Fermat’s principle is of least time rather than of least

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

What do the electrons affected by illumination do when they are made to vibrate with greater energy?

What is Fermat’s principle of least time?

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

Cite the law of reflection.

What fraction of the light shining straight at a piece of clear glass is reflected from the first surface?

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

How does the angle at which a ray of light strikes a pane of window glass compare with the angle at which the light passes out the other side?

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

In which medium does light travel faster: thin air or dense air? How does this affect the period of daylight?

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

Is a mirage the result of reflection or refraction?

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?

What is the angle between a light ray and its wavefront?

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

Are eyeglasses made with “high index of refraction” materials thin or thick?

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

Which travels more slowly in glass: red light or violet light?

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

Does a viewer see a single color or a spectrum of colors coming from a single faraway drop?

Why is a secondary rainbow dimmer than a primary bow?

What is meant by “critical angle”?

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

Light normally travels in straight lines, but it “bends” in an optical fiber. Explain.

Distinguish between a converging lens and a diverging lens.

What is the focal length of a lens?

Distinguish between a virtual image and a real image.

What kind of lens can be used to produce a real image? A virtual image?

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

What is astigmatism, and how can it be corrected?

Suppose you walk toward a mirror at 2 m/s. How fast do you and your image approach each other? (The answer is not 2 m/s.)

Text Grandma and convince her that in order to see her full-length image in a mirror, the mirror need be only half her height. Discuss also the intriguing role of distance in a mirror being half size. Perhaps rough sketches to accompany your explanations will help.

Show with a simple diagram that when a mirror with a fixed beam incident upon it is rotated through a certain angle, the reflected beam is rotated through an angle twice as large. (This doubling of displacement makes irregularities in ordinary window glass more evident.)

A butterfly at eye level is 20 cm in front of a plane mirror. You are behind the butterfly, 50 cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror?

When light strikes glass perpendicularly, about 4% is reflected at each surface. Show that 92% of light is transmitted through a pane of window glass.

No glass is perfectly transparent. Mainly because of reflections, about 92% of light passes through an average sheet of clear windowpane. The 8% loss is not noticed through a single sheet, but through several sheets, the loss is apparent. How much light is transmitted by a double-paned window (one with two sheets of glass)?

The diameter of the Sun makes an angle of \(0.53^\circ\) from Earth. How many minutes does it take the Sun to move 1 solar diameter in an overhead sky? (Remember that it takes 24 hours, or 1440 minutes, for the Sun to move through \(360^\circ\).) How does your answer compare with the time it takes the Sun to disappear, once its lower edge meets the horizon at sunset? (Does refraction affect your answer?)

She looks at her face in the handheld mirror. Rank the amounts of her face that she sees in the three locations, from greatest to least (or is it the same in all positions?).

Wheels from a toy cart are rolled from a concrete side walk onto the following surfaces: \(A\), a paved driveway; \(B\), a grass lawn; and \(C\), close-cropped grass on a golf-course putting green. Due to slowing, each set of wheels bends at the boundary and is deflected from its initial straight line course. Rank the surfaces according to the amount each set of wheels bends at the boundary, from greatest amount of bending to least. Equation Transcription: Text Transcription: A B C

Identical rays of light enter three transparent blocks composed of different materials. Light slows down upon entering the blocks. Rank the blocks according to the speed light travels in each, from highest to lowest.

\(46\). Identical rays of light in air are refracted upon entering three transparent materials: \(A\), water, where the speed of light is \(0.75 c\); \(B\), ethyl alcohol (speed \(0.7 c\)); and \(C\), crown glass (speed \(0.6 c\)). Rank the materials according to how much the light ray bends toward the normal, from most bending to least bending. Equation Transcription: Text Transcription: 46 A 0.75c B 0.7c C 0.6c

In the opening photo of the duck standing on the rock, why aren’t the duck’s feet shown in the reflected view?

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

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?

Her eye at point \(P\) looks into the mirror. Which of the numbered cards can she see reflected in the mirror? Equation Transcription: Text Transcription: P

Cowboy Joe wishes 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.

\(54\). Why is the lettering on the front of some vehicles “backward”? Equation Transcription: Text Transcription: 54

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

When you look at yourself in the mirror and wave your right hand, your beautiful image waves the left hand. Then why don’t the feet of your image wiggle when you shake your head?

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 is solved by the wedge shape of the mirror (see the sketch). When the mirror is tilted slightly upward to the “nighttime” position, glare is directed upward toward the ceiling, away from the driver’s eyes. Yet the driver can still see cars behind in the mirror. Explain.

A person in a dark room looking through a window can clearly see a person outside in the daylight, whereas the person outside cannot see the person inside. Explain.

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

What must be the minimum length of a plane mirror in order for you to see a full image of yourself?

What effect does your distance from the plane mirror have in your answer to the preceding exercise? (Try it and see!)

Hold a pocket mirror almost at arm’s length from your face and note how much of your face you can see. To see more of your face, should you hold the mirror closer or farther away, or would you have to have a larger mirror? (Try it and see!)

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 sketch shows a person and her twin at equal distances on opposite sides of a thin wall. Suppose a window is to be cut into the wall so that each twin can see a complete view of the other. Show the size and location of the smallest window that can be cut into the wall to do the job. (Hint: Draw rays from the top of each twin’s head to the other twin’s eyes. Do the same from the feet of each to the eyes of the other.)

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 nearsighted or farsighted?

If a nearsighted person wants thinner eyeglasses, is a higher or a lower index of refraction for the lenses recommended?

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?

A pair of toy cart wheels is rolled obliquely from a smooth surface onto two plots of grass, a rectangular plot and a triangular plot, as shown. The ground is on a slight incline so that, after slowing down in the grass, the wheels will speed up again when emerging on the smooth surface. Finish each sketch by showing some positions of the wheels inside the plots and on the other sides, thereby indicating the direction of travel.

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?

During a lunar eclipse, the Moon is not completely dark but is usually deep red. Explain this in terms of the refraction of all the sunsets and sunrises around the world.

What accounts for the large shadows cast by the ends of the thin legs of the water strider?

When you stand with your back to the Sun, you see a rainbow as a circular arc. Could you move off to one side and then see the rainbow as the segment of an ellipse rather than the segment of a circle (as Figure 28.33 suggests)? Defend your answer. Figure 28.33

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

If a fish wore goggles above the water surface, why would the fish’s vision be better if the goggles were filled with water? Explain.

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

Cover the top half of a camera lens. What effect does this have on the pictures taken?

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!)

How could a converging lens be made for sound waves? (Such a lens, a spherical bag of gas, is a feature of San Francisco’s Exploratorium.)

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

There is less difference between the speed of light in glass and the speed of light in water than there is between the speed of light in glass and the speed of light in air. Does this mean that a magnifying glass will magnify more or magnify less when it is used under water rather than in air?

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

Why doesn’t the sharpness of the image in a pinhole camera depend on the position of the viewing screen?

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

\(84\). If you point the pinhole camera of question \(82\) at the Sun, a clear and bright solar image will be seen on the viewing screen. How does this relate to the circular spots of light that surround Lillian beneath the sunlit tree shown in the photo? Equation Transcription: Text Transcription: 84 82

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

Why do you put slides into an old-fashioned slide projector upside down?

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

The images produced by a converging camera lens are upside down. Does this mean the photographs taken with cameras are upside down?

Maps of the Moon are upside down. Why?

Why do older people who do not wear glasses read books farther away from their eyes than younger people do?

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? Equation Transcription: Text Transcription: n

To reduce glare from the surroundings, the windows of some department stores, rather than being vertical, slant inward at the bottom. Discuss why this reduces glare.

Which kind of road surface is easier to see when driving at night: a pebbled, 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.

Why does reflected light from the Sun or Moon appear as a column in the body of water as shown? How would the reflected light appear if the water surface were perfectly smooth?

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

What is wrong with the cartoon of the man looking at himself in the mirror? (Have a friend face a mirror as shown, and you’ll see.)

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.

When a flashlight submerged in water shines up into the air above, does the speed of light increase or decrease when the light passes from water into the air?

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.

If the fish in the preceding exercise were small and blue and your laser light were red, what corrections should you make? Explain.

When a fish in a pond looks upward at an angle of \(45^{\circ}\), 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. Text Transcription: 45^circ

Rays of light moving upward through water toward the water–air boundary at angles larger than \(48^{\circ}\) to the normal are totally reflected. No rays larger than \(48^{\circ}\) refract outside. How about the reverse? Is there an angle at which light rays in air meeting the air–water boundary will totally reflect? Or will some light be refracted at all angles? Text Transcription: 48^circ

Two observers standing apart from each other do not see the “same” rainbow. Explain.

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.

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

How is a rainbow similar to the halo sometimes seen around the Moon on a frosty night? If you’re stumped, check the Internet and see how rainbows and halos differ

Transparent plastic swimming-pool covers called solar heat sheets have thousands of small air-filled bubbles that resemble lenses. The bubbles in these sheets are advertised to focus heat from the Sun into the water, thereby raising its temperature. Do you think these bubbles direct more solar energy into the water? Defend your answer.

Would the average intensity of sunlight measured by a light meter at the bottom of the pool in Figure 28.46 be different if the water were still?

When your eye is submerged in water, light rays bend only slightly when they pass from the water into your cornea. Why isn’t the bending as pronounced as when light passes from air into your cornea? (How do the indices of refraction differ for your cornea, air, and water?)

When your eye is submerged in water, does the speed of light increase, decrease, or remain constant as it passes from the water into your cornea?

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.