Solved: One technique for measuring the angle of a prism

How many 800-nm photons does it take to have the same total energy as four 200-nm photons? (a) 1 (b) 2 (c) 4 (d) 8 (e) 16

Carbon disulfi de (n _ 1.63) is poured into a container made of crown glass (n _ 1.52). What is the critical angle for internal refl ection of a ray in the liquid when it is incident on the liquid-to-glass surface? (a) 89 (b) 69 (c) 21 (d) 4.0 (e) 33

A monochromatic light source emits a wavelength of 495 nm in air. When passing through a liquid, the wavelength reduces to 434 nm. What is the liquids index of refraction? (a) 1.26 (b) 1.49 (c) 1.14 (d) 1.33 (e) 2.03

What happens to a light wave when it travels from air into glass? (a) Its speed remains the same. (b) Its speed increases. (c) Its wavelength increases. (d) Its wavelength remains the same. (e) Its frequency remains the same.

The index of refraction for water is about 4/3. What happens to light when it travels from air into water? (a) Its speed increases to 4c/3, and its frequency decreases. (b) Its speed decreases to 3c/4, and its wavelength decreases by a factor of 3/4. (c) Its speed decreases to 3c/4, and its wavelength increases by a factor of 4/3. (d) Its speed and frequency remain the same. (e) Its speed decreases to 3c/4, and its frequency increases.

Light can travel from air into water or from water into air, with some possible paths as shown in Figure MCQ22.6. Which path will the light most likely follow? (a) A (b) B (c) C (d) D (e) E

Light traveling in a medium of index of refraction n1 is incident on another medium having an index of refraction n2. Under which of the following conditions can total refl ection occur at the interface of the two media? (a) n2 > n1 (b) n1 > n2 (c) Light travels slower in the second medium than in the fi rst. (d) The angle of incidence is less than the critical angle. (e) The angle of incidence must equal the refraction angle.

A light ray containing both blue and red wavelengths is incident at an angle on a slab of glass. Which of the sketches in Figure MCQ22.8 represents the most likely outcome? (a) A (b) B (c) C (d) D (e) none of these

Which color light is bent the most when entering crown glass from air at some positive angle u with respect to the normal? (a) violet (b) blue (c) green (d) yellow (e) red

A light ray travels from vacuum into a slab of material with index of refraction n1 with incident angle u. It subsequently passes into a second slab of material with index of refraction n2 before passing back into vacuum again. The surfaces of the different materials are all parallel to one another. As the light exits the second slab, what can be said of the fi nal angle f that the light makes with the normal? (a) f u (b) f _ u (c) f _ u (d) The angle depends on the magnitudes of n1 and n2. (e) The angle depends on the wavelengths of the light.

A ray of light is moving from a material having a high index of refraction into a material with a lower index of refraction. (a) Is the ray bent toward the normal or away from it? (b) If the wavelength is 600 nm in the material with the high index of refraction, is it greater, smaller, or the same in the material with the lower index of refraction? (c) How does the frequency change as the light moves between the two materials? Does it increase, decrease, or remain the same?

Why does the arc of a rainbow appear with red on top and violet on the bottom?

A scientifi c supply catalog advertises a material having an index of refraction of 0.85. Is that a good product to buy? Why or why not?

Under what conditions is a mirage formed? On a hot day, what are we seeing when we observe a mirage of a water puddle on the road?

In dispersive materials, the angle of refraction for a light ray depends on the wavelength of the light. Does the angle of refl ection from the surface of the material depend on the wavelength? Why or why not?

A type of mirage called a pingo is often observed in Alaska. Pingos occur when the light from a small hill passes to an observer by a path that takes the light over a body of water warmer than the air. What is seen is the hill and an inverted image directly below it. Explain how these mirages are formed.

Explain why a diamond loses most of its sparkle when submerged in carbon disulfi de.

Suppose you are told that only two colors of light (X and Y) are sent through a glass prism and that X is bent more than Y. Which color travels more slowly in the prism?

The level of water in a clear, colorless glass can easily be observed with the naked eye. The level of liquid helium in a clear glass vessel is extremely diffi cult to see with the naked eye. Explain. Hint: The index of refraction of liquid helium is close to that of air.

Is it possible to have total internal refl ection for light incident from air on water? Explain.

Why does a diamond show fl ashes of color when observed under white light?

Explain why an oar partially submerged in water appears to be bent.

Why do astronomers looking at distant galaxies talk about looking backward in time?

During the Apollo XI Moon landing, a retrorefl ecting panel was erected on the Moons surface. The speed of light can be found by measuring the time it takes a laser beam to travel from Earth, refl ect from the panel, and return to Earth. If this interval is found to be 2.51 s, what is the measured speed of light? Take the center-to- center distance from Earth to the Moon to be 3.84 _ 108 m. Assume the Moon is directly overhead and do not neglect the sizes of Earth and the Moon.

(a) What is the energy in joules of an x-ray photon with wavelength 1.00 _ 10_10 m? (b) Convert the energy to electron volts. (c) If more penetrating x-rays are desired, should the wavelength be increased or decreased? (d) Should the frequency be increased or decreased?

Find the energy of (a) a photon having a frequency of 5.00 _ 1017 Hz and (b) a photon having a wavelength of 3.00 _ 102 nm. Express your answers in units of electron volts, noting that 1 eV _ 1.60 _ 1019 J.

(a) Calculate the wavelength of light in vacuum that has a frequency of 5.45 _ 1014 Hz. (b) What is its wavelength in benzene? (c) Calculate the energy of one photon of such light in vacuum. Express the answer in electron volts. (d) Does the energy of the photon change when it enters the benzene? Explain.

Find the speed of light in (a) water, (b) crown glass, and (c) diamond.

(a) Find a symbolic expression for the wavelength l of a photon in terms of its energy E, Plancks constant h, and the speed of light c. (b) What does the equation say about the wavelengths of higher-energy photons?

A ray of light travels from air into another medium, making an angle of 45 with the normal as in Figure P22.7. Find the angle of refraction u2 if the second medium is (a) quartz, (b) carbon disulfi de, and (c) water.

The two mirrors in Figure P22.8 meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown. (a) Determine the distance the refl ected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being refl ected from mirror 2?

An underwater scuba diver sees the Sun at an apparent angle of 45.0 from the vertical. What is the actual direction of the Sun?

A beam of light traveling in air strikes the surface of mineral oil at an angle of 23.1 with the normal to the surface. If the light travels at 2.17 _ 108 m/s in the oil, what are the (a) index of refraction of mineral oil and (b) angle of refraction?

A laser beam is incident at an angle of 30.0 to the vertical onto a solution of corn syrup in water. If the beam is refracted to 19.24 to the vertical, (a) what is the index of refraction of the syrup solution? Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its (b) wavelength, (c) frequency, and (d) speed in the solution.

Light containing wavelengths of 400 nm, 500 nm, and 650 nm is incident from air on a block of crown glass at an angle of 25.0. (a) Are all colors refracted alike, or is one color bent more than the others? (b) Calculate the angle of refraction in each case to verify your answer.

A ray of light is incident on the surface of a block of clear ice at an angle of 40.0 with the normal. Part of the light is refl ected, and part is refracted. Find the angle between the refl ected and refracted light.

A laser beam with vacuum wavelength 632.8 nm is incident from air onto a block of Lucite, as shown in Active Figure 22.6b. The line of sight of the photograph is per- pendicular to the plane in which the light moves. Find the (a) speed, (b) frequency, and (c) wavelength of the light in the Lucite. Suggestion: Use a protractor.

The light emitted by a heliumneon laser has a wavelength of 632.8 nm in air. As the light travels from air into zircon, fi nd its (a) speed, (b) wavelength, and (c) frequency, all in the zircon.

A fl ashlight on the bottom of a 4.00-m-deep swimming pool sends a ray upward and at an angle so that the ray strikes the surface of the water 2.00 m from the point directly above the fl ashlight. What angle (in air) does the emerging ray make with the waters surface?

How many times will the incident beam shown in Figure P22.17 be refl ected by each of the parallel mirrors?

A ray of light strikes a fl at, 2.00-cm-thick block of glass (n = 1.50) at an angle of 30.0 with respect to the normal (Fig. P22.18). (a) Find the angle of refraction at the top surface. (b) Find the angle of incidence at the bottom surface and the refracted angle. (c) Find the lateral distance d by which the light beam is shifted. (d) Calculate the speed of light in the glass and (e) the time required for the light to pass through the glass block. (f) Is the travel time through the block affected by the angle of incidence? Explain.

The light beam shown in Figure P22.19 makes an angle of 20.0 with the normal line NN_ in the linseed oil. Determine the angles u and u_. (The refractive index for linseed oil is 1.48.)

A laser beam is incident on a 454590 prism perpendicular to one of its faces, as shown in Figure P22.20. The transmitted beam that exits the hypotenuse of the prism makes an angle of 15 with the direction of the incident beam. Find the index of refraction of the prism.

Two light pulses are emitted simultaneously from a source. The pulses take parallel paths to a detector 6.20 m away, but one moves through air and the other through a block of ice. Determine the difference in the pulses times of arrival at the detector.

A narrow beam of ultrasonic waves refl ects off the liver tumor in Figure P22.22. If the speed of the wave is 10.0% less in the liver than in the surrounding medium, determine the depth of the tumor. FIGURE P22.22 50.0 12.0 cm Liver Tumor

A person looking into an empty container is able to see the far edge of the containers bottom, as shown in Figure P22.23a. The height of the container is h, and its width is d. When the container is completely fi lled with a fl uid of index of refraction n, the person can see a coin at the middle of the containers bottom, as shown in Figure P22.23b. (a) Show that the ratio h/d is given by h d 5 n2 2 1 4 2 n2 (b) Assuming the container has a width of 8.0 cm and is fi lled with water, use the expression above to fi nd the height of the container. FIGURE P22.23 d (a) h (b)

A submarine is 3.00 _ 102 m horizontally from shore and 1.00 _ 102 m beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water 2.10 _ 102 m from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to fi nd the height of the target above sea level. (a) Draw a diagram of the situation, identifying the two triangles that are important to fi nding the solution. (b) Find the angle of incidence of the beam striking the waterair interface. (c) Find the angle of refraction. (d) What angle does the refracted beam make with respect to the horizontal? (e) Find the height of the target above sea level.

A beam of light both refl ects and refracts at the surface between air and glass, as shown in Figure P22.25. If the index of refraction of the glass is ng, fi nd the angle of incidence, u1, in the air that would result in the refl ected ray and the refracted ray being perpendicular to each other. Hint: Remember the identity sin (90 _ u) _ cos u.

A cylindrical cistern, constructed below ground level, is 3.0 m in diameter and 2.0 m deep and is fi lled to the brim with a liquid whose index of refraction is 1.5. A small object rests on the bottom of the cistern at its center. How far from the edge of the cistern can a girl whose eyes are 1.2 m from the ground stand and still see the object?

An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely fi lled with water. When the afternoon Sun reaches an angle of 28.0 above the horizon, sunlight ceases to illuminate the bottom of the tank. How deep is the tank?

A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and an index of 1.615 for red light of wavelength 680 nm. If a beam containing these two colors is incident at an angle of 30.00 on a piece of this glass, what is the angle between the two beams inside the glass?

The index of refraction for red light in water is 1.331 and that for blue light is 1.340. If a ray of white light enters the water at an angle of incidence of 83.00, what are the underwater angles of refraction for the blue and red components of the light?

The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index of refraction is 1.530 at a wavelength of 410 nm (violet). If both wavelengths are incident on a slab of crown glass at the same angle of incidence, 60.0, what is the angle of refraction for each wavelength?

A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 50.00. The index of refraction of quartz is 1.455 at 660 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defi ned as the difference in the angles of refraction for the two wavelengths.

The index of refraction for violet light in silica fl int glass is 1.66 and that for red light is 1.62. What is the angular dispersion of visible light passing through an equilateral prism of apex angle 60.0 if the angle of incidence is 50.0? (See Fig. P22.32.)

A ray of light strikes the midpoint of one face of an equiangular (606060) glass prism (n _ 1.5) at an angle of incidence of 30. (a) Trace the path of the light ray through the glass and fi nd the angles of incidence and refraction at each surface. (b) If a small fraction of light is also refl ected at each surface, what are the angles of refl ection at the surfaces?

For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air: (a) fused quartz, (b) polystyrene, and (c) sodium chloride.

Repeat Problem 34, but this time assume the quartz, polystyrene, and sodium chloride are surrounded by water.

A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 30.0 and the angle of refraction is 22.0, fi nd the critical angle for the liquid when surrounded by air.

A plastic light pipe has an index of refraction of 1.53. For total internal refl ection, what is the minimum angle of incidence if the pipe is in (a) air and (b) water?

Determine the maximum angle u for which the light rays incident on the end of the light pipe in Figure P22.38 are subject to total internal refl ection along the walls of the pipe. Assume the light pipe has an index of refraction of 1.36 and the outside medium is air.

A light ray is incident normally to the long face (the hypotenuse) of a 454590 prism surrounded by air, as shown in Figure 22.26b. Calculate the minimum index of refraction of the prism for which the ray will totally internally refl ect at each of the two sides making the right angle.

A beam of laser light with wavelength 612 nm is directed through a slab of glass having index of refraction 1.78. (a) For what minimum incident angle would a ray of light undergo total internal refl ection? (b) If a layer of water is placed over the glass, what is the minimum angle of incidence on the glasswater interface that will result in total internal refl ection at the waterair interface? (c) Does the thickness of the water layer or glass affect the result? (d) Does the index of refraction of the intervening layer affect the result?

A room contains air in which the speed of sound is 343 m/s. The walls of the room are made of concrete, in which the speed of sound is 1 850 m/s. (a) Find the critical angle for total internal refl ection of sound at the concrete air boundary. (b) In which medium must the sound be traveling in order to undergo total internal refl ection? (c) A bare concrete wall is a highly effi cient mirror for sound. Give evidence for or against this statement.

Three adjacent faces (that all share a corner) of a plastic cube of index of refraction n are painted black. A clear spot at the painted corner serves as a source of diverging rays when light comes through it. Show that a ray from this corner to the center of a clear face is totally refl ected if n $ !3.

The light beam in Figure P22.43 strikes surface 2 at the critical angle. Determine the angle of incidence, u1.

A jewel thief hides a diamond by placing it on the bottom of a public swimming pool. He places a circular raft on the surface of the water directly above and centered over the diamond, as shown in Figure P22.44. If the surface of the water is calm and the pool is 2.00 m deep, fi nd the minimum diameter of the raft that would prevent the diamond from being seen.

A layer of ice having parallel sides fl oats on water. If light is incident on the upper surface of the ice at an angle of incidence of 30.0, what is the angle of refraction in the water?

A ray of light is incident at an angle 30.0 on a plane slab of fl int glass surrounded by water. (a) Find the refract tion angle. (b) Suppose the index of refraction of the surrounding medium can be adjusted, but the incident angle of the light remains the same. As the index of refraction of the medium approaches that of the glass, what happens to the refraction angle? (c) What happens to the refraction angle when the mediums index of refraction exceeds that of the glass?

A ray of light is incident on a fl at surface of a block of crown glass that is surrounded by water. The angle of refraction is 19.6. Find the angle of refl ection.

A light ray of wavelength 589 nm is incident at an angle u on the top surface of a block of polystyrene surrounded by air, as shown in Figure P22.48. (a) Find the maximum value of u for which the refracted ray will undergo total internal refl ection at the left vertical face of the block. (b) Repeat the calculation for the case in which the polystyrene block is immersed in water. (c) What happens if the block is immersed in carbon disulfi de?

As shown in Figure P22.49, a light ray is incident normal to one face of a 306090 block of dense fl int glass (a prism) that is immersed in water. (a) Determine the exit angle u4 of the ray. (b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal refl ection cease at point P?

A narrow beam of light is incident from air onto a glass surface with index of refraction 1.56. Find the angle of incidence for which the corresponding angle of refraction is one-half the angle of incidence. Hint: You might want to use the trigonometric identity sin 2u _ 2 sin u cos u.

One technique for measuring the angle of a prism is shown in Figure P22.51. A parallel beam of light is directed onto the apex of the prism so that the beam refl ects from opposite faces of the prism. Show that the angular separation of the two refl ected beams is given by B _ 2A.

An optical fi ber with index of refraction n and diameter d is surrounded by air. Light is sent into the fi ber along its axis, as shown in Figure P22.52. (a) Find the smallest outside radius R permitted for a bend in the fi ber if no light is to escape. (b) Does the result for part (a) predict reasonable behavior as d approaches zero? As n increases? As n approaches unity? (c) Evaluate R, assuming the diameter of the fi ber is 100 mm and its index of refraction is 1.40.

A piece of wire is bent through an angle u. The bent wire is partially submerged in benzene (index of refraction _ 1.50) so that, to a person looking along the dry part, the wire appears to be straight and makes an angle of 30.0 with the horizontal. Determine the value of u.

A light ray traveling in air is incident on one face of a rightangle prism with index of refraction n _ 1.50, as shown in Figure P22.54, and the ray follows the path shown in the fi gure. Assuming u _ 60.0 and the base of the prism is mirrored, determine the angle f made by the outgoing ray with the normal to the right face of the prism.

A transparent cylinder of radius R _ 2.00 m has a mirrored surface on its right half, as shown in Figure P22.55. A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and the exiting light ray are parallel, and d _ 2.00 m. Determine the index of refraction of the material.

A laser beam strikes one end of a slab of material, as in Figure P22.56. The index of refraction of the slab is 1.48. Determine the number of internal refl ections of the beam before it emerges from the opposite end of the slab.

A light ray enters a rectangular block of plastic at an angle u1 _ 45.0 and emerges at an angle u2 _ 76.0, as shown in Figure P22.57. (a) Determine the index of refraction of the plastic. (b) If the light ray enters the plastic at a point L _ 50.0 cm from the bottom edge, how long does it take the light ray to travel through the plastic?

Students allow a narrow beam of laser light to strike a water surface. They arrange to measure the angle of refraction for selected angles of incidence and record the data shown in the following table: Use the data to verify Snells law of refraction by plotting the sine of the angle of incidence versus the sine of the angle of refraction. From the resulting plot, deduce the index of refraction of water.

Figure P22.59 shows the path of a beam of light through several layers with different indices of refraction. (a) If u1 _ 30.0, what is the angle u2 of the emerging beam? (b) What must the incident angle u1 be to have total internal refl ection at the surface between the medium with n _ 1.20 and the medium with n _ 1.00?

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2, and a laser beam is directed onto the sheets from above so that it strikes the interface at an angle of 26.5 with the normal. The refracted beam in sheet 2 makes an angle of 31.7 with the normal. The experiment is repeated with sheet 3 on top of sheet 2, and with the same angle of incidence, the refracted beam makes an angle of 36.7 with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, what is the expected angle of refraction in sheet 3? Assume the same angle of incidence.