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WileyPLUS Assignment 3 is Available Chapters 21, 22, 24, 25 Due Thursday, March 11 at 11 pm Week of March 9-11 Experiment 4: Geometrical Optics Monday, March 8, 2010 66 Thin lens equation 1 ho 3 ! ! ! ! 1 3 f Object distance Thin lens equation: Image distance 1 1 1 + = do di f Linear magnification: m = Monday, March 8, 2010 hi di =− ho do 67 Conventions for the thin lens equation Draw ray diagrams with rays travelling from left to right. Normal situation: Object Real object to left of lens, object distance do is positive Lens Image Real image to right of lens, image distance di is positive Virtual object to right of lens, do is negative (2 or more lenses) Virtual image to left of lens, di is negative Converging (positive) lens, focal length f is positive Diverging (negative) lens, focal length f is negative Monday, March 8, 2010 68 Example: A 1.7 m tall person stands 2.5 m in front of a camera. The focal length of the lens is 0.05 m. a) Find the image distance b) Find the magnification and the height of the image on the film. a) di = 51 mm, real image b) m = -0.0204, hi = -35 mm Monday, March 8, 2010 69 Prob. 26.54/50: To focus a camera on objects at different distances, the converging lens is moved toward or away from the film, so a sharp image always falls on the film. A camera with a lens of focal length f = 200 mm is to be focussed on an object located at a distance of 3.5 m and then at 50 m. Over what distance must the lens be movable? 11.3 mm Monday, March 8, 2010 70 Clicker Question An object is located a distance do in front of a lens. The lens produces an upright image that is twice as tall as the object. What kind of lens is it? What is the image distance, di ? A) Converging lens, di = 2do B) Converging lens, di = -2do C) Diverging lens, di = 2do D) Diverging lens, di = -2do E) Diverging lens, di = do/2 B) Must be a virtual image at twice the object distance. That is, di = -2do and f > 0 (converging lens) from thin lens equation. Monday, March 8, 2010 71 Combinations of lenses – microscope • Find the location of the image formed by the first lens as if the second lens did not exist. • Use that image as an object (source of light) for the second lens using the sign convention for real and virtual objects. 1 3´ 2 3 1´ 2 Lens 2: light appears to come from intermediate image A microscope producing a virtual, inverted and magnified final image. The eyepiece acts as a magnifying glass. Monday, March 8, 2010 72 Prob. 26.65/59: Two identical diverging lenses are separated by 16 cm. The focal length of each lens is –8 cm. An object is located 4 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right. di2 = -5.6 cm, virtual image, to left of lens 2 Monday, March 8, 2010 73 26.-/66: Two converging lenses (f1 = 9 cm, f2 = 6 cm) are separated by 18 cm. The lens on the left has the longer focal length. An object stands 12 cm to the left of the left-hand lens. a) Locate the final image relative to the lens on the right. b) Obtain the overall magnification. c) Is the final image real or virtual, upright or inverted, larger or smaller than the object? a) di2 = 4.5 cm, real image, to right of lens 2 b) m = m1m2 = -0.75 c) Real, inverted, 0.75 times as large as object Monday, March 8, 2010 74 Thin Lens Thin lens equation: 1 1 1 + = do di f Linear magnification: m = hi di =− ho do do = object distance ho = height of object di = image distance hi = height of image f = focal length of lens Two Lenses Overall linear magnification, m = m1 m2 Monday, March 8, 2010 75 The Human Eye, from above n = 1.33-1.34 n = 1.38 Most of the refraction occurs at the cornea n = 1.41-1.45 n = 1.34 Blind spot Sharpest image, best colour discrimination Biomedical Applications of Introductory Physics, Tuszynski & Dixon Monday, March 8, 2010 76 Existence of the blind spot (Zinke-Allmang, Physics for the Life Sciences) 6 cm on printed page The blue dot (~140 off axis) Monday, March 8, 2010 77 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. Eye lens has its Ciliary muscle, relaxed longest focal length Greatest distance at which eye can focus: “far point” Normal value: infinity Eye lens compressed, focal length decreased Closest distance at which eye can focus: “near point” Normal value: N = 25 cm Monday, March 8, 2010 78 Nearsightedness Objects in focus The eye lens forms an image of a distant object in front of the retina ! blurred image on the retina Correction is with a diverging lens that moves the image back onto the retina. The corrective lens forms a virtual image in front of the eye that is close enough for the eye to focus on. Monday, March 8, 2010 79 Farsightedness Objects in focus The eye lens forms an image of a nearby object behind the retina blurred image on the retina Correct with a converging lens that forms a virtual image far enough away for the eye to focus on. Monday, March 8, 2010 80 Correction of near and farsightedness Use a corrective lens to form a virtual image at a distance at which the eye can focus. Nearsighted: • The corrective lens forms an image of a distant object at the person’s far point, or closer. Farsighted: • The corrective lens forms an image of a nearby object at the person’s near point, or further. Power of a lens: • Power is 1/f, focal length in metres, power in diopters. Example, f = –10 cm, power = 1/(– 0.1) = –10 diopters. Monday, March 8, 2010 81