Physics 222, October 25

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1 Physics 222, October 25 Key Concepts: Image formation by refraction Thin lenses The eye Optical instruments

2 A single flat interface Images can be formed by refraction, when light traverses a boundary between two transparent media with different indices of refraction. When we are looking at an object under water, we are seeing a virtual image of the object.

3 A single spherical interface A single spherical interfaces with radius of curvature R can also act as a image forming system. Example: (As R infinity, the interface becomes flat.)

4 Thin lenses can be converging or diverging. Images formed by thin lenses Where is the image located? Lens equation: 1/x o + 1/x i = 1/f, M = -x i /x o Convention: x o is positive. x i is positive if x o and x i are on the opposite sides of the lens. x i is negative if x o and x i are on the same side of the lens. f is positive for a converging lens. f is negative for a diverging lens.

5 Geometrical construction: Real images Images formed by thin lenses Virtual images Diverging lenses only form virtual images. Converging lenses form real inverted images if x o > f and virtual upright images if x o < f.

6 Lens equation: 1/x o + 1/x i = 1/f, M = -x i /x o Here are some things that always go together for a thin lens. Real image <--> inverted image <--> x i is positive <--> M is negative Virtual image <--> upright image <--> x i is negative <--> M is positive Virtual image produced by converging lens <--> M > 1, (image is larger than object) Virtual image produced by diverging lens <--> M < 1, (image is smaller than object)

7 An object is located a distance x o in front of a lens. The lens produces an inverted image that is four times as tall as the object. What kind of lens is it? What is the image distance, x i? 1. Converging lens, x i = 2x o 2. Converging lens, x i = x o /4 3. Converging lens, x i = 4x o 4. Diverging lens, x i = -4x o 5. Diverging lens, x i = -x o /4

8 A light source with an arrow pointing up is placed at the zero mark on an optical bench. A convex lens of unknown focal length is placed with its center at the 30 cm mark on the bench. A focused image appears on a collector when placed at the 45 cm mark on the bench. What must be true about the image? 1. It is real and inverted. 2. It is virtual and inverted. 3. It is real and upright. 4. It is virtual and upright.

9 An object is placed at 20 cm in front of a diverging lens with a focal length of -10 cm. What is the image distance? cm in front of the lens cm in front of the lens cm behind the lens cm in front of the lens cm in front of the lens

10 You d like to look through a lens at your dog and see it standing right side up shrunk to 1/4 its normal height. If the absolute value of the focal length is f, determine what kind of lens is needed (i.e. converging or diverging) as well as the focal length in term of the object distance x o. Hint M = -x i /x o = 1/4 1. Converging lens, f = x o /5. 2. Diverging lens, f = -x o /5. 3. Converging lens, f = x o /3. 4. Diverging lens, f = -x o /3. 5. Converging lens, f = x o /4. 6. Diverging lens, f = -x o /4.

11 Lens power Lens power P, measured in diopters D: D = 1/f(m) For two thin lenses in contact: 1/f = 1/f 1 + 1/f 2 P = P thin(1) + P thin(2) The powers of thin lenses in contact add algebraically.

12 Two very thin lenses, each with focal length 20 cm, are placed in contact. What is the focal length of this compound lens? cm cm cm cm

13 The human eye The eye focuses an image onto the retina by adjusting the focal length of the eye lens. This is known as accommodation. Normal eye: Eye: image distance = 2 cm focal length (cm) object distance (cm)

14 Your eye focuses on an moving motorcycle by changing its focal length. As the motorcycle moves away from you, the focal length of the eye must A. increase. B. decrease. C. stay the same. Hint: 1/x o + 1/x i = 1/f x i is fixed.

15 Nearsighted eye

16 Farsighted eye

17 A person s left eye is corrected by a 2.50-diopter lens, 1.0 cm from the eye. Is this person s left eye near- or farsighted? 1. Nearsighted 2. Farsighted

18 Simple image-forming optical instruments One lens: One lens + eye:

19 Two lenses + eye: Keplerian telescope Simple image-forming optical instruments Galilean telescope Angular magnification: M = -f o /f e Compound microscope MP = MP objetive *Mp eypiece = -(g/f o )*(25cm/f e )

20 You want to build a Galilean telescope. You have two convex lenses and two concave lenses available. The larger lenses have focal lengths +100 cm and 100 cm respectively and the smaller lenses have focal lengths +10 cm and 10 cm respectively. Which lenses should you use and how far apart should you place them? What is the angular magnification of your telescope? and 100, 100 cm apart and +10, 110 cm apart and - 10, 110 cm apart and 10, 90 cm apart

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