Figure 30.23 shows light passing through a spherical raindrop, undergoing two

Why is it usually inappropriate to consider low-frequency sound waves as traveling in rays? Why is the ray approximation more appropriate for high-frequency sound and for light?

Why does a spoon appear bent when its in a glass of water?

Why do a diamond and an identically shaped piece of glass sparkle differently?

White light goes from air through a glass slab with parallel surfaces. Will its colors be dispersed when it emerges from the glass?

You send white light through two identical glass prisms, oriented as shown in Fig. 30.17. Describe the beam that emerges from the right-hand prism.

In glass, which end of the visible spectrum has the smallest critical angle for total internal reflection?

Why cant you walk to the end of the rainbow?

An attempt to rework Example 30.4 with an isosceles prism results in imaginary numbers for the two angles of refraction. What could this mean?

Why are polarizing sunglasses better than glasses that simply reduce the total amount of light?

Under what conditions will the polarizing angle be smaller than 45?

Through what angle should you rotate a mirror so that a reflected ray rotates through 30?

The mirrors in Fig. 30.18 make a 60 angle. A light ray enters parallel to the symmetry axis, as shown. (a) How many reflections does it make? (b) Where and in what direction does it exit the mirror system?

To what angular accuracy must two ostensibly perpendicular mirrors be aligned so that an incident ray returns within 1 of its incident direction?

If a light ray enters the mirror system of Fig. 30.18 propagating in the plane of the page and parallel to one mirror, through what angle will it be turned?

In which substance in Table 30.1 does the speed of light have the value 2.292*108 m/s?

Information in a compact disc is stored in pits whose depth is essentially one-fourth the wavelength of the laser light used to read the information. That wavelength is 780 nm in air, but the wavelength on which the pit depth is based is measured in the n = 1.55 plastic that makes up most of the disc. Find the pit depth.

Light is incident on an airglass interface, and the refracted light in the glass makes a 40 angle with the normal to the interface. The glass has refractive index 1.52. Find the incidence angle

A light ray propagates in a transparent material at 15 to the normal to the surface. It emerges into the surrounding air at 24 to the normal. Find the materials refractive index.

Light propagating in the glass 1n = 1.522 wall of an aquarium tank strikes the walls interior surface with incidence angle 12.4. Whats the angle of refraction in the water?

Find the polarizing angle for diamond when light is incident from air

Find the refractive index of a material for which the polarizing angle in air is 62

Find the critical angle for total internal reflection in (a) ice, (b) polystyrene, and (c) rutile, when the surrounding medium is air.

A drop of water is trapped in a block of ice. Whats the critical angle for total internal reflection at the waterice interface?

What is the critical angle for light propagating in glass with n = 1.52 when the glass is immersed in (a) water, (b) benzene, and (c) diiodomethane?

Total internal reflection occurs at an interface between plastic and air at incidence angles greater than 37. Find the plastics refractive index.

Blue and red laser beams strike an airglass interface with incidence angle 50. If the glass has refractive indices of 1.680 for the blue light and 1.621 for the red, what will be the angle between the two beams in the glass?

White light propagating in air is incident at 45 on the equilateral prism of Fig. 30.19. Find the angular dispersion g of the outgoing beam if the prism has refractive indices nred = 1.582 and nviolet = 1.633.

Suppose the 60 angle in Fig. 30.18 is changed to 75. A ray enters the mirror system parallel to the axis. (a) How many reflections does it make? (b) Through what angle is it turned when it exits the system?

The refractive index of a human cornea is 1.40. If 550-nm light strikes a cornea at incidence angle 25, find (a) the angle of refraction and (b) the wavelength in the cornea.

Two plane mirrors make an angle f. A light ray enters the system and is reflected once off each mirror. Show that the ray is turned through an angle 360 - 2f.

An unlabeled bottle of liquid has spilled, and youre trying to find out whether its relatively harmless ethyl alcohol or toxic benzene. You submerge a glass block with n = 1.52 in the liquid, and shine a laser beam so it strikes the submerged glass with incidence angle 31.5. You measure the angle of refraction in the glass at 27.9. Which liquid is it? (See Table 30.1.)

A meter stick lies on the bottom of the rectangular tank in Fig. 30.20, with its zero mark at the tanks left edge. You look into the long dimension of the tank at a 45 angle, with your line of sight just grazing the top edge, as shown. What mark on the meter stick do you see when the tank is (a) empty, (b) half full of water, and (c) full of water?

You look at the center of one face of a solid glass cube of glass, on a line of sight making a 55 angle with the normal to the cube face. What minimum refractive index of the glass will let you see through the cubes opposite face?

At the aquarium where you work, a fish has gone missing in a 10-m-deep, 11-m-diameter cylindrical tank. You shine a flashlight in from the top edge of the tank, hoping to see if the missing fish is on the bottom. Whats the smallest angle your flashlight beam can make with the horizontal if its to illuminate the bottom?

Youre standing 2.3 m horizontally from the edge of a 4.5-m-deep lake, with your eyes 1.7 m above the waters surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a 42 angle with the vertical, at what horizontal distance is the diver from the edge of the lake?

Youve dropped your car keys at night off the end of a dock into water 1.6 m deep. A flashlight held directly above the dock edge and 0.50 m above the water illuminates the keys when its aimed at 40 to the vertical, as shown in Fig. 30.21. Whats the horizontal distance x from the edge of the dock to the keys?

Laser eye surgery uses ultraviolet light with wavelength 193 nm. Whats the UV lights wavelength within the eyes lens, where n = 1.39?

The prism in Fig. 30.22 has n = 1.52 and a = 60 and is surrounded by air. A light beam is incident at u1 = 37. Find the angle d through which the beam is deflected.

Repeat Problem 38 for the case n = 1.75, a = 40, and u1 = 25

Find the minimum refractive index for the prism in Fig. 30.11 if total internal reflection occurs as shown when the prism is surrounded by air.

Where and in what direction would the main beam emerge if the prism in Fig. 30.11 were made of ice, surrounded by air?

Find the speed of light in a material for which the critical angle at an interface with air is 61.

The prism of Fig. 30.11 has n = 1.52. When its immersed in a liquid, a beam incident as shown in the figure ceases to undergo total reflection. Whats the minimum value for the liquids refractive index?

For the interface between air (refractive index 1) and a material with refractive index n, show that the critical angle and the polarizing angle are related by sin uc = cot up.

A scuba diver sets off a camera flash at depth h in water with refractive index n. Show that light emerges from the waters surface through a circle of diameter 2h/2n2 - 1.

Suppose the red and blue beams of Exercise 26 are now propagating in the same direction inside the glass. For what range of incidence angles on the glassair interface will one beam be totally reflected and the other not?

In cataract surgery, ophthalmologists replace the eyes natural lens with a synthetic intraocular lens, or IOL. A particular IOL has refractive index 1.452. Find the angle of refraction for a light ray striking this lens with incidence angle 77.0. The medium before the IOL is the eyes aqueous humor, a liquid with n = 1.337.

In a ruby laser, light is produced in a solid rod of ruby, with refractive index 1.77. The light emerges from the end of the rod into the surrounding air. At what angle should the rod end be cut so the emerging light is fully polarized?

Reconsider Example 30.4, now in a glass with n700 = 1.482 and n400 = 1.615. Determine what happens to the red and violet light with these respective wavelengths, and speculate on what happens to the entire incident beam of white light.

A cylindrical tank 2.4m deep is full to the brim with water. Sunlight first hits part of the tank bottom when the rising Sun makes a 22 angle with the horizon. Find the tanks diameter

For what diameter tank in Problem 50 will sunlight strike some part of the tank bottom whenever the Sun is above the horizon?

Light is incident from air on the flat wall of a polystyrene water tank. If the incidence angle is 40, what is the angle of refraction in the water?

Youre an optometrist, mounting a projector at the back of your 4.2-m-long exam room, 2.6 m above the floor. It shines an eyetest pattern on a white wall opposite the projector. Patients will sit with their eyes 3.3 m from the wall and 1.4m above the floor to view the pattern. At what height should you center the pattern on the wall?

Find an expression for the displacement x in Fig. 30.6, in terms of u1, d, and n.

Figure 30.23 shows light passing through a spherical raindrop, undergoing two refractions and total internal reflection, resulting in an angle f between the incident and outgoing rays. Show that f = 4 sin-1 1sin u/n2 - 2u, where u is the incidence angle.

(a) Differentiate the result of Problem 55 to show that the maximum value of f occurs when the incidence angle u is given by cos2 u = 1 3 1n2 - 12. (b) Use this result and that of Problem 55 to find the maximum f in a raindrop with n = 1.333. This is the angle at which the rainbow appears, as shown in the Application on pages 573574

Figure 30.24 shows the approximate path of a light ray that undergoes internal reflection twice in a spherical water drop. Repeat Problems 55 and 56 for this case to find the angle at which the secondary rainbow occurs.

Show that a three-dimensional corner reflector (three mutually perpendicular mirrors, or a solid cube in which total internal reflection occurs) turns an incident light ray through 180. (Hint: Let q ! = qxni + qy nj + qzk n be a vector in the propagation direction. How does this vector get changed on reflection by a mirror in a plane defined by two of the coordinate axes?)

Fermats principle states that a light rays path is such that the time to traverse that path is an extremum (a minimum or a maximum) when compared with times for nearby paths. Show that Fermats principle implies Snells law by proving that a light ray going from point A in one medium to point B in a second medium will take the least time if it obeys Snells law

Youre an automotive engineer charged with evaluating safety glass, which is made by bonding a layer of flexible plastic between two layers of glass, thus eliminating dangerous glass fragments during accidents. A new product uses glass with refractive index n = 1.55 and plastic with n = 1.48. Youre asked to determine whether total internal reflection at the glassplastic interface could cause problems with visibility. What do you conclude, and why?

A slab of transparent material has thickness d and refractive index n that varies across the material: n1x2 = n1 + 1n2 - n121x/d22 , where x is measured from one face of the slab. A light ray is incident normally on the slab. Find an expression for the time it takes to traverse the slab

For common materials like glass, the wavelength dependence of the refractive index at visual wavelengths is given approximately by n1l2 = b + c/l2 , where b and c are constants. The table below gives values of l and n for the crown glass of Example 30.4. Determine a quantity that, when you plot n against it, should give a straight line. Make your plot, establish a best-fit line, and use the line to determine the constants b and c.

Mirages occur when airs refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eyes lens and Earths ionosphere, an electrically conductive layer in the upper atmosphere, where the refractive index for radio waves varies with altitude. Figure 30.25a depicts lights path over a hot road, producing a mirage. From the path shown, you can conclude that the airs refractive index a. increases from left to right. b. increases from right to left. c. increases upward. d. increases downward.

Mirages occur when airs refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eyes lens and Earths ionosphere, an electrically conductive layer in the upper atmosphere, where the refractive index for radio waves varies with altitude. The observer in Fig. 30.25a sees a shimmering mirage that looks like water but actually results from sky light following the curved path. To the observer, the mirage appears to be at a. point A. b. point B. c. point C. d. point D.

Mirages occur when airs refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eyes lens and Earths ionosphere, an electrically conductive layer in the upper atmosphere, where the refractive index for radio waves varies with altitude. Figure 30.25b shows how continuous refraction in the ionosphere enables long-distance radio communication. Waves launched at angles steeper than u dont refract enough to return to Earth, so they propagate through the ionosphere and on to space. You can therefore conclude that a. all points between A and B receive stronger signals from A than point B receives. b. points between A and B cant receive signals from A via the ionosphere. c. the refractive index must become infinite at the maximum altitude of the radio signal.

Mirages occur when airs refractive index varies with position as a result of uneven heating. Under such conditions, light undergoes refraction continually and thus follows a curved path. Other examples where a varying refractive index is important include the eyes lens and Earths ionosphere, an electrically conductive layer in the upper atmosphere, where the refractive index for radio waves varies with altitude. The refractive index in the ionosphere is strongly dependent on radio-wave frequency, approaching 1 for high frequencies. Therefore, a. long-distance communication via the ionosphere is more likely at higher frequencies. b. higher frequencies wont penetrate as far into the ionosphere. c. higher frequencies are more appropriate for satellite-based communication.