Chapter 11: Light — Review and Exercises

Choose the four statements that represent Maxwell’s equations.

A. Electric field lines originate on positive charges and terminate on negative charges.

B. Magnetic field lines have no beginning or end.

C. A changing magnetic field induces an electric field.

D. Magnetic fields can be produced by electric currents or changing electric fields.

E. An object maintains constant velocity unless acted on by a net force.

F. Energy is conserved.

Which selected statement contains Maxwell’s addition to the theory?

Which of the following motions of an electric charge produces electromagnetic radiation: remaining at rest, moving with constant velocity, or oscillating back and forth? Explain what distinguishes the radiating motion from the others.

An electromagnetic wave travels horizontally to the right, and its electric field oscillates vertically. Describe the direction in which its magnetic field oscillates. Explain why this is a transverse wave.

IKAROS demonstrated propulsion using a reflecting solar sail.

(a) Explain how sunlight can exert a force on the solar sail and accelerate the spacecraft.

(b) Why use a reflecting sail rather than one that absorbs the sunlight? Explain in terms of momentum transfer.

Two radio waves travel through vacuum. One has a frequency of 1 MHz and the other 100 MHz. (a) How do their speeds compare? (b) Which has the longer wavelength, and by what factor? Explain without calculating either wavelength separately.

Compare red and blue light traveling through vacuum. Which has the higher frequency? Which has the longer wavelength? How do their speeds compare?

How do fluorescent soap residues make clothing look “brighter and whiter” in outdoor light? Would this be effective in candlelight?

Give an example of resonance in the reception of electromagnetic waves.

Ultraviolet microscopes can reveal smaller details than visible-light microscopes. Explain how this is related to the wavelengths of ultraviolet and visible light.

Why don’t buildings block radio waves as completely as they do visible light?

Make a list of some everyday objects and decide whether they are transparent or opaque to each of the types of electromagnetic waves.

Your friend says that more patterns and colors can be seen on the wings of birds if viewed in ultraviolet light. Would you agree with your friend? Explain your answer.

Optical fibers can carry far more telephone conversations than a narrow-band radio link because they offer much greater communication bandwidth. Why would the very narrow bandwidth available for ELF communication limit the information sent to submarines?

Give an example of energy carried by an electromagnetic wave.

An MRI scan can resolve details much smaller than the wavelength of the radio waves it uses. Explain how this is possible.

Laser vision correction often uses an excimer laser that produces 193-nm electromagnetic radiation. This wavelength is extremely strongly absorbed by the cornea and ablates it in a manner that reshapes the cornea to correct vision defects. Explain how the strong absorption helps concentrate the energy in a thin layer and thus give greater accuracy in shaping the cornea. Also explain how this strong absorption limits damage to the lens and retina of the eye.

Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?

Does the law of reflection apply to a curved mirror? Explain how you would determine the normal used to measure the angles of incidence and reflection at a particular point on the mirror.

Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

Why is the index of refraction always greater than or equal to 1?

Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Would measuring the delay between the flash and the thunder be enough to determine the speed of light? Explain what additional information you would need.

Will light change direction toward or away from the perpendicular when it goes from air to water? Water to glass? Glass to air?

Explain why an object in water always appears to be at a depth shallower than it actually is? Why do people sometimes sustain neck and spinal injuries when diving into unfamiliar ponds or waters?

Explain why a person’s legs appear very short when wading in a pool. Justify your explanation with a ray diagram showing the path of rays from the feet to the eye of an observer who is out of the water.

A ray of light enters a glass pane obliquely from air and emerges into air on the other side. The pane’s two faces are parallel. Sketch the ray’s path through both boundaries. Is the emerging ray parallel to the incident ray? Is it on the same line? Explain.

The diagrams show possible paths of a light ray entering a transparent prism from air on the left and emerging into air on the right. The ray strikes the first face perpendicularly. Which diagram correctly shows the direction of bending at each face? Explain your choice.

What is the speed of light in water? In glycerine?

What is the speed of light in air? In crown glass?

Calculate the index of refraction for a medium in which the speed of light is $2.012\times {10}^8\text{m/s}$, and identify the most likely substance based on Table 11.7.1.

In what substance in Table 11.7.1 is the speed of light $2.290\times {10}^8\text{m/s}$?

There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is $3.84\times {\text{10}}^5\text{km}$ away, would the light first arrive on Earth?

Components of some computers communicate with each other through optical fibers having an index of refraction $n=1\text{.}\text{55}$. What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?

Astronauts placed retroreflectors on the Moon that return laser pulses sent from Earth. The distance to a reflector is calculated from the round-trip travel time. Suppose the Moon is directly overhead, and take the distance from the observing station to the reflector to be $3.84\times {10}^8\text{m}$. For this estimate, model Earth’s atmosphere as an equivalent uniform layer 8.0 km thick with a constant index of refraction $n=1.000293$; treat the rest of the path as vacuum. By what percentage would the calculated distance exceed the actual distance if the slowing of light in the atmosphere were ignored?

(a) What is the ratio of the speed of red light to violet light in diamond, based on Table 11.8.1? (b) What is this ratio in polystyrene? (c) Which is more dispersive?

White light passes through a glass prism and emerges as a spectrum. Is the prism creating these colors or separating colors already present in the light? Explain why different colors emerge in different directions.

It can be argued that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are $d_{\text{i}}$ and $d_{\text{o}}$ related?

You can often see a reflection when looking at a sheet of glass, particularly if it is darker on the other side. Explain why you can often see a double image in such circumstances.

When you focus a camera, you adjust the distance of the lens from the film. If the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?

A thin lens has two focal points, one on either side, at equal distances from its center, and should behave the same for light entering from either side. Look through your eyeglasses (or those of a friend) backward and forward and comment on whether they are thin lenses.

A converging glass lens is moved from air into water. Will its focal length increase, decrease, or remain unchanged? Explain using refraction at the lens surfaces.

Two thin glass lenses are surrounded by air. One is thicker at its center than at its edges; the other is thinner at its center. Classify each as converging or diverging, and sketch what happens to parallel rays passing through each lens.

What are the differences between real and virtual images? How can you tell (by looking) whether an image formed by a single lens or mirror is real or virtual?

Can you see a virtual image? Can you photograph one? Can one be projected onto a screen with additional lenses or mirrors? Explain your responses.

Can you see a real image without projecting it onto a screen? Explain.

Under what circumstances will an image be located at the focal point of a lens or mirror?

What is meant by a negative magnification? What is meant by a magnification that is less than 1 in magnitude?

(a) Figure 11.10.4 shows an image that is larger than the object, yet its magnification is negative. Explain how the sign and magnitude of the magnification describe different features of this image. (b) Keeping the same mirror, could you move the object so that its real image is smaller than the object? Draw a ray diagram to support your answer.

Figure 11.E.2 shows a light bulb between two mirrors. One mirror produces a beam of light with parallel rays; the other keeps light from escaping without being put into the beam. Where is the filament of the light in relation to the focal point or radius of curvature of each mirror?

Devise an arrangement of mirrors allowing you to see the back of your head. What is the minimum number of mirrors needed for this task?

If you wish to see your entire body in a flat mirror (from head to toe), how tall should the mirror be? Does its size depend upon your distance away from the mirror? Provide a sketch.

It can be argued that a flat mirror has an infinite focal length. If so, where does it form an image? That is, how are $d_{\text{i}}$ and $d_{\text{o}}$ related?

Why are diverging mirrors often used for rear-view mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?

Can a sound wave in air be polarized? Explain.

No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

(a) Light scattered by air molecules is partially polarized. Explain how you could demonstrate this using a polarizing filter while looking at a clear sky.

(b) When the scattering particles are much smaller than the wavelength of light, the amount of scattering is proportional to $1/{\lambda }^4$. Which is scattered more strongly: red light or blue light? Use this to explain why the daytime sky appears blue.

(c) Near sunset, sunlight travels through more of Earth’s atmosphere before reaching your eyes than it does at midday. Explain why the Sun often appears red or orange near sunset.

(a) What does the direction of polarization specify about an electromagnetic wave?

(b) Light reflected from a horizontal water surface is often predominantly horizontally polarized. How should the transmission axis of a polarizing filter be oriented to reduce this glare? Explain.