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33. Geometric Optics
Thin Lens And Lens Maker Equations

33. Geometric Optics

Thin Lens And Lens Maker Equations

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Textbook Question
Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (b) The of the converging lens serves as the object for the diverging lens. What is the object distance for the diverging lens? (c) Where is the final ? Compare your answer to Fig. 34.43a.
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Textbook Question
High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun's light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 μm. Your calculations indicate that the laser must be focused to a 5.0-μm-diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?
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Textbook Question
FIGURE CP35.50 shows a lens combination in which the lens separation is less than the focal length of the converging lens. The procedure for combination lenses is to let the of the first lens be the object for the second lens, but in this case the of the first lens—shown as a dot—is on the far side of the second lens. This is called a virtual object, a point that light rays are converging toward but never reach. The top half of Figure CP35.50 shows that the converging rays are refracted again by the diverging lens and come to a focus farther to the right. The procedure for combination lenses will continue to work if we use a negative object distance for a virtual object. b. Equation 35.1 defined the effective focal length fₑբբ of a lens combination, but we didn't discuss how it is used. Although an actual ray refracts twice, once at each lens, we can extend the output rays leftward to where they need to bend only once in a plane called the principal plane. The principal plane is similar to the lens plane of a single lens, where a single bend occurs, but the principal plane generally does not coincide with the physical lens; it's just a mathematical plane in space. The effective focal length is measured from the principal plane, so parallel input rays are focused at distance fₑբբ beyond the principal plane. Find the positions of the principal planes for lens separations of 5 cm and 10 cm. Give your answers as distances to the left of the diverging lens.
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Textbook Question
A simple and relatively inexpensive microscope eyepiece is the Ramsden eyepiece shown in FIGURE P35.40. Two plano-convex lenses have their curved surfaces facing each other, which a more advanced analysis shows is the orientation that minimizes spherical aberration. That same analysis finds that chromatic aberration is minimized with lens spacing L = 1/2 (f₁ + f₂). Your task is to design a 10x Ramsden eyepiece in which the first lens has a focal length of 30 mm. What are (a) the focal length and (b) the spacing of the second lens?
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Textbook Question

(III) A bright object is placed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance d_T = dᵢ + dₒ between the object and the screen is kept fixed, but the lens can be moved.


(a) Show that if d_T > 4ƒ, there will be two positions where the lens can be placed and a sharp image will be produced on the screen.

(b) If d_T < 4ƒ, show that there will be no lens position where a sharp image is formed.

(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

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Textbook Question

Students in a physics lab are assigned to find the location where a bright object may be placed in order that a converging lens with ƒ = 12 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.

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