Chapter 28 Reflection and Refraction

Distinguish between a converging lens and a diverging lens.

A converging lens is thickest in the middle, causing parallel rays to come together at a point. A diverging lens is thickest at the edges.

You can tell whether people are nearsighted or farsighted by looking at the size of their eyes through their glasses. When a person's eyes seem magnified, is the person near-sighted or farsighted?

A farsighted person's eyes seem magnified.

When a fish in a pond looks upward at an angle of 45 degrees, does it see the sky above the water's surface or a reflection from the water-air boundary of the bottom of the pond? Defend your answer.

A fish sees the sky (as well as some reflection from the bottom) when it looks upward at 45 degrees because the critical angle is 48 degrees for water. If the fish looks at and beyond 48 degrees, it sees only a reflection of the bottom.

Converging lens

A lens that is thicker in the middle than at the edges and that refracts parallel rays to a focus.

Diverging lens

A lens that is thinner in the middle than at the edges, causing parallel rays to diverge as if from a point.

Waves don't overlap in the image of a pinhole camera. Does this feature contribute to a sharp image or to a blurry image?

A pinhole image is one of sharpness.

Distinguish between a virtual image and a real image.

A real image can be cast on a screen; a virtual image cannot.

Why is a secondary rainbow dimmer than a primary bow?

A secondary bow is dimmer due to additional internal reflection.

Your friend says that the wavelength of light waves is shorter in water than in air and cites Figure 28.25 as evidence. Do you agree or disagree, and why?

Agree, as inspection of Figure 28.24 shows. Note that the wavefronts are closer together in water than in the air above.

Real image

An image formed by light rays that converge at the location of the image. A real image, unlike a virtual image, can be displayed on a screen.

Virtual image

An image formed by light rays that do not converge at the location of the image.

In terms of focal length, how far behind the camera lens is a photosensitive surface located when very distant objects are being photographed?

For very distant objects, effectively at "infinity," light comes into focus at the focal plane of the lens. So the photosensitive surface is one focal length in back of the lens for very distant shots. For shorter distances, it is farther from the lens.

In the opening photo of physics teacher Fred Myers taking a photo of his daughter McKenzie, how many mirrors were involved? Explain.

Fred and McKenzie are between two parallel mirrors. The reflection from one mirror is incident on the other, and so on. Ideally there would be an infinite number of images, but light is lost with each reflection.

If you were to send a beam of laser light to a space station above the atmosphere that appears just above the horizon, would you aim the laser above, below, or at the visible space station? Defend your answer.

In sending a laser beam to a space station, make no corrections and simply aim at the station you see. This is like zapping the fish while standing on the shore in question 99. The path of refraction is the same in either direction.

Would refracting telescopes and microscopes magnify if light had the same speed in glass as in air? Defend your answer.

If light had the same average speed in glass lenses that it has in air, no refraction of light would occur in lenses, and no magnification would occur. Magnification depends on refraction, which in turn depends on speed changes.

How does incident light that falls on an object affect the motion of electrons in the atoms of the object?

Incident light sets electrons into vibration.

At what angle inside glass is light totally internally reflected? At what angle inside a diamond is light totally internally reflected?

Inside glass light is totally internally reflected at about 43 degrees, depending on the type of glass; in a diamond, 24.5 degrees

Aberration

Distortion in an image produced by a lens, which to some degree is present in all optical systems.

Does a single raindrop illuminated by sunlight deflect light of a single color, or does it disperse a spectrum of colors?

Each drop disperses a spectrum of colors.

Fermat's principle is of least time rather than of least distance. Would least distance apply as well for reflection? For refraction? Why are your answers different?

Fermat's principle for refraction is of least time, but for reflection it could be of least distance as well. This is because light does not change mediums for reflection so no change in speed occurs and least-time paths and least-distance paths are equivalent. But for refraction, light goes from a medium where it has a certain speed to another medium where its speed is different. When this happens the least-distance straight-line paths take a longer time to travel than the non-straight-line least-time paths. See, for example, the difference in the least-distance and least-time paths in Figure 28.13.

What is Fermat's principle of least time?

Fermat's principle states that light will take the path that requires the least time when going from one point to another.

Fermat's principle of least time

Light takes the path that requires the least time when it goes from one place to another.

Trucks often have signs on their back ends that say, "If you can't see my mirrors, I can't see you." Explain the physics here.

Light that takes a path from point A to point B will take the same reverse path in going from point B to point A, even if reflection or refraction is involved. So if you can't see the driver, the driver can't see you. (This independence of direction along light's path is the "principle of reciprocity.")

Maps of the Moon are upside down. Why?

Moon maps are upside-down views of the Moon to coincide with the upside-down image that Moon watchers see in an astronomical telescope.

A beam of light bends as shown in (a), while the edges of the immersed square bend as shown in (b). Do these pictures contradict each other? Explain. (see question 97-chapter 28 for figure.)

No. In both cases light is bent away from the normal upon emerging from the water. That's why the corner of the immersed square appears to be shallower. Notice that it's easy to confuse the beam of the left-hand picture with the edge of the immersed square in the right-hand picture. Light travels from the edge, not along the edge of the square.

Why will goggles allow a swimmer under water to focus more clearly on what he or she is looking at?

Normal sight depends on the amount of refraction that occurs for light traveling from air to the eye. The speed change ensures normal vision. But if the speed change is from water to eye, then light will be refracted less and an unclear image will result. A swimmer uses goggles to make sure that the light travels from air to eye, even if underwater.

This chapter opened with a photo of physics instructor Peter Hopkinson seeming to hover above the table. He isn't. Explain how he creates this illusion.

Peter's left foot is firmly planted on the table, behind the mirror between his legs.

A pulse of red light and a pulse of blue light enter a glass block at the same time normal to its surface. Strictly speaking, after passing through the block, which pulse exits first?

Red light travels faster through glass and exits first.

Does the refraction of light make a swimming pool appear deeper or shallower than it really is?

Refraction makes the pool bottom appear shallower.

What is the advantage of having matte (nonglossy) pages i this book rather than pages with a glossier surface?

Rough pages provide diffuse reflection, which can be viewed from any angle. If the page were smooth, it could be viewed well at only certain angles.

Why is vision sharpest when the pupils of the eye are very small?

Small pupils mean small openings, which means less overlapping of out-of-focus rays.

What accounts for the large shadows cast by the ends of the thin legs of the water strider? (see question 71-chapter 28 for photo.)

The "nonwettable" leg of the water strider deperesses and curves the surface of the water, which effectively produces a lens that directs light away from its path to form an extended shadow region. (Close observation shows a bright ring around the darker region. Interestingly, the shadow and the bright ring have the same average brightness---"conservation of light.")

Law of reflection

The angle of reflection equals the angle of incidence.

When is the angle at which a ray of light strikes glass not the same as the angle at which it exists?

The angles are not the same when the faces of the glass are not parallel, as with a prism.

Does a diamond under water sparkle more or less than in air? Defend your answer.

The diamond sparkles less because there are smaller angles of refraction between the water and the diamond. Light is already slowed when it meets the diamond, so the amount of further slowing, and refraction, is reduced.

What effect does your distance from the plane mirror have in your answer to the following exercise? (Try it and see!) *What must be the minimum length of a plane mirror in order for you to see a full image of yourself?*

The half-height mirror works at any distance, as shown in the sketch. This is because if you move closer, your image moves closer as well, If you move farther away, your image does the same. Many people must actually try this before they believe it. Distinguish this from looking at a tall building in a pocket mirror and looking at yourself in the pocket mirror!

Relative to the distance of an object in front of a plane mirror, how far behind the mirror is the image?

The image distance and object distance are the same.

Whereas pinholes provide sharp images, lenses with large apertures are advantageous for spy cameras of high-flying aircraft. Why?

The image produced by a pinhole is sharp but very dim---a serious liability for a spy camera. A spy camera needs all the light it can get because the image is highly enlarged, so the light is spread way out. Hence, a large aperture is advantageous.

What will happen to the image projected onto a screen by a lens when you cover one-third of the lens with a red filter, one-third with a green filter, and one-third with a blue filter? (Try it and see!)

The image will be a bit dimmer with original colors, but otherwise unaffected.

When the wheel of a cart rolls from a smooth sidewalk onto a plot of grass, the interaction of the wheel with blades of grass slows the wheel. What slows light when it passes from air into glass or water?

The interaction of light with a transparent material lowers the speed of light in the material.

What is the relationship between refraction and the speed of light?

The light speed slow when light is refracted in a medium.

Critical angle

The minimum angle of incidence inside a medium at which a light ray is totally reflected.

Which kind of road surface is easier to see when driving at night: a peppled, uneven surface or a mirror-smooth surface? Discuss why is it difficult to see the roadway in front of you when driving on a rainy night.

The pebbled, uneven surface is easier to see. Light reflected back from your headlights is what lets you see the road. The mirror-smooth surface might reflect more light, but it reflects the light forward, not backward, so it wouldn't help you see. Whereas diffuse reflection from a rough road allows a motorist to see the road illuminated by headlights on a dry night, on a rainy night the road is covered with water and acts like a plane mirror. Very little of the illumination from the headlights returns to the driver and is instead reflected ahead (causing glare for oncoming motorists).

Reflection

The return of light rays from a surface.

When Stephanie Hewitt dips a glass rod into vegetable oil, the submerged part of the rod is invisible. What does this say about the relative speeds of light in the glass and in the oil? Or asked another way, how do the indices of refraction, n, compare for the glass and oil?

The speeds of light in the glass rod and in the oil are the same. Said another way, both oil and glass have the same index of refraction. You'd see only the submerged transparent rod if light underwent a change in speed as it passes from oil to glass and back to oil again. No change in light speed means no visual evidence of its presence.

Total internal reflection

The total reflection of light traveling within a denser medium when it strikes the boundary with a less dense medium at an angle larger than the critical angle.

On a steamy mirror, wipe away just enough to see your full face. How tall will the wiped area be compared with the vertical dimension of your face?

The wiped area will be half as tall as your face.

If, while standing on a riverbank, you wish to spear a fish beneath the water surface in front of you, should you aim above, below, or directly at the observed fish to make a direct hit? If, instead, you zap the fish with a laser, should you aim above, below, or directly at the observed fish? Defend your answers.

Throw the spear below the apparent position of the fish because refraction makes the fish appear closer to the surface than it really is. But in zapping a fish with a laser, make no corrections and simply aim directly at the fish. This is because the light from the fish you see has been refracted in getting to you, and the laser light will refract along the same path in getting to the fish. A slight correction may be necessary, depending on the colors of the laser beam and the fish.

Car mirrors are uncoated on the front surface and silvered on the back surface. When the mirror is properly adjusted, light from behind reflects from the silvered surface into the driver's eyes. Good. But this is not so good at nighttime with the glare of headlights behind. This problem is solved by the wedge shape of the mirror (see the sketch). When the mirror is tilted slightly upward toward the ceiling, away from the driver's eyes. Yet the driver can still see cars behind in the mirror. Explain.

Two surfaces of the mirror reflect light. The front surface reflects about 4% of the incident light, and the silvered surface reflects most of the rest. When the mirror is tilted in the "daytime" position, the driver sees light reflecting from the silvered surface. In the "nighttime" position, with the mirror tilted upward, light reflecting from the silvered surface is directed above the driver's view and the driver sees light reflected from the front surface of the mirror. That 4% of rearview light is adequate for night driving.

A rainbow viewed from an airplane may form a complete circle. Where will the shadow of the airplane appear? Explain.

When the Sun is high in the sky and people on the airplane are looking down toward a cloud opposite to the direction of the Sun, they may see a rainbow that makes a complete circle. The shadow of the airplane will appear in the center of the circular bow. This is because the airplane is directly between the Sun and the drops or rain cloud producing the bow.

Can a surface be considered polished for some waves and not others? Give an example.

Yes. A surface may be polished for short-wavelength waves and not for longer ones. The mesh on a parabolic dish is rough for short waves, but not for long waves.

The image produced by a converging lens is upside down. Our eyes have converging lenses. Does this mean the images we see are upside down on our retinas? Explain.

Yes. The images are indeed upside-down! The brain re-inverts them.

Does the law of reflection hold for curved mirrors? Explain.

Yes. The law of reflection holds locally at each tiny part of the curved surface, but not for the curved mirror as a whole.

Cowboy Joe wishers to shoot his assailant by ricocheting a bullet off a mirrored metal plate. To do so, should he simply aim at the mirrored image of his assailant? Explain.

Yes. The ricocheting bullet will follow the same changes in direction when its momentum changes (angle of incidence = angle of rebound) that light follows when it reflects from a plane surface.

What exactly are you seeing when you observe a "water on the road" mirage?

You are seeing skylight refracted upward near the road surface.