Optics

The electric field of a sinusoidal electromagnetic wave obeys the equation . (a) What is the speed of the wave? (b) What are the amplitudes of the electric and magnetic fields of this wave? (c) What are the frequency, wavelength, and period of the wave? Is this light visible to humans?

In the United States, household electrical power is provided at a frequency of 60 Hz, so electromagnetic radiation at that frequency is of particular interest. On the basis of the ICNIRP guidelines, what is the maximum intensity of an electromagnetic wave at this frequency to which the general public should be exposed? (a) $\mathbf{7}\mathbf{.}\mathbf{7}\mathit{W}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$; (b) $\mathbf{160}\mathit{W}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$; (c) $\mathbf{45}\mathit{W}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$; (d) $\mathbf{260}\mathit{W}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$.

Doubling the frequency of a wave in the range of $\mathbf{24}\mathit{H}\mathit{z}$ to represents what change in the maximum allowed electromagnetic-wave intensity? (a) A factor of 2; (b) A factor of $\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}$; (c) A factor of 1/2; (d) A factor of 1/4.

Answer:

The ICNIRP also has guidelines for magnetic-field exposure for the general public. In the frequency range of \(25Hz\) to\(3kHz\), this guidelines states that the maximum allowed magnetic field amplitude is \(\frac{5}{f}T\), where\(f\) is the frequency is kHZ. Which is a more stringent limit on allowable electromagnetic-wave intensity in this frequency range: the electric-field guideline or the magnetic-field guideline? (a) The magnetic-field guideline, because at a given frequency the allowed magnetic field is smaller than the allowed electric field. (b) The electric field guideline, because at a given frequency, the allowed intensity calculated from the electric-field guideline is smaller. (c) It depends on the particular frequency chosen (both guidelines are frequency dependent). (d) Neither – for any given frequency, the guidelines represent the same electromagnetic-wave intensity.

Light requires about 8 minutes to travel from the sun to the earth. Is it delayed appreciably by the earth’s atmosphere? Explain.

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?

Sunlight or starlight passing through the earth’s atmosphere is always ben toward the vertical. Why? Does this mean that a star is not really where it appears to be? Explain.

A beam of light goes from one material into another. On physical grounds, explain why the wavelength changes but the frequency and period do not.

A student claimed that, because of atmospheric refraction (see Discussion Question Q33.2), the sun can be seen after it has set and that the day is therefore longer than it would be if the earth had no atmosphere. First, what does she mean by saying that the sun can be seen after it has set? Second, comment on the validity of her conclusion.

When hot air rises from a radiator or heating duct, objects behind it appear to shimmer or waver. What causes this?

Devise straightforward experiments to measure the speed of light in a given glass using (a) Snell’s law; (b) total internal reflection; (c) Brewster’s law

Sometimes when looking at a window, you see two reflected images slightly displaced from each other. What causes this?

If you look up from underneath toward the surface of the water in your aquarium, you may see an upside-down reflection of your pet fish in the surface of the water. Explain how this can happen.

A ray of light in air strikes a glass surface. Is there a range of angles for which total internal reflection occurs? Explain.

When light is incident on an interface between two materials, the angle of the refracted ray depends on the wavelength, but the angle of the reflected ray does not. Why should this be?

A salesperson at a bargain counter claims that a certain pair of sunglasses has Polaroid filters; you suspect that the glasses are just tinted plastic. How could you find out for sure?

Does it make sense to talk about the polarization of a longitudinal wave, such as a sound wave? Why or why not?

How can you determine the direction of the polarizing axis of a single polarizer?

It has been proposed that automobile windshields and headlights should have polarizing filters to reduce the glare of oncoming lights during night driving. Would this work? How should the polarizing axes be arranged? What advantages would this scheme have? What disadvantages?

When a sheet of plastic food wrap is placed between two crossed polarizers, no light is transmitted. When the sheet is stretched in one direction, some light passes through the crossed polarizers. What is happening?

If you sit on the beach and look at the ocean through Polaroid sunglasses, the glasses help to reduce the glare from sunlight reflecting off the water. But if you lie on your side on the beach, there is little reduction in the glare. Explain why there is a difference.

When unpolarized light is incident on two crossed polarizers, no light is transmitted. A student asserted that if a third polarizer is inserted between the other two, some transmission will occur. Does this make sense? How can adding a third filter increase transmission?

For the old “rabbit-ear” style TV antennas, it’s possible to alter the quality of reception considerably simply by changing the orientation of the antenna. Why?

In Fig. 33.31, since the light that is scattered out of the incident beam is polarized, why is the transmitted beam not also partially polarized?

You are sunbathing in the late afternoon when the sun is relatively low in the western sky. You are lying flat on your back, looking straight up through Polaroid sunglasses. To minimize the amount of sky light reaching your eyes, how should you lie: with your feet pointing north, east, south, west, or in some other direction? Explain your reasoning

Light scattered from the blue sky is strongly polarized because of the nature of the scattering process described in Section 33.6. But light scattered from white clouds is usually not polarized. Why not?

Atmospheric haze is due to water droplets or smoke particles (“smog”). Such haze reduces visibility by scattering light so that the light from distant objects becomes randomized and images become indistinct. Explain why visibility through haze can be improved by wearing red-tinted sunglasses, which filter out blue light.  

The explanation given in Section 33.6 for the color of the setting sun should apply equally well to the rising sun, since sunlight travels the same distance through the atmosphere to reach your eyes at either sunrise or sunset. Typically, however, sunsets are redder than sunrises. Why? (Hint: Particles of all kinds in the atmosphere contribute to scattering.)

Huygens’s principle also applies to sound waves. During the day, the temperature of the atmosphere decreases with increasing altitude above the ground. But at night, when the ground cools, there is a layer of air just above the surface in which the temperature increases with altitude. Use this to explain why sound waves from distant sources can be heard more clearly at night than in the daytime. (Hint: The speed of sound increases with increasing temperature. Use the ideas displayed in Fig. 33.36 for light.)

Can water waves be reflected and refracted? Give examples. Does Huygens’s principle apply to water waves? Explain.

The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

A beam of light has a wavelength of 650 nm in vacuum. (a) What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.47? (b) What is the wavelength of these waves in the liquid?

Light with a frequency of $\mathbf{5}\mathbf{.}\mathbf{80}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{Hz}$ travels in a block of glass that has an index of refraction of 1.52. What is the wavelength of the light (a) in vacuum and (b) in the glass?

A light beam travels at$\mathbf{1}\mathbf{.}\mathbf{94}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{m}\mathbf{/}\mathbf{s}$in quartz. The wavelength of the light in quartz is 355 nm. (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?

Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?

A parallel beam of light in air makes an angle of 47.5º with the surface of a glass plate having a refractive index of 1.66. (a) What is the angle between the reflected part of the beam and the surface of the glass? (b) What is the angle between the refracted beam and the surface of the glass?

A laser beam shines along the surface of a block of transparent material (see Fig. E33.8). Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the two light beams at the detector is 6.25 ns. What is the index of refraction of this material?

A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. (a) If the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the air at this surface? (b) What would be the minimum angle in part (a) if the cube were immersed in water?

A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass– water interface at an angle to the normal larger than 48.7°, no light is refracted into the water. What is the refractive index of the glass?

At the very end of Wagner’s series of operas Ring of the Nibelung, Brünnhilde takes the golden ring from the finger of the dead Siegfried and throws it into the Rhine, where it sinks to the bottom of the river. Assuming that the ring is small enough compared to the depth of the river to be treated as a point and that the Rhine is 10.0 m deep where the ring goes in, what is the area of the largest circle at the surface of the water over which light from the ring could escape from the water?

Light is incident along the normal on face AB of a glass prism of refractive index 1.52, as shown in Fig. E33.21. Find the largest value the angle$\mathbf{\infty }$can have without any light refracted out of the prism at face AC if (a) the prism is immersed in air and (b) the prism is immersed in water.

The indexes of refraction for violet light ($\mathit{\lambda }$= 400 nm) and red light ($\mathit{\lambda }$= 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through airstrikes the diamond surface at an angle of 53.5° to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in Fig. E33.23. For the transmitted light inside the glass, through what angle $\mathbf{∆}\mathit{\theta }$is the portion of the visible spectrum between 400 nm and 700 nm dispersed? (Consult the graph in Fig. 33.17.)

A beam of light strikes a sheet of glass at an angle of 57.0° with the normal in air. You observe that red light makes an angle of 38.1° with the normal in the glass, while violet light makes a 36.7° angle. (a) What are the indexes of refraction of this glass for these colors of light? (b) What are the speeds of red and violet light in the glass?

Unpolarized light with intensity ${\mathit{I}}_{\mathbf{o}}$ is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed through the second filter?

(a) At what angle above the horizontal is the sun if sunlight reflected from the surface of a calm lake is completely polarized? (b) What is the plane of the electric-field vector in the reflected light?

A beam of unpolarized light of intensity ${\mathit{I}}_{\mathbf{0}}$ passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in Fig. E33.27. (a) What is the light intensity (in terms of ${\mathit{I}}_{\mathbf{0}}$) at points A, B, and C? (b) If we remove the middle filter, what will be the light intensity at point C?

Light of original intensity ${\mathit{I}}_{\mathbf{0}}$ passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle $\mathit{\varphi }$ so that the intensity at point P is equal to ${\mathit{I}}_{\mathbf{0}}\mathbf{/}\mathbf{10}$ . (a) If the original light is unpolarized, what should $\mathit{\varphi }$ be? (b) If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should$\mathit{\varphi }$be?

A parallel beam of unpolarized light in air is incident at an angle of 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam?

The refractive index of a certain glass is 1.66. For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in (a) air and (b) water?