Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 31, Problem 78P
To determine
The proof that
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A ray is incident at an angle of incidence i on one surface of a
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the material of the prism is µ then the angle of incidence is
nearly equal to:
(a) In the figure, light from ray A refracts from material 1 into a thin layer of material 2, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (i) What is the value of incident angle θA? Draw a sketch of the situation. (ii) If θA is decreased, does part of the light refract into material 3? (b) Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (iii) What is the value of incident angle θB? Draw a sketch of the situation. (iv) If θB is decreased, does part of the light refract into material 3? Answer: 54.3°, yes, 51.1°, no
(a) The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 54.0°?
(b) What If? What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 90°?
Chapter 31 Solutions
Physics for Scientists and Engineers
Ch. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4PCh. 31 - Prob. 5PCh. 31 - Prob. 6PCh. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Prob. 10P
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- Light coming from a fish makes an incidence angle of 30° to normal under the water. The index of refraction of water is 1.33. A fisherman is looking at the fish through air. At what angle with the normal (6, ) will the fish appear to the fisherman? Use Snell's law: n, sin e, = n, sine,arrow_forwardIn the figure, light from ray A refracts from material 1 (n₁ = 1.73) into a thin layer of material 2 (n2 = 1.80), crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 (n3 = 1.40). (a) What is the value of incident angle BA? (b) If 8A is decreased, does part of the light refract into material 3? Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (c) What is the value of incident angle Og? (d) If Og is decreased, does part of the light refract into material 3? OB I ng no 121arrow_forward106 In Fig. 33-78, where n, = 1.70, n2 = 1.50, and nz = 1.30, light re- %3D fracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface be- tween materials 2 and 3, what are (a) the angle of refraction at point B and (b) the initial angle 0? If, in- stead, light is incident at B at the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at point A and (d) the initial angle e? If, instead of all that, light is incident at point A at Brewster's angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point B and (f) the initial angle 6? Figure 33-78 Problem 106.arrow_forward
- 10. A light ray of given wavelength, initially in air, strikes a 90° prism at P (see Fig. 39-53) and is refracted there and at Q to such an extent that it just grazes the right-hand prism surface at Q. (a) Determine the index of retraction of the prism for this wavelength in terms of the angle of incidence , that gives rise to this situation. (b) Give a numerical upper bound for the index of refraction of the prism. Show, by ray dia- grams, what happens if the angle of incidence at P is (c) slightly greater or (d) slightly less than 0₁. 90 FIGURE 39-53. Problem 10.arrow_forwardIn the figure, light initially in material 1 refracts into material 2, crosses that material, and is then incident at the critical angle on the interface between materials 2 and 3. The indices of refraction are n, = What is angle 0? (b) If 0 is increased, is there refraction of light into material 3? 1.60, n2 1.40, n3 = 1.18. (а) %3D le n2 (a) Number Units (b)arrow_forwardA glass plate of thickness t and refractive index n is to be placed in a convergent beam normally. The point of convergence, under small angle approximation, will shift away from the glass plate by: (a) t(1-¹) (b) t(n-1) (c) 2t (d) t(1-2¹) n 01arrow_forward
- A ray of light is incident on a glass prism (n = 1.6) with an angle of incidence 0, emerges from the opposite side of the prism with an angle 0,. The apex angle of the prism is 60° The deviation angle, 8, between the incident ray and the emerging ray is then: = 40°. The ray 60° 0, = 40° Nair =1 O 21.7° O 51.3 O 44.5° 38.4 13.8arrow_forwardA ray of light crosses the boundary between some substance with n = 1.4 and air, going from the substance into air. If the angle of incidence is 24◦ what is the angle of refraction? Calculate to 1decimal.arrow_forwardIn the figure, light from ray A refracts from material 1 (n1 = 1.60) into a thin layer of material 2 (n2 = 1.80), crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 (n3 = 1.3). (a) What is the value of incident angle θA? (b) If θA is decreased, does part of the light refract into material 3? Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (c) What is the value of incident angle θB? (d) If θB is decreased, does part of the light refract into material 3?arrow_forward
- 109 In Fig. 34-54, a fish watcher at point P watches a fish through a glass wall of a fish tank. The watcher is level with the fish; the index of re- fraction of the glass is 8/5, and that Watcher of the water is 4/3. The distances are di = 8.0 cm, dz = 3.0 cm, and dz = 6.8 cm. (a) To the fish, how far away does the watcher appear to be? (Hint: The watcher is the object. Light from that object passes through the wall's outside surface, which acts as a refracting sur- face. Find the image produced by that surface. Then treat that im- age as an object whose light passes through the wall's inside sur- face, which acts as another refracting surface.) (b) To the watcher, how far away does the fish appear to be? de D Wall Figure 34-54 Problem 109.arrow_forwardThe numerical aperture (NA) of a fiber characterizes the ability of a fiber to collect light (a high NA means it collects more light). The NA is defined as the sine of the maximum external angle of a ray entering the fiber that can be trapped by total internal 1/2 reflection. Show that| NA= n, sin0, = (n – n;)" .arrow_forward
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