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21. Dispersion occurs when _____.
Answer: B Dispersion occurs when a single material bends certain colors of light more than other colors of light. The cause is the fact that different colors of light have different speeds within the same material. 

Dispersion of Light by Prisms 
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22. A 3.0 cm tall object is placed along the principal axis of a thin converging lens of 30.0 cm focal length. If the object distance is 40.0 cm, which of the following best describes the image distance and height, respectively?
a. 17.3 cm and 7.0 cm 
b. 120. cm and 9.0 cm 
c. 17.3 cm and 1.3 cm 
d. 120. cm and 1.0 cm 
Answer: B Use the lens equation: where d_{o} = 40.0 cm and f = 30.0 cm. Solve for d_{i}. d_{i} = 1/(0.00833 /cm) = 120. cm Then use the d_{i}/d_{o} = h_{i}/h_{o} to find h_{i} It is now known that h_{o} = 3.0 cm; d_{o} = 40.0 cm; d_{i} = 120. cm. Substitute and solve. 

The Mathematics of Lenses 
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23. Which of the following best describes the image for a thin converging lens that forms whenever the object is at a distance less than one focal length from the lens?
a. inverted, enlarged and real 
b. upright, enlarged and virtual 
c. upright, reduced and virtual 
d. inverted, reduced and real 
Answer: B When an object is located inside of the focal point of a converging lens, the image will be virtual, upright, larger than the object and located on the same side of the lens as the object. In essence, the lens would serve as a magnifying glass. 


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24. Which of the following best describes the image for a thin diverging lens that forms whenever the magnitude of the object distance is less than that of the lens' focal length?
a. inverted, enlarged and real 
b. upright, enlarged and virtual 
c. upright, reduced and virtual 
d. inverted, reduced and real 
Answer: C A diverging lens always produces an image with the same characteristics, regardless of the object distance. The image is always virtual, upright and reduced in size. 


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25. An object is placed at a distance of 30.0 cm from a thin converging lens along its axis. The lens has a focal length of 10.0 cm. What are the values of the image distance and magnification (respectively)?
a. 60.0 cm and 2.00 
b. 15.0 cm and 2.00 
c. 60.0 cm and 0.500 
d. 15.0 cm and 0.500 
Answer: D Use the lens equation: where d_{o} = 30.0 cm and f = 10.0 cm. Solve for d_{i} : d_{i} = 1 / (0.0666/cm) = 15.0 cm Then use the M =d_{i}/d_{o} to find M (d_{o} = 30.0 cm; d_{i} = 15.0 cm) Substitute and solve for M: 

The Mathematics of Lenses 
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26. An object is placed at a distance of 6.0 cm from a thin converging lens along its axis. The lens has a focal length of 9.0 cm. What are the values, respectively, of the image distance and magnification?
a. 18 cm and 3.0 
b. 18 cm and 3.0 
c. 3.0 cm and 0.50 
d. 18 cm and 3.0 
Answer: A Use the lens equation: where d_{o} = 6.0 cm and f = 9.0 cm. Solve for d_{i}: d_{i} = 1 / (0.0556/cm) = 18 cm Then use the M =d_{i}/d_{o} to find M (d_{o} = 6.0 cm; d_{i} = 18 cm) Substitute and solve for M: 

The Mathematics of Lenses 
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27. An object is placed at a distance of 30.0 cm from a thin converging lens along the axis. If a real image forms at a distance of 10.0 cm from the lens, what is the focal length of the lens?
a. 30.0 cm 
b. 15.0 cm 
c. 10.0 cm 
d. 7.50 cm 
Answer: D Use the lens equation: where d_{o} = 30.0 cm and d_{i} = 10.0 cm. Solve for f: f = 1 / (0.133/cm) = 7.50 cm 

The Mathematics of Lenses 
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28. An object is placed at a distance of 40.0 cm from a thin lens along the axis. If a virtual image forms at a distance of 50.0 cm from the lens, on the same side as the object, what is the focal length of the lens?
a. 22.2 cm 
b. 45.0 cm 
c. 90.0 cm 
d. 200. cm 
Answer: D Use the lens equation: where d_{o} = 40.0 cm and d_{i} = 50.0 cm (Note that d_{i} is a negative number since it is a virtual image  i.e., formed on the same side of the lens as the object.) Solve for f: f = 1 / (0.00500/cm) = 200. cm 

The Mathematics of Lenses 
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29. Which of the following statements are true of converging lenses? Identify all that apply.
Answer: ADFG


The Anatomy of a Lens  Converging Lenses  ObjectImage Relations 
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30. Which of the following statements are true of diverging lenses? Identify all that apply.
Answer: CEF


The Anatomy of a Lens  Diverging Lenses ObjectImage Relations 
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31. Which of the following statements are true of real images? Identify all that apply.
Answer: ABDEG


Converging Lenses  ObjectImage Relations  Diverging Lenses ObjectImage Relations  The Mathematics of Lenses 
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32. Which of the following statements are true of virtual images? Identify all that apply.
Answer: ABE


Converging Lenses  ObjectImage Relations  Diverging Lenses ObjectImage Relations  The Mathematics of Lenses 
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33. Several characteristics of images are described below. Determine whether these images are real or virtual and whether they are formed by converging, diverging lenses or either type. (In all cases, assume that the object is an upright and real object.)
Answer: See answers below


Converging Lenses  ObjectImage Relations  Diverging Lenses ObjectImage Relations  The Mathematics of Lenses 
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34. Which of the following statements are true of total internal reflection (TIR)? Include all that apply.
Answer: ABE


Total Internal Reflection  The Critical Angle 
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