PHYSICS:F/SCI.+ENGRS.(LL)-W/SINGLE CARD
10th Edition
ISBN: 9781337888547
Author: SERWAY
Publisher: CENGAGE L
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Chapter 34, Problem 31P
An optical fiber has an index of refraction n and diameter d. It is surrounded by vacuum. Light is sent into the fiber along its axis as shown in Figure P34.31. (a) Find the smallest outside radius Rmin permitted for a bend in the fiber if no light is to escape. (b) What If? What result does part (a) predict as d approaches zero? Is this behavior reasonable? Explain. (c) As n increases? (d) As n approaches 1? (c) Evaluate Rmin assuming the fiber diameter is 100 μm and its index of refraction is 1.40.
Figure P34.31
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The figure shows an optical fiber in which a central plastic core of index of refraction n, = 1.60 is surrounded by a plastic sheath of
index of refraction n2 = 1.52. Light can travel along different paths within the central core, leading to different travel times through the
fiber. This causes an initially short pulse of light to spread as it travels along the fiber, resulting in information loss. Consider light that
travels directly along the central axis of the fiber and light that is repeatedly reflected at the critical angle along the core-sheath
interface, reflecting from side to side as it travels down the central core. If the fiber length is 370 m, what is the difference in the travel
times along these two routes?
NUmber
i
98.7
Units
ns
Light of wavelength 471 nm is incident on the face of a silica prism at an angle of θ1 = 75◦ (with respect to the normal to the surface). The apex angle of the prism is φ = 57.5◦.
Given: The value of the index of refraction for silica is n = 1.455.
Find the angle of refraction at this first
surface.
Answer in units of degrees.
Find the angle of incidence at the second surface.
Answer in units of degrees.
Find the angle of refraction at the second surface.
Answer in units of degrees.
Find the angle between the incident and emerging rays.
Answer in units of degrees.
Measuring n Using a Prism
Although we do not prove it here, the minimum angle of deviation &min for a prism occurs when the angle of incidence 0, is such
that the refracted ray inside the prism makes the same angle with the normal to the two prism faces as shown in the figure.
Obtain an expression for the index of refraction of the prism material in terms of the minimum angle of deviation and the apex
angle 0.
Ф
2k8min
A light ray passing through a prism at the minimum angle of deviation 6min:
SOLUTION
Conceptualize Study the figure carefully and be sure you understand why the light ray comes out of the prism traveling in
a different
direction.
Categorize In this example, light enters a material through one surface and leaves the material at another surface. Let's apply
the wave under refraction
v model to the light passing through the prism.
Analyze
Ф
Consider the geometry in the figure, where we have used symmetry to label several angles. The reproduction of the angle
at
2
the…
Chapter 34 Solutions
PHYSICS:F/SCI.+ENGRS.(LL)-W/SINGLE CARD
Ch. 34.3 - Prob. 34.1QQCh. 34.4 - If beam is the incoming beam in Figure 34.10b,...Ch. 34.4 - Light passes from a material with index of...Ch. 34.6 - In photography, lenses in a camera use refraction...Ch. 34.7 - Prob. 34.5QQCh. 34 - Prob. 1PCh. 34 - The Apollo 11 astronauts set up a panel of...Ch. 34 - As a result of his observations, Ole Roemer...Ch. 34 - A dance hall is built without pillars and with a...Ch. 34 - You are working for an optical research company...
Ch. 34 - Prob. 6PCh. 34 - Prob. 7PCh. 34 - Two flat, rectangular mirrors, both perpendicular...Ch. 34 - Prob. 9PCh. 34 - A ray of light strikes a flat block of glass (n =...Ch. 34 - Prob. 11PCh. 34 - Prob. 12PCh. 34 - A laser beam is incident at an angle of 30.0 from...Ch. 34 - A ray of light strikes the midpoint of one face of...Ch. 34 - When you look through a window, by what time...Ch. 34 - Light passes from air into flint glass at a...Ch. 34 - You have just installed a new bathroom in your...Ch. 34 - A triangular glass prism with apex angle 60.0 has...Ch. 34 - You are working at your university swimming...Ch. 34 - Prob. 20PCh. 34 - Prob. 21PCh. 34 - A submarine is 300 m horizontally from the shore...Ch. 34 - Prob. 23PCh. 34 - A light beam containing red and violet wavelengths...Ch. 34 - Prob. 25PCh. 34 - The speed of a water wave is described by v=gd,...Ch. 34 - For 589-nm light, calculate the critical angle for...Ch. 34 - Prob. 28PCh. 34 - A room contains air in which the speed of sound is...Ch. 34 - Prob. 30PCh. 34 - An optical fiber has an index of refraction n and...Ch. 34 - Consider a horizontal interface between air above...Ch. 34 - How many times will the incident beam in Figure...Ch. 34 - Consider a beam of light from the left entering a...Ch. 34 - Why is the following situation impossible? While...Ch. 34 - Prob. 36APCh. 34 - When light is incident normally on the interface...Ch. 34 - Refer to Problem 37 for its description of the...Ch. 34 - A light ray enters the atmosphere of the Earth and...Ch. 34 - A light ray enters the atmosphere of a planet and...Ch. 34 - Prob. 41APCh. 34 - Prob. 42APCh. 34 - Prob. 43APCh. 34 - Prob. 44APCh. 34 - Prob. 45APCh. 34 - As sunlight enters the Earths atmosphere, it...Ch. 34 - A ray of light passes from air into water. For its...Ch. 34 - Prob. 48APCh. 34 - Prob. 49APCh. 34 - Figure P34.50 shows a top view of a square...Ch. 34 - Prob. 51APCh. 34 - Prob. 52CPCh. 34 - Prob. 53CPCh. 34 - Pierre de Fermat (16011665) showed that whenever...Ch. 34 - Prob. 55CPCh. 34 - Suppose a luminous sphere of radius R1 (such as...Ch. 34 - Prob. 57CP
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- How many times will the incident beam in Figure P34.33 (page 922) be reflected by each of the parallel mirrors? Figure P34.33arrow_forwardFigure P23.28 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 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 P23.28arrow_forwardFigure P26.72 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens. (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the final image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forward
- The index of refraction for violet light in silica flint glassis 1.66 and that for red light is 1.62. What is the angulardispersion of visible light passing through an equilateralprism of apex angle 60.0° if the angle of incidence is 50.0°?(See Fig. P22.62.)arrow_forwardAn optical cable in air is orientated horizontally. The cable has a core and a cladding layer. The index of refraction for the core is 1.3 and the index of refraction for the cladding layer is 1.2. A light ray enters the center of the cable with an incident angle ß=58°. The ray is subsequently refracted at the core-cladding interface and the cladding-air interface. The angle between the exit ray and the cable wall is a. What is the angle a? The index of refraction of air is 1. ←cladding -corearrow_forwardIn the figure, light is incident at angle 6, = 41.0° 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, n, = 1.38, ng = 1.30 and n4 = 1.43, what is the value of (a) 05 and (b) 04? Air (a) 05 = NumberT32.02 UnitsTo (degrees) (b)04 = NumberT43.1 Units (degrees)arrow_forward
- Q. 1. A ray of light incident at an angle 0 on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5° and the prism is made of a material of refractive index 1.5, the angle of incidence is : (a) 7.5° (c) 15° (b) 5° (d) 2.5°arrow_forwardAn optical fiber has an index of refraction n and diameter d. It is surrounded by vacuum. Light is sent into the fiber along its axis as shown. (a) Find the smallest outside radius Rmin permitted for a bend in the fiber if no light is to escape. (b) What If? What result does part (a) predict as d approaches zero? Is this behavior reasonable? Explain. (c) As n increases? (d) As n approaches 1? (e) Evaluate Rmin assuming the fiber diameter is 100 mm and its index of refraction is 1.40.arrow_forwardThe figure shows an optical fiber in which a central plastic core of index of refraction n1 = 1.60 is surrounded by a plastic sheath of index of refraction n2 = 1.52. Light can travel along different paths within the central core, leading to different travel times through the fiber. This causes an initially short pulse of light to spread as it travels along the fiber, resulting in information loss. Consider light that travels directly along the central axis of the fiber and light that is repeatedly reflected at the critical angle along the core-sheath interface, reflecting from side to side as it travels down the central core. If the fiber length is 370 m, what is the difference in the travel times along these two routes? NUmber i 99 Units nsarrow_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