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* Moving laser beam An aquarium open at the top has 30-cm-deep water in it. You shine a laser pointer into the top opening so it is incident on the air-water interface at a
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Chapter 22 Solutions
Pearson eText for College Physics: Explore and Apply -- Instant Access (Pearson+)
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- A Fermats principle of least time for refraction. A ray of light traveling in a medium with speed v1 leaves point A and strikes the boundary between the incident and transmitted media a horizontal distance x from point A as shown in Figure P38.98. The refracted ray travels with speed v2 in the second medium, eventually reaching point B. The horizontal distance between points A and B is L. a. Calculate the time t required for the light to travel from A to B in terms of the parameters labeled in the figure. b. Now take the derivative of t with respect to x. What is the condition for which the ray of light will take the shortest time to travel from A to B? Figure P38.98arrow_forwardEndoscopes are medical instruments used to examine the gastrointestinal tract and other cavities inside the body. The light required for examination is conducted from an outside source along a long, flexible bundle of optical fibers to the tip, where it exits and illuminates the internal cavity. A lens on the lip collects an image of the lighted cavity and another fiber bundle conducts the image back along the endoscope to an eyepiece for viewing (Fig. P22.52). If each fiber in the bundle has diameter d = 1.00 104 m and refractive index n = 1.40, find the smallest outside radius R permitted for a bend in the fiber if no light is to escape. Figure P22.52arrow_forwardPierre de Fermat (16011665) showed that whenever light travels from one point to another, its actual path is the path that requires the smallest time interval. This statement is known as Fermats principle. The simplest example is for light propagating in a homogeneous medium. It moves in a straight line because a straight line is the shortest distance between two points. Derive Snells law of refraction from Fermats principle. Proceed as follows. In Figure P34.54, a light ray travels from point P in medium 1 to point Q in medium 2. The two points are, respectively, at perpendicular distances a and b from the interface. The displacement from P to Q has the component d parallel to the interface, and we let x represent the coordinate of the point where the ray enters the second medium. Let t = 0 be the instant the light starts from P. (a) Show that the time at which the light arrives at Q is t=r1v1+r2v2=n1a2+x2c+n2b2+(dx)2c (b) To obtain the value of x for which t has its minimum value, differentiate t with respect to x and set the derivative equal to zero. Show that the result implies n1xa2+x2=n2(dx)b2+(dx)2 (c) Show that this expression in turn gives Snells law. n1sin1=n2sin2 Figure P34.54 Problems 54 and 55.arrow_forward
- Figure P22.16 shows a light ray traveling in a slab of crown glass surrounded by air. The ray is incident on the right surface at an angle of 55 with the normal and then reflects from points A. B, and C. (a) At which of these points does part of the ray enter the air? (b) If the glass slab is surrounded by carbon disulfide, at which point does part of the ray enter the carbon disulfide?arrow_forwardUnreasonable results Light traveling from water to a gemstone strikes the surface at an angle of 80.00 and has an angle of refraction of 15.2°. (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forwardFigure P38.10 on the next page shows a monochromatic beam of light of wavelength 575 nm incident on a slab of crown glass surrounded by air. Use a protractor to measure the angles of incidence and refraction. a. What is the speed of the beam of light within the glass slab? b. What is the frequency of the beam of light within the glass slab? c. What is the wavelength of the beam of light within the glass slab? FIGURE P38.10arrow_forward
- Iridescent peacock feathers are shown in Figure P27.68a (page 938). The surface of one microscopic barbule is composed of transparent keratin that supports rods of dark brown melanin in a regular lattice, represented in Figure P27.68b. (Your fingernails are made of keratin, and melanin is the dark pigment giving color to human skin.) In a portion of the feather that can appear turquoise (blue-green), assume the melanin rods are uniformly separated by 0.25 m, with air between them. (a) Explain how this structure can appear turquoise when it contains no blue or green pigment. (b) Explain how it can also appear violet if light falls on it in a different direction. (c) Explain how it can present different colors to your two eyes simultaneously, which is a characteristic of iridescence. (d) A compact disc can appear to be any color of the rainbow. Explain why the portion of the feather in Figure P27.68b cannot appear yellow or red. (e) What could be different about the array of melanin rods in a portion of the feather that does appear to be red? Figure P27.68 (a) Iridescence in peacock feathers. (b) Microscopic section of a feather showing dark melanin rods in a pale keratin matrix.arrow_forwardUnreasonable Results Light traveling from water to a gemstone strikes the surface at an angle of 80.0° and has an angle of refraction of 15.2°. (a) What is the speed at light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?arrow_forward
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