1. Preview Section 1 Refraction Section 2 Thin Lenses
Section 3 Optical Phenomena

2. What do you think?
Suppose you are reaching for swim goggles floating below the surface of a pool or trying to net a fish while out in a lake. Would you reach at the point where you see the object, or above it, or below it?
Describe personal experiences that helped you answer this question.
Make a sketch showing how you think light behaves when leaving the goggles, passing into the air, and then entering your eyes.
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 experiences that give them ideas about the position of objects underwater, such as reaching under water or fishing or cleaning a swimming pool. Listen and question them to clarify their beliefs. After gathering ideas, you can set up a demonstration with an object in the bottom of a fish tank and a piece of PVC pipe. Have students aim the pipe so that they are looking at the object in the bottom of the tank. Other students off to the side will see that they are aiming well above the actual position.

3. Refraction Why does the lawnmower turn when it strikes the grass?
The right wheel slows down before the left one.
Light waves behave in the same way.
Refraction is the bending (change in direction) of light when it travels from one medium into another.
Caused by a change in speed

4. How does it bend?
Upper
edge
Lower
edge
Wave fronts (dashed lines) slow down when entering glass.
The lower edge slows before the upper edge, so the wave turns to the right.
Also, the wavelength is shortened.

5. Wave Model of Refraction
Click below to watch the Visual Concept.
Visual Concept

6. Ray Diagrams Light rays reflect and refract.
If the light slows down, it bends toward the normal line (glass < air).
Angles are measured with the normal line.
Light rays are reversible.
Point out to students that normal lines are drawn
(1) perpendicular to the surface, not the ray, and
(2) at the point where the ray strikes the surface.
The web site below is useful:
Choose “Easy Java Simulations,” then “Optics,” then “reflection/refraction.”
Using this web site, you can adjust the wavelength in air (slide bar on left) and the angle of incidence (slide bar on top). Show students how the amount of bending increases as the angle of incidence increases. Also show them how the wavelength is shortened as the waves slow down.
Ask them to predict the effect of a change in the index of refraction for the upper media, then the lower media. Test their predictions.

7. Law of Refraction c = 3  108 m/s
v is always less than c, so n >1 for all media.
nair =
n is dimensionless.
n is a measure of the optical density of a material.
Show students why n is dimensionless.

8. Indices of Refraction
Remind students that these indices are true for yellow light (wavelength of 589 nm) and are slightly different for other colors of light.

9. Snell’s Law
Angles must be measured with the normal.

10. Classroom Practice Problems
Find the angle of refraction of a light ray (589 nm) entering diamond from water at an angle of 30.00° with the normal.
Answer: 15.99°
A light ray (589 nm) traveling through air strikes an unknown substance at 60.00° and forms an angle of 41.42° with the normal inside. What material is it?
Answer: n = 1.309, so the material is ice
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 may need help deciding when to use sin and when to use sin-1.

11. Refraction Where does the cat see the fish?
Help students understand that objects appear to be located where two diverging rays of light from the object meet. This may actually be at the point where the object is located. However, if the light has changed direction, the image will not be at that point.
In both cases, the image is above the true position.
The web site below is useful:
Choose “Easy Java Simulations,” then “Optics,” then “The wonderful world of refraction.”
Using this web site, you can view a fish as it moves through the water as seen by a person above the water. The simulation shows actual and apparent positions for the fish and allows you to adjust the indices of refraction.
After viewing, ask students:
How does the apparent depth change as the fish swims to the right?
How does refraction change the shape of the image?
Where does the cat see the fish?
Where does the fish see the cat?
Objects appear to be in line with the observed rays.

12. Now what do you think?
Suppose you are reaching for swim goggles floating below the surface of a pool. Would you reach at the point where you see the object, or above it, or below it?
Make a sketch showing how light behaves.
If you are under water looking at a person standing on the side of the pool, where is the image?
The image is above the true position. To grab the goggles, you would need to reach below the apparent position. If students still have questions about this concept, review the diagram on the previous slide again.
Note that in order to locate the exact position of an image, you need at least two rays, and must back them up to their common point of intersection. That is where the image is seen.

13. What do you think?
How will the light bend as it enters and leaves the three glass blocks?
Draw the rays as they change direction. Make sure your drawing includes normal lines at each interface.
Would you describe the combination of blocks as converging or diverging with respect to the incoming light?
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.
Check students’ drawings as they work on them. It is important that they draw the normal lines correctly and this is often a problem, particularly at the 2nd surface. Remind them that normal lines are perpendicular to the surface, not the ray. They should recall the rule that light bends toward the normal when slowing, and away from the normal when speeding up. This drawing is simply a check of their knowledge of refraction, but leads into lenses. Ask them how the drawing would be different if the glass was a smooth curved surface on each side (like a lens) instead of with abrupt changes as shown here.

14. Lenses
A lens is a transparent object that converges or diverges light by refraction.
A converging lens is thicker at the middle.
A diverging lens is thinner at the middle.
Light actually bends at each surface. However, for thin lenses, we can show light bending only once at the center of the lens.
Focal length (f) is the distance from the focal point (F) to the center of the lens.

15. Rule # 1 Any ray through the focus will refract parallel to the principle axis.
Rule # 2 : Any ray parallel to the principle axis will refract so that it passes through the focus.
Rule # 3 : Any ray that passes through the center of the lens will come out the other side with refraction ( bend) .

16. Converging and Diverging Lenses
Click below to watch the Visual Concept.
Visual Concept

17. Ray Diagrams for Lenses
Complete the ray drawing to locate the image using the rules above.
Students should be able to apply the rules for converging lenses at the top of the page to complete the ray drawing. They can compare it to the one shown on the next slide.

18. Ray Tracing for a Converging Lens
Click below to watch the Visual Concept.
Visual Concept

19. Images Created by Converging Lenses
Configurations 1 and 2:
Discuss the six possibilities shown in the text. (This is continued on the next two slides.)
For situation 1, the pencil is so far away that the rays leaving the tip are parallel when they arrive. This requires an infinite distance, but practically speaking, if the pencil is on the other side of the room, the rays leaving the top are almost parallel. The image of the pencil will be really small, not quite infinitesimally small but close.

20. Images Created by Converging Lenses
Configurations 3 and 4:
Discuss the six possibilities shown in the text. (This is continued on the next slide.)

21. Images Created by Converging Lenses
Configurations 5 and 6:
Discuss the six possibilities shown in the text.
Situation 6 is a little tricky. You can hand the students a converging lens (such as a magnifying glass), and allow them to look at a distant object (such as a book standing up on a lab table). Ask them look through the lens at the book as they move toward the book, until the cover is very near the lens. They should see the image switch to upright once the book cover is inside the focal point. They should also notice a point where all they see is a big blur because the book is at the focal point and there is no image. Have them do this, then discuss their observations afterward. See how many students made good observations.

22. Diverging Lens Diagram
Complete the ray diagram for the lens shown to the left using the three rules from Table 2.
Students may need to see slide 4 again, with the table of rules. The video clip on the next slide shows the process of drawing the diagram.

23. Ray Tracing for a Diverging Lens
Click below to watch the Visual Concept.
Visual Concept

24. Thin-Lens Equations
Point out that the equations are the same as those for concave and convex mirrors. Only the sign conventions are different. (These are shown on the next slide.)

25. Nearsightedness
The image forms in front of the retina, possibly because the retina is too long.
What type of lens is needed in front of the eye to correct the problem, converging or diverging? Explain your reasoning.
Answer: a diverging lens
A diverging lens is needed to spread the light out before entering the eye. The eye converges the light in front of the retina.
Many of the students are likely to be nearsighted. This may have occurred after a growth spurt when the retina just became too long for their lens system. Ask them if they know their prescription. The power of their lens should be a negative number, such as diopters. Power = 1/focal length (in meters), so the d lens has a focal length of m.
Students may want to know about astigmatisms. An astigmatism is an irregularity in the shape of the cornea, so prescription lenses must adjust for it.

26. Farsightedness
The image forms behind the retina, possibly because the lens is inflexible.
What type of lens is needed in front of the eye to correct the problem, converging or diverging? Explain your reasoning.
Answer: a converging lens
A converging lens is needed to bring the light to a focus at the retina. The eye does not converge the light enough without a corrective lens.

27. Combinations of Lenses
Microscopes and refracting telescopes use two lenses.
The objective lens forms a real image that is located inside the focal point of the eyepiece.
The eyepiece magnifies the first image, creating a large virtual image.
With a microscope, the first image (real) is larger than the object, and the second image (virtual) is larger still. Therefore, the magnification is the product of the two magnifications.
Telescopes do not produce “magnified” images. The image seen of the moon is not actually larger than the moon. The advantage that telescopes have is the image is much closer to you than the actual object. Therefore, even though it is smaller, it looks larger and is easier to see. Remind students that distant objects form small images on the retina, while nearby objects form large images on the retina.

28. Refracting Telescope Click below to watch the Visual Concept.

29. Now what do you think?
How will the light bend as it enters and leaves the three glass blocks?
Draw the rays.
How is this similar to a lens?
Which type of lens?
How would the rays exit the three blocks if there were six equally spaced rays instead of three?
How would those same six rays exit a converging lens?
It is similar to a converging lens. The primary difference is that the lens is smoothly curved. If there were more than three rays, for example two at the top, two in the middle, and two at the bottom, then they would not all meet at a common point. The two at the top would each bend exactly the same amount and exit parallel to each other. A thin lens is curved so that the rays entering near the top or bottom edge are refracted more than those near the middle. As a result, they all meet at a common point, the focal point.

30. What do you think?
Suppose a beam of light entering a tank of water strikes at a 60.00° angle with the normal. What angle does it make with the normal after entering the water? Sketch it.
Suppose a beam of light emerging from beneath the water surface strikes at a 60.00° angle with the normal. What angle does it make with the normal after entering the air? Sketch 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.
Provide the values for n (water is and air is 1.000) and allow students to work on these problems. They will get an answer of 40.52° for the first problem and, unless they notice that they are trying to take the sin-1 of a number greater than 1, their calculators will give them an error on the second problem. Ask them to think about the situation and try to explain why they can’t calculate the angle in air. Have them try an angle of 48.60° instead of 60° and they will get an angle of nearly 90° in the air. This might help them understand that, if the angle is too great in the denser medium, the light can’t emerge.

31. Total Internal Reflection
Total internal reflection occurs if the angle in the denser medium is too great.
Light can’t emerge so it is reflected back internally.
Occurs if the angle is greater than the critical angle (c).
Used in fiber optics, right angle prisms, and diamond cutting.
Prisms are used in optical instruments instead of mirrors because the reflection is total. Draw a right angle prism and show students how the light enters the longest side perpendicularly and then totally internally reflects twice before emerging opposite the original direction.

32. Critical Angle
c occurs when the angle in the less dense medium is 90°.
At the critical angle, the emerging ray travels along the surface.
At greater angles, the rays are totally internally reflected.
Show how the equation is simply Snell’s Law with the angle of refraction at 90°. Since sin 90° = 1, Snell’s law is simplified.
If the less dense medium is air, it is even simpler (ni sin c = 1 ).

33. Total Internal Reflection
Click below to watch the Visual Concept.
The video shows what happens to light as it tries to emerge from water at different incident angles.

34. Classroom Practice Problems
Find the critical angle for light emerging from a diamond into air. The index of refraction for diamond is Repeat for cubic zirconium with n =
Answers: 24.42° for diamond and 27.04° for cubic zirconium
Which material is more likely to trap light entering the top surface in such a way that it reflects many times internally before emerging?
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.
These problems are a straightforward application of the equation. Diamonds are cut in such a way that light entering the top strikes the inside surfaces at angles greater than the critical angle, so multiple reflections occur inside the diamond (it sparkles).

35. Atmospheric Refraction
Make a sketch like that above. On your drawing, show how light will bend when it strikes the atmosphere.
Remember that this is a very slight change in the index of refraction, and it occurs gradually as the atmosphere becomes denser.
This bending allows us to see the sun before it rises and after it sets.
Picture is NOT TO SCALE. The atmosphere is a very thin layer.
The drawing should show the light bending very gradually downward (toward the normal line). This makes the sun appear to be higher in the sky, particularly at sunrise and sunset.

36. Mirages
Mirages are caused by the refraction of light as it strikes the hot air near the earth’s surface.
This phenomena can be observed when driving on blacktop roads on hot summer days.
Inverted cars can be seen approaching, with the actual cars up above them.

37. Dispersion Refraction or n depends on the wavelength.
Longer wavelengths refract less.
Prisms disperse the light into a spectrum.
Chromatic aberration is a lens problem where different colors focus at different points.
Can lead to imperfect images for cameras with less expensive lenses.

38. Rainbows Point out the following:
The two refractions and one reflection cause the red to come out below the violet.
The woman sees red when looking at the upper raindrop and violet when looking at the lower drops.
A person slightly taller than her would see violet when looking at the same raindrop that appears red to her.
Each raindrop produces all the colors; depending on our angle, we see only the one that enters our eye.
Rainbows are really circular but Earth gets in the way. From an airplane, they are a full circle.

39. Dispersion of Light Click below to watch the Visual Concept.

40. Now what do you think?
How do fiber optic cables keep the light trapped inside the cable as it travels great distances and bends around corners?
What phenomena is responsible for trapping the light?
Why do different people see different colors for a water drop when observing a rainbow?
What phenomena is responsible for the rainbow?
Total internal reflection traps the light (see the feature in this section of the Student Edition for more details). If students are confused by the second set of questions, revisit slide 9.