Show Explanation of the refraction of light through different lenses. Encyclopædia Britannica, Inc.TranscriptWe see objects when light waves bounce off their surfaces and travel toward our eyes. This behavior of light is called reflection. 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. [ | | | | | | | | | | | | | ] 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: 1/di + 1/do = 1/fwhere do = 40.0 cm and f = 30.0 cm. Solve for di. 1/di = 1/f - 1/do =1/(30.0 cm) - 1/(40.0 cm) = 0.00833 /cmdi = 1/(0.00833 /cm) = 120. cm Then use the -di/do = hi/ho to find hi It is now known that ho = 3.0 cm; do = 40.0 cm; di = 120. cm. Substitute and solve. hi = -ho *(di/do) = -(3.0 cm) *(120. cm)/(40.0 cm) = -9.0 cm
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.
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. 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: 1/di + 1/do = 1/fwhere do = 30.0 cm and f = 10.0 cm. Solve for di : 1/di = 1/f - 1/do = 1/(10.0 cm) - 1/(30.0 cm) = 0.0666/cmdi = 1 / (0.0666/cm) = 15.0 cm Then use the M =-di/do to find M (do = 30.0 cm; di = 15.0 cm) Substitute and solve for M: M = -(15.0 cm) / (30.0 cm) = - 0.500
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: 1/di + 1/do = 1/fwhere do = 6.0 cm and f = 9.0 cm. Solve for di: 1/di = 1/f - 1/do = 1/(9.0 cm) - 1/(6.0 cm) = -0.0556/cmdi = 1 / (-0.0556/cm) = -18 cm Then use the M =-di/do to find M (do = 6.0 cm; di = -18 cm) Substitute and solve for M: M = -(-18 cm) / (6.0 cm) = 3.0
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: 1/di + 1/do = 1/fwhere do = 30.0 cm and di = 10.0 cm. Solve for f: 1/f = 1/di + 1/do = 1/(10.0 cm) + 1/(30.0 cm) = 0.133/cmf = 1 / (0.133/cm) = 7.50 cm
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: 1/di + 1/do = 1/fwhere do = 40.0 cm and di = -50.0 cm (Note that di 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: 1/f = 1/di + 1/do = 1/(-50.0 cm) + 1/(40.0 cm) = 0.00500/cmf = 1 / (0.00500/cm) = 200. cm
Part B: Multiple-Multiple Choice29. Which of the following statements are true of converging lenses? Identify all that apply.
Answer: ADFG
30. Which of the following statements are true of diverging lenses? Identify all that apply.
Answer: CEF
31. Which of the following statements are true of real images? Identify all that apply.
Answer: ABDEG
32. Which of the following statements are true of virtual images? Identify all that apply.
Answer: ABE
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
34. Which of the following statements are true of total internal reflection (TIR)? Include all that apply.
Answer: ABE
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