COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 23, Problem 93QAP
To determine
The minimum diameter of raft so that it can obscure the ball from sight
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•• ENGINEERING APPLICATION An optical fiber allows rays
of light to propagate long distances by using total internal reflec-
tion. Optical fibers are used extensively in medicine and in digital
communications. As shown in Figure 31-58 the fiber consists of a
core material that has an index of refraction n, and radius b sur-
rounded by a cladding material that has an index of refraction
n3 < n2. The numerical aperture of the fiber is defined as sine,
where 0, is the angle of incidence of a ray of light that impinges
on the center of the end of the fiber and then reflects off the core-
cladding interface just at the critical angle. Using the figure as
a guide, show that the numerical aperture is given by
sine, = Vn3 - n? assuming the ray is initially in air. Hint: Use of the
Pythagorean theorem may be required.
44
•4 In Fig. 35-32a, a beam of light in material 1 is incident on a
boundary at an angle of 30°. The extent to which the light is ben
due to refraction depends, in part, on the index of refraction n, o
material 2. Figure 35-32b gives the angle of refraction Oz versus n
for a range of possible n2 values, from n, = 1.30 to n, = 1.90. Wha
is the speed of light in material 1?
в,
40°
300!
30°
в,
20°
по
(a)
(b)
Light is an incident on a vertical interface between two mediums as shown in the picture. The medium on the left has an index of refraction n(left) & the medium on the right has an index of refraction n(right). The light comes from the bottom left.
If n(left)=1.3, n(right)=2.3, & angle of incidence = 41degrees. What is the angle of refraction?
-68.2
-49.0
-0
-41.0
-21.8
If n(left)=1.3, n(right)=2.3, & angle of incidence= 41degrees, what is the angle of reflection?
*same choices as first question*
Chapter 23 Solutions
COLLEGE PHYSICS
Ch. 23 - Prob. 1QAPCh. 23 - Prob. 2QAPCh. 23 - Prob. 3QAPCh. 23 - Prob. 4QAPCh. 23 - Prob. 5QAPCh. 23 - Prob. 6QAPCh. 23 - Prob. 7QAPCh. 23 - Prob. 8QAPCh. 23 - Prob. 9QAPCh. 23 - Prob. 10QAP
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- A fish is 3.25 m below the surface of still water (Fig. P38.16). You do not want the fish to see your fishing boat. Is it possible to place your boat so that total internal reflection keeps it hidden from the fish? If so, explain how this is done. If not, explain why not. FIGURE P38.16 Problems 16 and 17.arrow_forwardA person looking into an empty container is able to see the far edge of the containers bottom, as shown in Figure P22.23a. The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the containers bottom, as shown in Figure P22.23b. (a) Show that the ratio h/d is given by hd=n214n2 (b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container.arrow_forwardA light ray is incident normally to the long face (the hypotenuse) of a 454590 prism surrounded by air, as shown m Figure 22.26b. Calculate the minimum index of refraction of the prism for which the ray will totally internally reflect at each of the two sides making the tight angle.arrow_forward
- •48 In Fig. 33-48a, a light ray in water is incident at angle 61 on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction 6, versus the incident angle 6, is given in Fig. 33-48b. The vertical axis scale is set by 6, = 90°. %3D Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water (n = 1.33). What is the index of refraction of (c) material 1 and (d) material 2? Ө, в2. Water 0° 45° 90° (a) (6)arrow_forwardQ3) If n: > n¡ and the thickness of the material slab is = t, then answer the following questions: a) Analytically, show that ray 1 and ray 4 are parallel. b) Analytically, show that ray 2 and ray 3 are parallel. c) Find the total lateral displacement (d) in terms of nt and t of the material. гay1 Aray2 aray3 ne ni ray4arrow_forward•45 When the rectangular metal tank in Fig. 33-46 is filled to the top with an unknown liquid, observer o- O, with eyes level with the top of the tank, can just see corner E. A ray that refracts toward O at the top surface of the liquid is shown. If D = 85.0 cm and L = 1.10 m, what -Normal to liquid surface is the index of refraction of the liquid? -L-arrow_forward
- Construct Your Own ProblemConsider sunlight entering the Earth’s atmosphere at sunrise and sunset—that is, at a 90.0° incident angle. Taking the boundary between nearly empty space and the atmosphere to be sudden, calculate the angle ofrefraction for sunlight. This lengthens the time the Sun appears to be above the horizon, both at sunrise and sunset. Now construct a problem in which you determine the angle of refraction for different models ofthe atmosphere, such as various layers of varyingdensity. Your instructor may wish to guide you on the level of complexity to consider and on how the index of refraction varies with air density.arrow_forwardYou can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 69.2° when submerged in ethanol, which has an index of refraction of 1.361? (b) What would the critical angle be for this substance in air? °arrow_forward3arrow_forward
- Establish the relevant theoretical model:- Write a first general equation giving the angle of refraction (r) as a function of the angle of incidence (i) on a rectangular piece of acrylic and the refractive index (n) of the acrylic.- Write down a second general equation giving the lateral deviation (d)of an incident beam as a function of the angle of incidence (i), the angle of refraction (r) and the thickness (e) of the rectangular piece of acrylic. Note that there are two ways of calculating &, which give two mathematically equivalent equations.Using the relationships you've just obtained, calculate the lateral deviation for the following fictitious situation: angle of incidence i = 45°, acrylic refractive index = 1.49 +- 0.01 and blade thickness e = 6.5 cm.arrow_forwardThe answer of this questionarrow_forward(a) An opaque cylindrical tank with an open top has a diameter of 2.60 m and is completely filled with water. When the afternoon sun reaches an angle of 31.5° above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank (in m)? 4 Determine how the depth of the tank is related to the angle of refraction for the geometry described in the question. Drawing a diagram may be helpful. Then apply Snell's law to find the angle of refraction and use it to determine the depth of the water in the tank. m (b) What If? On winter solstice in Seattle, the sun reaches a maximum altitude of 19° above the horizon. What would the depth of the tank have to be (in m) for the sun not to illuminate the bottom of the tank on that day? marrow_forward
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Laws of Refraction of Light | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=4l2thi5_84o;License: Standard YouTube License, CC-BY