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UF PHY 2054 - Optical Instruments

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25Optical InstrumentsQUICK QUIZZES 1. (c). The corrective lens for a farsighted eye is a converging lens, while that for a nearsighted eye is a diverging lens. Since a converging lens is required to form a real image of the Sun on the paper to start a fi re, the campers should use the glasses of the farsighted person. 2. (a). We would like to reduce the minimum angular separation for two objects below the angle subtended by the two stars in the binary system. We can do that by reducing the wavelength of the light — this in essence makes the aperture larger, relative to the light wavelength, increasing the resolving power. Thus, we would choose a blue fi lter.ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Diffraction of light as it passes through, or refl ects from, the objective element of a telescope can cause the images of two sources having a small angular separation to overlap and fail to be seen as separate images. The minimum angular separation two sources must have in order to be seen as sepa-rate sources is inversely proportional to the diameter of the objective element. Thus, using a large diameter objective element in a telescope increases its resolution, making (c) the correct choice. 2. The power of a lens in diopters equals the reciprocal of the focal length when that focal length is expressed in meters. Hence, the power of a lens having a focal length of 25 cm is P = = =1 10 254 0f .. m diopters and choice (b) is the correct answer. 3. The amount of light focused on the fi lm by a camera is proportional to the area of the aperture through which the light enters the camera. Since the area of a circular opening varies as the square of the diameter of the opening, the light reaching the fi lm is proportional to the square of the diameter of the aperture. Thus, increasing this diameter by a factor of 3 increases the amount of light by a factor of 9, and (c) is the correct choice. 4. When the eye is shorter than normal, the lens-cornea system fails to bring light from near objects to a focus by the time it reaches the retina, resulting in a blurry image. Light rays entering the pupil from distant objects are less divergent than those from near objects, and the lens-cornea system can focus them on the retina. Such an eye is farsighted, or has hyperopia, and needs a converging corrective lens to help bring rays from near objects to focus sooner. The correct choice is (c). 5. When the eye is longer than normal, the lens-cornea system will bring light from distant objects to focus before it reaches the retina. Rays from near objects are more divergent and the lens-cornea system brings them to focus farther from the lens, on the retina. This means that the eye can see near objects clearly, but is unable to focus on distant objects. Such an eye is nearsighted (myopia), and needs a diverging corrective lens to make the rays from distant objects more diver-gent before they enter the eye. Choice (b) is the correct answer.36156157_25_ch25_p361-381.indd 36156157_25_ch25_p361-381.indd 361 3/20/08 3:36:43 PM3/20/08 3:36:43 PM362 Chapter 25 6. Stars are very distant and the reciprocal of the object distance in the lens or mirror equation 1 1 1p q f+ = is essentially zero. This means that q f=, or the images are formed at a distance equal to the focal length from the objective element. Thus, the angular separation of the images, and hence the stars, is απ= =×= ×−−sf20 0 101 00 1032.. m2.00 m rad360°2 rrad= °0 573. and we see that choice (d) is the correct answer. 7. The corrective lens must form an upright, virtual image located 55 cm in front of the lens (q = −55 cm) when the object is 25 cm in front of the lens (p = +25 cm). The thin lens equation then gives the required focal length as fpqp q=+=()−()−= +25 5525 5546 cm cm cm cm cm and the correct choice is (c). 8. When a compound microscope is adjusted for most relaxed viewing (i.e., the fi nal image formed by the eyepiece is at infi nity), the approximate overall magnifi cation produced by the microscope is given by the expression mLf fo e= −25 cm where L is the length of the microscope, fois the focal length of the objective lens, and feis the focal length of the eyepiece. With the microscope described, the approximate magnifi cation is m = −= − ×154 0250 801 2 102 cm cm cm cm. .. or m ≈120 and the correct answer is choice (d). 9. The angular separation of the two stars is θ= = = ×− −s r (10 5 105 8 ly) (200 ly) radians. The limiting angle of resolution for a circular aperture is θ λmin. ( )= 1 22 D. Requiring that θθmin=, and assuming a wavelength at the center of the visible spectrum (550 nm), the required diameter of the aperture is found to be D = =×()×= ×−−1 221 22 550 105 101 10981..λθ m rad m == 10 m so (c) is the best choice of the listed possible answers.10. When using light of wavelength λ, the resolving power needed to distinguish two closely spaced spectral lines having a difference in wavelength of ∆λ is R =λλ∆ . Thus, if two lines in the visible spectrum differ in wavelength by ∆λ= 0 1. nm, the minimum resolving power of a diffrac-tion grating that might be used to separate them is Rminmin= = = × =λλ∆4004 10 4 0003 nm0.1 nm and the correct choice is (b).56157_25_ch25_p361-381.indd 36256157_25_ch25_p361-381.indd 362 3/20/08 3:36:44 PM3/20/08 3:36:44 PMOptical Instruments 363ANSWERS TO CONCEPTUAL QUESTIONS 2. The objective lens of the microscope must form a real image just inside the focal point of the eyepiece lens. In order for this to occur, the object must be located just outside the focal point of the objective lens. Since the focal length of the objective lens is typically quite short ~1 cm(), this means that the microscope can focus properly only on objects close to the end of the barrel and will be unable to focus on objects across the room. 4. For a lens to operate as a simple magnifi er, the object should be located just inside the focal point of the lens. If the power of the lens is +20.0 diopters, its focal length is f =()=()+ = =1 00 1 00 20 0 0 050 0 5 00. . . . . m m m cmP The object should be placed slightly less than 5.00 cm in front of the lens. 6. The aperture of a camera is a close approximation to the iris of the eye. The retina of the eye cor-responds to the fi lm of the camera, and a close


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