Gaze into the Crystal Ball A set of coins is embedded in a spherical plastic paperweight having a radius of 5.0 cm. The index of refraction of the plastic is n, = 1.50. One coin is located 2.5 cm from the edge of the sphere (see the figure below). Find the position of the image of the coin. Light rays from a coin embedded in a plastic sphere form a virtual image between the surface of the object and the sphere surface. Because the object is inside the sphere, the front of the refracting surface is the interior of the sphere. d SOLUTION Conceptualize Because n, > n2, where n2 = 1.00 is the index of refraction for air , the rays originating from the coin in the figure are refracted away from the normal at the surface and diverge outward. Extending the outgoing rays backward shows an image point within the sphere. Categorize Because the light rays originate in one material and then pass through a curved surface into another material, this example involves an image formed by refraction Analyze (Use the following as necessary: n,, n2, P, 9, and R.) Apply n1 + "2 = "2 "1, noting from this table that R is negative: R n2 Substitute numerical values and solve for q (in cm): q = -1.7 |x cm Finalize The negative sign for q indicates that the image is in front of the surface; in other words, it is in the same medium as the object as shown in the figure. Therefore, the image must be virtual. The coin appears to be closer to the paperweight surface than it actually is.
Gaze into the Crystal Ball A set of coins is embedded in a spherical plastic paperweight having a radius of 5.0 cm. The index of refraction of the plastic is n, = 1.50. One coin is located 2.5 cm from the edge of the sphere (see the figure below). Find the position of the image of the coin. Light rays from a coin embedded in a plastic sphere form a virtual image between the surface of the object and the sphere surface. Because the object is inside the sphere, the front of the refracting surface is the interior of the sphere. d SOLUTION Conceptualize Because n, > n2, where n2 = 1.00 is the index of refraction for air , the rays originating from the coin in the figure are refracted away from the normal at the surface and diverge outward. Extending the outgoing rays backward shows an image point within the sphere. Categorize Because the light rays originate in one material and then pass through a curved surface into another material, this example involves an image formed by refraction Analyze (Use the following as necessary: n,, n2, P, 9, and R.) Apply n1 + "2 = "2 "1, noting from this table that R is negative: R n2 Substitute numerical values and solve for q (in cm): q = -1.7 |x cm Finalize The negative sign for q indicates that the image is in front of the surface; in other words, it is in the same medium as the object as shown in the figure. Therefore, the image must be virtual. The coin appears to be closer to the paperweight surface than it actually is.
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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Question
Transcribed Image Text:Gaze into the Crystal Ball
A set of coins is embedded in a spherical plastic paperweight having a radius of 5.0 cm. The index of refraction of the plastic is n,
= 1.50. One coin is located 2.5 cm from the edge of the sphere (see the figure below). Find the position of the image of the coin.
Light rays from a coin embedded in a plastic sphere form a
virtual image between the surface of the object and the
sphere surface. Because the object is inside the sphere, the
front of the refracting surface is the interior of the sphere.
d
SOLUTION
Conceptualize Because n, > n,, where n, = 1.00 is the index of refraction for air
,the rays originating from the
coin in the figure are refracted away from the normal at the surface and diverge outward. Extending the outgoing rays backward
shows an image point within the sphere.
Categorize Because the light rays originate in one material and then pass through a curved surface into another material, this
example involves an image formed by refraction
Analyze
(Use the following as necessary: n,, n2, p, q, and R.)
n1
n.
+
n2
"1, noting from this table that R is negative:
R
Apply
%3D
n2
Substitute numerical values and solve for q (in cm):
q = -1.7
X cm
Finalize The negative sign for g indicates that the image is in front of the surface; in other words, it is in the same medium as the
object as shown in the figure. Therefore, the image must be virtual. The coin appears to be closer to
the paperweight
surface than it actually is.
EXERCISE
A coin is embedded 1.89 cm from the surface of a similar ball of transparent substance having radius 3.4 cm and unknown
composition. If the coin's image is virtual and located 1.44 cm from the surface, find the index of refraction of the substance.
Hint
n =
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