53 SSM www ILW In Fig. 33-53, a ray is incident on one face of a triangular glass prism in air. The angle of incidence e is chosen so that the emerging ray also makes the same angle e with the nor- mal to the other face. Show that the index of refraction n of the glass prism is given by sin ( + 6) sin o where o is the vertex angle of the prism and is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle u has the smallest possible value, which is called the angle of mini- mum deviation.) Figure 33-53 Problems 53 and 64.

53 SSM www ILW In Fig. 33-53, a ray is incident on one face of a triangular glass prism in air. The angle of incidence e is chosen so that the emerging ray also makes the same angle e with the nor- mal to the other face. Show that the index of refraction n of the glass prism is given by sin ( + 6) sin o where o is the vertex angle of the prism and is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle u has the smallest possible value, which is called the angle of mini- mum deviation.) Figure 33-53 Problems 53 and 64.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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The critical angle for a beam of light passing from water into air is 47.6°. This means that all light rays with an angle of incidence in the water that is less than 47.6° will be totally absorbed by the water. not enough information to answer. partially reflected and partially refracted. O totally reflected. O totally refracted.
12 In Fig. 33-35, light travels from material a, through three layers of other materials with surfaces parallel to one another, and then back into an- other layer of material a. The refrac- tions (but not the associated reflec- tions) at the surfaces are shown. Rank the materials according to index of re- fraction, greatest first. (Hint: The par- allel arrangement of the surfaces al- lows comparison.) Figure 33-35 Question 12.
77 E Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflec- tion (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation Bdev- (a) Show that 6sey is Odey = 180° + 20, – 48, where e, is the angle of incidence of the ray on the drop and 0, is the angle of refraction of the ray within the drop. (b) Using Snell's law, substitute for 6, in terms of 6, and the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph Osey versus 0, for the range of possible 6; values and for n = 1.331 for red light (at one end of the visible spectrum) and n = 1.333 for blue light (at the other end). The red-light curve and the blue-light curve have different minima, which means that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that color's angle of…
A ray of light crosses the boundary between some substance with n = 1.54 and air, going from the substance into air. If the angle of incidence is 29◦ what is the angle of refraction? Calculate to 1decimal.
Laser light is passed through a rod made out of a material with an index of refraction of 1.62, a length L = 45.0 cm, and square cross section of length h = 3.00 mm on a side as shown in the figure. If the light enters at the center of the rod with an angle of incidence in air of 0₁ = 49.7°, determine the number of total internal reflections before it emerges from the opposite end of the rod. 42.0 cm 3.10 mm
..54 Dispersion in a window pane. In gle e Fig. 33-54, a beam of white light is incident at an- 50° on a common window pane (shown in cross section). For the pane's type of glass, the index of refraction for visible light ranges from 1.524 at the blue end of the spectrum to 1.509 at the red end. The two sides of the pane are paral- lel. What is the angular spread of the colors in the beam (a) when the light enters the pane and (b) when it emerges from the opposite side? (Hint: When you look at an object through a window pane, are the colors the light from the object dispersed as shown in, say, Fig. 33-20?) = Ꮎ Figure 33-54 Problem 54.
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Problem 13: A ray of light is incident on an air/water interface. The ray makes an angle of 01 = 22 degrees with respect to the normal of the surface. The index of the air is n = 1 while water is n₂ = 1.33. Part (b) Numerically, what is the angle in degrees? 0₂=1 Part (a) Choose an expression for the angle (relative to the normal to the surface) for the ray in the water, 02. Answer Saved Successfully! 8₂=asin (sin()) sin() cos() cotan() asin() atan() acotan() cosh() sinh() tanh() cotanh() Degrees O Radians Submit tan() acos() E 4 5 6 1 2 3 () Hint * Feedback 7 8 9 HOME 1 + 0 VO BACKSPACE DEL CLEAR - I give up! . ni END n2 0₁ 02₂
In the figure, light is incident at angle 8₁ = 39° on a boundary between two transparent materials. 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 = 1.28, n₂ = 1.38, n3 = 1.34 and n4 = 1.45, what is the value of (a) 05 and (b) 04? 18₁ Air m n₂ 173 na
78 E The primary rainbow described in Problem 77 is the type commonly seen in regions where rainbows appear. It is pro- duced by light reflecting once inside the drops. Rarer is the sec- ondary rainbow described in Module 33-5, produced by light reflecting twice inside the drops (Fig. 33-68a). (a) Show that the angular deviation of light entering and then leaving a spherical water drop is Odev = (180°)k + 20, – 2(k + 1)8,, where k is the number of internal reflections. Using the procedure of Problem 77, find the angle of minimum deviation for (b) red light and (c) blue light in a secondary rainbow. (d) What is the angular width of that rainbow (Fig. 33-21d)? The tertiary rainbow depends on three internal reflections (Fig. 33-68b). It probably occurs but, as noted in Module 33-5, cannot be seen with the eye because it is very faint and lies in the bright sky surrounding the Sun. What is the angle of minimum de- viation for (e) the red light and (f) the blue light in this rainbow? (g)…
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