*Chapter 33, Problem 051 GO In the figure, light is incident at angle 01 Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.32, n2 = what is the value of (a) es and (b) 04? 39.0° on a boundary between two transparent materials. %3D 1.42, n3 = 1.34 and n4 = 1.47,

*Chapter 33, Problem 051 GO In the figure, light is incident at angle 01 Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.32, n2 = what is the value of (a) es and (b) 04? 39.0° on a boundary between two transparent materials. %3D 1.42, n3 = 1.34 and n4 = 1.47,

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter38: Refraction And Images Formed By Refraction

Section: Chapter Questions

Problem 87PQ

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Unreasonable 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?
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?
Figure P35.20 (page 958) shows a curved surface separating a material with index of refraction n1 from a material with index n2. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to Snells law, n1 sin 1 = n2 sin 2. For paraxial rays, we assume 1, and 2 are small, so we may write n1 tan 1 = n2 tan 2. The magnification is defined as M = h/h. Prove that the magnification is given by M = n1q/n2p. Figure P35.20
A jellyfish is floating in a water-filled aquarium 1.00 m behind a flat pane of glass 6.00 cm thick and having an index of refraction of 1.50. (a) Where is the image of the jellyfish located? (b) Repeat the problem when the glass is so thin that its thickness can be neglected. (c) How does the thickness of the glass affect the answer to part (a)?
A diverging lens has a focal length of 20.0 cm. Use graph paper to construct accurate ray diagrams for object distance of (a) 40.0cm and (b) 10.0 cm. In each case, determine the location of the image from the diagram and the image magnification, and state whether the image is uptight or inverted. (c) Estimate the magnitude of uncertainty in locating the points in the graph. Are your answers and the uncertainty consistent with the algebraic answers found in Problem 33?
Pierre 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.
A ray of light is incident at an angle 30.0 on a plane slab of flint glass surrounded by water. (a) Find the refraction 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 light ray navels from vacuum into a slab of material with index of refraction n1 at incident angle with respect to the surface. 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 final angle that the outgoing light makes with the normal? (a) (b) (c) = (d) The angle depends on the magnitudes of n1 and n2. (e) The angle depends on the wavelength of the light.
Unreasonable 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?
In many applications, it is necessary to expand or decrease the diameter of a beam of parallel rays of light, which can be accomplished by using a converging lens and a diverging lens in combination. Suppose you have a converging lens of focal length 21.0 cm and a diverging lens of focal length 12.0 cm. (a) How can you arrange these lenses to increase the diameter of a beam of parallel rays? (b) By what factor will the diameter increase?
When light is incident normally on the interface between two transparent optical media, the intensity of the reflected light is given by the expression S1=(n2n1n2+n1)2S1 In this equation, S1 represents the average magnitude of the Poynting vector in the incident light (the incident intensity), S1 is the reflected intensity, and n1 and n2 are the refractive indices of the two media. (a) What fraction of the incident intensity is reflected for 589-nm light normally incident on an interface between air and crown glass? (b) Does it matter in part (a) whether the light is in the air or in the glass as it strikes the interface?
(a) Under what conditions is a mirage formed? While driving on a hot day, sometimes you see what appears to be water on the road far ahead. When you arrive at the location of the water, however, the road is perfectly dry. Explain this phenomenon, (b) The mirage called fata morgana often occurs over water or in cold regions covered with snow or ice. It can cause islands to sometimes become visible, even though they are not normally visible because they are below the horizon due to the curvature of the Earth. Explain this phenomenon.