Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 32, Problem 81GP
Fermat’s principle slates that “light travels between two points along the path that requires the least time, as compared to other nearby paths.” From Fermat’s principle derive (a) the law of reflection (θi = θr) and (b) the law of refraction (Snell’s law). [Hint: Choose two appropriate points so that a ray between them can undergo reflection or refraction. Draw a rough path for a ray between these points, and write down an expression of the time required for light to travel the arbitrary path chosen. Then take the derivative to find the minimum.]
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Let v, be the velocity of light in air and vz the velocity of
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sin 0
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where 01 (the angle of incidence) and 02 (the angle of
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When the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in Fig. Since our perception is based on the idea that light travels in straight lines, we perceive the light to be coming from an apparent position that is an angle d above the sun’s true position. (a) Make the simplifying assumptions that the atmosphere has uniform density, and hence uniform index of refraction n, and extends to a height h above the earth’s surface, at which point it abruptly stops. Show that the angle d is given by as attached. where R = 6378 km is the radius of the earth. (b) Calculate d using n = 1.0003 and h = 20 km. How does this compare to the angular radius of the sun, which is about one quarter of a degree? (In actuality a light ray from the sun bends gradually, not abruptly, since the density and refractive index of the…
Chapter 32 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 32.1 - Does the result of Example 322 depend on your...Ch. 32.1 - Return to the Chapter-Opening Question, page 837,...Ch. 32.1 - Suppose you are standing about 3 m in front of a...Ch. 32.5 - Light passes from a medium with n = 1.3 into a...Ch. 32.7 - Fill a sink with water. Place a waterproof watch...Ch. 32.7 - It 45.0 plastic lenses are used in binoculars,...Ch. 32 - What would be the appearance of the Moon if it had...Ch. 32 - Archimedes is said to have burned the whole Roman...Ch. 32 - What is the focal length of a plane mirror? What...Ch. 32 - An object is placed along the principal axis of a...
Ch. 32 - Using the rules for the three rays discussed with...Ch. 32 - Prob. 6QCh. 32 - If a concave mirror produces a real image, is the...Ch. 32 - Prob. 8QCh. 32 - When you look at the Moons reflection from a...Ch. 32 - How can a spherical mirror have a negative object...Ch. 32 - Prob. 11QCh. 32 - When you look down into a swimming pool or a lake,...Ch. 32 - Draw a ray diagram to show why a stick looks bent...Ch. 32 - Prob. 14QCh. 32 - You look into an aquarium and view a fish inside....Ch. 32 - Prob. 16QCh. 32 - A ray of light is refracted through three...Ch. 32 - Can a light ray traveling in air be totally...Ch. 32 - When you look up at an object in air from beneath...Ch. 32 - What type of mirror is shown in Fig. 3244?Ch. 32 - Light rays from stars (including our Sun) always...Ch. 32 - (I) When you look at yourself in a 60-cm-tall...Ch. 32 - (I) Suppose that you want to take a photograph of...Ch. 32 - (II) Two plane mirrors meet at a 135 angle, Fig....Ch. 32 - (II) A person whose eyes are 1.64 m above the...Ch. 32 - (II) Show that if two plane mirrors meet at an...Ch. 32 - (II) Suppose you are 88 cm from a plane mirror....Ch. 32 - (II) Stand up two plane minors so they form a 90.0...Ch. 32 - (III) Suppose a third mirror is placed beneath the...Ch. 32 - (I) A solar cooker, really a concave mirror...Ch. 32 - (I) How far from a concave mirror (radius 24.0cm)...Ch. 32 - (I) When walking toward a concave mirror you...Ch. 32 - (II) A small candle is 35 cm from a concave mirror...Ch. 32 - (II) You look at yourself in a shiny...Ch. 32 - (II) A mirror at an amusement park shows an...Ch. 32 - (II) A dentist wants a small mirror that, when...Ch. 32 - (II) Some rearview mirrors produce images of cars...Ch. 32 - (II) You are standing 3.0 m from a convex security...Ch. 32 - (II) An object 3.0 mm high is placed 18 cm from a...Ch. 32 - (II) The image of a distant tree is virtual and...Ch. 32 - (II) Use two techniques, (a) a ray diagram, and...Ch. 32 - (II) Show, using a ray diagram, that the...Ch. 32 - (II) Use ray diagrams to show that the mirror...Ch. 32 - (II) The magnification of a convex mirror is +0.55...Ch. 32 - (II) (a) Where should an object be placed in front...Ch. 32 - (II) A 4.5-cm tall object is placed 26 cm in front...Ch. 32 - (II) A shaving or makeup mirror is designed to...Ch. 32 - (II) Let the focal length of a convex mirror be...Ch. 32 - (II) A spherical mirror of focal length f produces...Ch. 32 - Prob. 30PCh. 32 - (III) A short thin object (like a short length of...Ch. 32 - (I) The speed of light in ice is 2.29 108 m/s....Ch. 32 - (I) What is the speed of light in (a) ethyl...Ch. 32 - (I) Our nearest star (other than the Sun) is 4.2...Ch. 32 - (I) How long does it take light to reach us from...Ch. 32 - (II) The speed of light in a certain substance is...Ch. 32 - (II) Light is emitted from an ordinary lightbulb...Ch. 32 - (I) A diver shines a flashlight upward from...Ch. 32 - (I) A flashlight beam strikes the surface of a...Ch. 32 - Prob. 40PCh. 32 - (I) A light beam coming from an underwater...Ch. 32 - (II) A beam of light in air strikes a slab of...Ch. 32 - (II) A light beam strikes a 2.0-cm-thick piece of...Ch. 32 - (II) An aquarium filled with water has flat glass...Ch. 32 - (II) In searching the bottom of a pool at night, a...Ch. 32 - (II) The block of glass (n = 1.5) shown in cross...Ch. 32 - (II) A laser beam of diameter d1 = 3.0 mm in air...Ch. 32 - (II) Light is incident on an equilateral glass...Ch. 32 - (II) A triangular prism made of crown glass (n =...Ch. 32 - (II) Show in general that for a light beam...Ch. 32 - (III) A light ray is incident on a flat piece of...Ch. 32 - (I) By what percent is the speed of blue light...Ch. 32 - (I) A light beam strikes a piece of glass at a...Ch. 32 - (II) A parallel beam of light containing two...Ch. 32 - (III) A ray of light with wavelength is incident...Ch. 32 - (III) For visible light, the index of refraction n...Ch. 32 - (I) What is the critical angle for the interlace...Ch. 32 - (I) The critical angle for a certain liquidair...Ch. 32 - (II) A beam of light is emitted in a pool of water...Ch. 32 - (II) A ray of light, after entering a light fiber,...Ch. 32 - (II) A beam of light is emitted 8.0cm beneath the...Ch. 32 - (II) Figure 3257 shows a liquid-detecting prism...Ch. 32 - (II) Two rays A and B travel down a cylindrical...Ch. 32 - (II) (a) What is the minimum index of refraction...Ch. 32 - (III) Suppose a ray strikes the left face of the...Ch. 32 - (III) A beam of light enters the end of an optic...Ch. 32 - (II) A 13.0-cm-thick plane piece of glass (n =...Ch. 32 - (II) A fish is swimming in water inside a thin...Ch. 32 - (III) In Section 32-8, we derived Eq. 32-8 for a...Ch. 32 - Two identical concave mirrors are set facing each...Ch. 32 - A slab of thickness D, whose two faces are...Ch. 32 - Two plane mirrors are facing each other 2.2 m...Ch. 32 - We wish to determine the depth of a swimming pool...Ch. 32 - A 1.80-m-tall person stands 3.80 m from a convex...Ch. 32 - Prob. 76GPCh. 32 - Each student in a physics lab is assigned to find...Ch. 32 - A kaleidoscope makes symmetric patterns with two...Ch. 32 - When light passes through a prism, the angle that...Ch. 32 - If the apex angle of a prism is = 72 (see Fig....Ch. 32 - Fermats principle slates that light travels...Ch. 32 - Suppose Fig. 3236 shows a cylindrical rod whose...Ch. 32 - An optical fiber is a long transparent cylinder of...Ch. 32 - An object is placed 15 cm from a certain mirror....Ch. 32 - The end faces of a cylindrical glass rod (n =...Ch. 32 - The paint used or highway signs often contains...
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