM waves consistent of vibrating perpendicular electric and magnetic fields. Table 1 shows the types of waves and different wavelengths, frequencies and applications. All EM waves have the same speed in a vacuum (3.0 x 108 m/s).

11. What do you think?
We use our depth perception to determine the distance to an object. When you look in a flat mirror, you see your image.
How far away does the image appear?
Is the image at the mirror, farther away than the mirror, or closer than the mirror?
Make a sketch showing the following:
a side view of yourself as a stick figure, the mirror, and the reflected light that creates the image
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
It is likely that answers will vary, and there will be at least some who believe the image is closer, some who believe it is farther, and some who think it is the same distance as the mirror. Ask them what experiences have led them to believe this way. See if any can back up their belief by showing how the light reflects off the mirror.

12. What do you think?
Imagine a small flat mirror mounted on a vertical wall. You are about a meter away. Because the mirror is small, you see only from your nose to your belt buckle. Now you start backing away from the mirror.
As you back up, will you see more of your body, less of your body, or the same nose to belt image?
Why do you think so? (Explain your answer through personal experiences or a sketch.)
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Generally students expect to see more of their body as they back up and less as they move forward. They may site personal experiences with bathroom mirrors. Listen carefully to their reasons and then, when asking them this question again at the end, discuss those reasons.

13. Reflection
Diffuse reflection is reflection from a rough surface, such as notebook paper or the wall.
Specular reflection is reflection from a smooth surface, such as a mirror or shiny metal.
We will study specular reflection.
We do not see images with diffuse reflection because the rays scatter in all directions.

14. Angle of Reflection
At what angle will the incoming ray reflect from the mirror?
Angle of incidence () = Angle of reflection (’)
By convention, angles are measured with a normal line.
Angles with the surface are also equal.
Using a normal line is important when refraction and Snell’s Law is studied. Therefore, it is a good idea to acquaint students with this method of measuring incoming and reflected angles.

15. Image in a Flat Mirror - Ray Diagram
Ray 1 strikes the mirror and reflects at the same angle (90°).
Ray 2 reflects at the same angle it strikes.
Our eyes see the two reflected rays and many others.
The brain assumes that they came from a common point, and the image is seen at that point.
Before starting, ask students how our eyes and brain determine where an object is when we look at it. Hold up a pencil and ask them to point where they see the tip of the pencil. Point out to them that their eyes see rays of light leaving the pencil and entering each eye. The brain assumes that the light traveled in a straight line. So, when backing up the rays that enter the two eyes, they meet at a common point. That is where we believe the pencil is located. If the light changes direction between the pencil and your eye, it won’t be where we think it is located. For example, if you held the pencil behind a tank of water, the light would bend twice, and the image seen would not be located at the real pencil tip.
This image is continued on the next slide.

16. Image in a Flat Mirror - Ray Diagram
The image is behind the mirror.
The image distance (q) equals the object distance (p).
The image size (h’) equals the object size (h).
The image is virtual, not real.
Reflected rays do not actually meet, they only appear to come from a common point.
Point out to students that any additional rays leaving the tip, striking the mirror, and reflecting at the same angle would back up to the same common point at the tip of the image.
Be sure students understand that this diagram only shows rays that locate the tip of the pencil. The rest of the pencil was drawn in where it would appear. The process could be continued to locate the images of the middle of the pencil, the eraser, and so on.

17. Comparing Real and Virtual Images
Click below to watch the Visual Concept.
Visual Concept

18. Flat Mirrors
Imagine a small mirror as shown. The man will only see the portion of his body shown. How would that change if he were closer to the mirror? Farther away?
Try drawing a diagram similar to that shown.
Tape a mirror to the blackboard so students can see a portion of their body similar to the diagram. Ask them to stand very straight and move backward and forward. They should see exactly the same portion of their body. (If they do not, it is because the mirror is not vertical, so the segment they see may shift up or down slightly.) This may surprise students. Ask them to measure the amount of their body that they see and the size of the mirror. If the mirror is a 12” mirror, they will see 24” of their body.

19. Now what do you think?
We use our depth perception to determine the distance to an object. When you look in a flat mirror, you see your image.
How far away does the image appear?
Is the image at the mirror, farther away than the mirror, or closer than the mirror?
Make a sketch showing the following:
a side view of yourself as a stick figure, the mirror, and the reflected light that creates the image
The image is behind the mirror for the same reason the image of the pencil was behind the mirror. Ask students: How far behind the mirror is the image located? What is its size compared to the object? (The image distance equals the object distance, and the image size equals the object size.)

20. Now what do you think?
Imagine a small flat mirror mounted on a vertical wall. You are about a meter away. Because the mirror is small, you see only from your nose to your belt buckle. Now you start backing away from the mirror.
As you back up, will you see more of your body, less of your body, or the same nose to belt image?
Why do you think so? (Explain your answer through personal experiences or a sketch.)
Students will see exactly the same amount. It will just look farther away.

21. What do you think?
Suppose a concave makeup mirror is held against a vertical wall while you look at yourself from the the opposite side of the room.
Would your image appear the same as it would in a plane mirror? If not, how is it different?
How would this image change in size and appearance as you approached the mirror?
How would the image appear if you were only a foot (30 cm) from the mirror?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
If possible, have students perform this experiment in class after they make predictions. Use a standard makeup mirror with a diameter of about 6 inches so it is large enough for them to make the observations. You can have several set ups around the room to speed up the process. Point out to students unfamiliar with this type of mirror that it is concave.
This is similar to the demonstration with the plane mirror, but the students should see changes as they move toward or away from the mirror. Discuss their observations afterward. Ask them if they noticed a point where they could not see any image at all. Hopefully, all saw that the image was inverted and small, then changed to inverted and larger, and eventually flipped over to upright and larger.

22. Concave Spherical Mirrors
Mirrors that are a small portion of the inside of a sphere
The angle of incidence still equals the angle of reflection.
Called converging mirrors
The focal length (f) is one-half the radius (R).
Point out the incident and reflected angles. You can draw a normal line or just measure the angle with the surface of the mirror to show the equality.

23. Real Images
The image shown is real because the reflected rays actually pass through each other.
Virtual images only appear to come from a single point.
Object distance (p)
Image distance (q)
Object height (h)
Image height (h’)
Use the makeup mirror to show the students an image of a light bulb on a white sheet of paper. Ask them if the image will still be clear if you move the paper. They should note that the paper must be at the location where the rays meet or the image will be blurry.
Understanding the lengths and heights is important for problem solving and ray diagrams.

24. Ray Diagrams - Rules
These rules describe three rays that are easily drawn without the need to measure angles.
Others can be drawn after the image point is located using at least two of these rays.

25. Rules for Drawing Reference Rays for Mirrors
Click below to watch the Visual Concept.
Visual Concept

26. Ray Diagram
Is the image real or virtual? Inverted or upright? Larger than or smaller than or equal to the object in size?
Try drawing the ray diagram locating the image of the pencil if the object is placed at C.
Now try it for the object between C and F.
See the next slide for drawings.
Students need practice at drawing ray diagrams. This can be done most easily on a sheet of graph paper. It is also helpful if they draw the mirror with a very slight curve. This will eliminate some of the problems associated with spherical aberration. The above drawing shows a very curved mirror so students can observe the angles. However, spherical mirrors are generally very small portions of a very large sphere, so they are nearly flat.
Ask students the questions at the top before clicking to reveal the answers at the bottom of the diagram.
To draw the suggested ray diagrams, have students copy this diagram, then do the two suggested diagrams right below it. They will point out that the 3rd ray (through C) will never hit the mirror. They can either imagine that the mirror wraps all the way around and draw it coming straight back, or just draw two rays (because that is all you need to locate the image). Their drawings should look like those on the next slide.

27. Is each image real or virtual. Inverted or upright
Is each image real or virtual? Inverted or upright? Larger than or smaller than or equal to the object in size?
Now try drawing the ray diagram locating the image of the pencil if the object is placed at F.
Finally, try it for an object beyond F (closer to the mirror).
See the next slide for drawings.
Ask students the questions at the top before clicking to reveal the answers at the bottom of the diagrams.

28. Is each image real or virtual. Inverted or upright
Is each image real or virtual? Inverted or upright? Larger than or smaller than or equal to the object in size?
Ask students the questions at the top before clicking to reveal the answers at the bottom of the diagrams.
The last diagram is difficult to draw. The dashed line indicates that that ray 2 appears to have passed through the focal point since it is along a line from the focal point to the tip of the pencil. Therefore, it reflects parallel to the axis.

29. Ray Tracing for a Concave Spherical Mirror
Click below to watch the Visual Concept.
Visual Concept

30. Mirror Equation
p and q have a positive value if they are on the front side or reflecting side of the mirror.
Real images
q has a negative value if the image is on the back side of the mirror.
Virtual image
f is positive for concave mirrors.
Look back at the ray diagrams and ask students which have + values.

31. Equation for Magnification
h is positive if it is upright and negative when inverted.
M is positive for virtual (upright) images.
Simple geometry shows that the ratio between image and object height is the same as the ratio between image and object distance. The negative sign is required because images on the back side of the mirror have negative image distances.

32. Classroom Practice Problem
When an object is placed 30.0 cm in front of a concave mirror, a real image is formed 60.0 cm from the mirror’s surface. Find the focal length.
Answer: 20.0 cm
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Students are likely to have trouble using the reciprocals in the equation. Some will use fractions, some will use decimals, and some will use the inverse key (1/x or x-) on their calculator. You may want to show them a standard way of solving these problems. Since answers are generally given in decimal form, have them convert each quantity into a decimal equivalent, and then solve for the unknown. Often they will solve for 1/p or 1/q or 1/f and forget to invert the result to get the value for p or q or f.
Because the image is real, it must be in front of the mirror so that the image distance is +.

33. Classroom Practice Problems
A square object is placed 15 cm in front of a concave mirror with a focal length of 25 cm. A round object is placed 45 cm in front of the same mirror. Find the image distance, magnification, and type of image formed for each object. Draw a ray diagram for each.
Answers: Square - virtual image, q = -38 cm, M = 2.5
Answers: Round - real image, q = 56 cm, M = -1.2
Ray diagrams should look similar to (4) and (6) in Table 4.
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Students are likely to have trouble using the reciprocals in the equation. Some will use fractions, some will use decimals, and some will use the inverse key (1/x or x-) on their calculator. You may want to show them a standard way of solving these problems. Since answers are generally given in decimal form, have them convert each quantity into a decimal equivalent, and then solve for the unknown. Often they will solve for 1/p or 1/q or 1/f and forget to invert the result to get the value for p or q or f.

34. Convex Mirrors
Called a diverging mirror because rays are spread out by the mirror
Image is always virtual and smaller than the object.

35. Convex Mirrors Used as side-view mirrors on cars
What warning is written on these mirrors? Why?
Images are small so they appear to be farther away.
Also used in stores to monitor shoppers
Equations are the same as those for concave mirrors.

36. Ray Tracing for a Convex Spherical Mirror
Click below to watch the Visual Concept.
Visual Concept

37. Classroom Practice Problems
A convex mirror has a radius of curvature of 12.0 cm. Where is the focal point?
Answer: f = cm (behind the mirror)
Find the position of the image for an object placed the following distances from the mirror: 50.0 cm, 30.0 cm, 12.0 cm and 2.00 cm.
Answers: cm, cm, cm, cm
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow students some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
Students are likely to have trouble using the reciprocals in the equation. Some will use fractions, some will use decimals, and some will use the inverse key (1/x or x-) on their calculator. You may want to show them a standard way of solving these problems. Since answers are generally given in decimal form, have them convert each quantity into a decimal equivalent, and then solve for the unknown. Often they will solve for 1/p or 1/q or 1/f and forget to invert the result to get the value for p or q or f.
Note that the image distance places it between the mirror and the focal point, always behind the mirror.

38. Parabolic Mirrors & Spherical Aberration
With spherical mirrors, rays not near the principal axis do not all meet at the image point.
Parabolic mirrors eliminate this problem and produce sharper images.

39. Parabolic Mirrors & Spherical Aberration
Using rays near the axis on spherical mirrors reduces the aberration or blurriness of the image.
A very small section of a sphere is nearly identical to a paraboloid.
Parabolic mirrors are used in telescopes to sharpen the image.

40. Reflecting Telescope Click below to watch the Visual Concept.

41. Now what do you think?
Suppose a concave makeup mirror is held against a vertical wall while you look at yourself from the the opposite side of the room.
Would your image appear the same as it would in a plane mirror? If not, how is it different?
How would this image change in size and appearance as you approached the mirror?
How would the image appear if you were only a foot (30 cm) from the mirror?
The image is not the same as it would be in a plane mirror. At a certain distance from the mirror, the image is inverted (and real). As you move closer, the image gets larger. After the focal point, the image is upright (and virtual), as with a regular plane mirror.
If students still have trouble with these questions, refer back to the video clip showing how the image changes (slide 9).

42. What do you think?
Imagine a darkened room with two projectors shining light on a screen. One shines blue light while the other shines yellow light.
What color will be seen when these two colors overlap each other on the screen?
Why do you think this is the case?
What experiences have you had that helped you decide on the color?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Many students will choose green, but other answers are likely. There is often confusion between primary colors (addition) and primary pigments (subtraction).
This can be done nicely as a demonstration with either two slide projectors or two overhead projectors and some colored filters. It is important that the colors have roughly equal intensity. Students are generally very surprised when they see white.

43. What do you think? Suppose the colors are switched to red and green.
What color will be seen when these two colors overlap each other on the screen?
Why do you think this is the case?
What experiences have you had that helped you decide on the color?
Students may pick yellow or orange. Others often choose brown. Be sure you ask them to explain why they have their ideas about colors.

44. Color Why does a leaf appear green?
Why do parts of the U.S. flag appear red?
Objects appear a certain color because they absorb the other colors of the spectrum.
The leaf absorbs all but green (see diagram).
The flag absorbs all but red.

45. Color Addition
White light is a mixture of all of the colors of the spectrum (ROYGBV).
The primary additive colors are red, green, and blue.
Addition of these colors with differing intensities produces all other colors.
TVs use closely spaced red, green, and blue pixels.

46. Color Addition Red + green ---> yellow Red + blue ---> magenta
Blue + green ---> cyan
Any two colors forming white are said to be complimentary colors.
Yellow and blue
Magenta and green
Cyan and red

47. Additive Color Mixing Click below to watch the Visual Concept.

48. Color Subtraction and Pigments
Another way to form different colors is by subtraction.
Pigments and dyes absorb (or subtract) some colors and reflect (or transmit) others.
Leaves subtract red and blue but reflect green.
The primary pigments for color subtraction are cyan, magenta, and yellow.
Color printers use CYM cartridges.
These have three colors of ink and mix them to produce all other colors.

49. Color Subtraction and Pigments
Yellow is a combination of red and green. A yellow pigment reflects both red and green or it removes blue.
In other words, yellow pigments subtract blue light.
Similarly, cyan pigments subtract red light.
Therefore, if you mix yellow and cyan pigments, blue and red are both subtracted, and you see green reflected.
Use subtraction to determine the color seen if you mix
cyan and magenta
yellow and cyan
See the color combinations on the next slide for answers.

50. Color Subtraction and Pigments
Mixing all three pigments produces black.
Different quantities of cyan, magenta, and yellow can produce the “millions” of colors possible on printers.
Newspapers also print in black over any portions of the picture with all three pigments in order to darken it.
At this point you can use the following web site to show color addition, subtraction, and color printing. The color printing allows you to adjust the amount of each pigment. The name of the simulation is “Color Box Applet”. There is also a pull down menu at the bottom showing how to produce colors like orange and turquoise.
This applet is downloadable as well.

51. Subtractive Color Mixing
Click below to watch the Visual Concept.
Visual Concept

52. Polarization of Light
Unpolarized light consists of light with the electric and magnetic fields vibrating in all directions.
Polarized light waves have fields vibrating in only one plane.
In this case, the electric field is vertically polarized.

53. Polarizing Light
Polarizing filters only allow light with the electric field aligned with the transmission axis to pass through.

54. Naturally Polarized Light
Light reflected off a shiny surface like water is polarized by the reflective process.
Which way should the transmission axis be oriented to block out “glare” light?
Why do fishermen like polarized sunglasses?
The light is polarized perpendicular to the page or parallel to the surface. Since the light is vibrating in a horizontal plane, the transmission axis should be vertical to block the light. Fishermen use polarized sunglasses to reduce the reflected glare from the water.

55. Naturally Polarized Light
The light scattered off particles in the atmosphere is also polarized.
Photographers use polarized filters to darken the blue sky and make clouds stand out.
If students have polarized sunglasses, they can hold them up to a nice, deep blue sky and rotate them. When doing so, the sky should get lighter and darker, depending on the orientation of the transmission axis.

56. Polarization by Reflecting and Scattering
Click below to watch the Visual Concept.
Visual Concept

57. Now what do you think?
Imagine a darkened room with two projectors shining light on a screen. One shines blue light while the other shines yellow light.
What color will be seen when these two colors overlap each other on the screen?
What color would be produced if they were red and green? Blue and green? Red and blue? Magenta and green? Cyan and red? Cyan and yellow?
Blue and yellow = white
Red and green = yellow
Blue and green = cyan
Red and blue = magenta
Magenta and green = white
Cyan and red = white
The last one is a little tricky:
Cyan and yellow is really (blue + green) + (red + green) so this would be the same as white + green or a pale green.