ssm_ch34 - Chapter 34 5 The light bulb is labeled O and its...

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Chapter 34 5 The light bulb is labeled O and its image is la- beled I on the digram to the right. Consider the two rays shown on the diagram to the right. One enters the water at A and is reflected from the mirror at B. This ray is perpendicular to the wa- ter line and mirror. The second ray leaves the lightbulb at the angle μ , enters the water at C, where it is refracted. It is reflected from the mir- roratDandleavesthewateratE.AtCtheangle of incidence is μ and the angle of refraction is μ 0 . At D the angles of incidence and reflection are both μ 0 . At E the angle of incidence is μ 0 and the angle of refraction is μ . The dotted lines that meet at I represent extensions of the emerging rays. Light appears to come from I. We want to compute d 3 . ² O ² I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A B C D E μ μμ μ 0 μ 0 μ 0 μ 0 water line mirror " j d 1 j # " j d 2 j # " j d 3 j # Consideration of the triangle OBE tells us that the distance d 2 + d 3 is L tan(90 ± ¡ μ )= L= tan μ , where L is the distance between A and E. Consideration of the triangle OBC tells us that the distance between A and C is d 1 tan μ and consideration of the triangle CDE tells us that the distance between C and E is 2 d 2 tan μ 0 ,so L = d 1 tan μ +2 d 2 tan μ 0 , d 2 + d 3 =( d 1 tan μ + 2 d 2 tan μ 0 ) = tan μ ,and d 3 = d 1 tan μ d 2 tan μ 0 tan μ ¡ d 2 : Apply the law of refraction at point C: sin μ = n sin μ 0 ,whe re n is the index of refraction of water. Since the angles μ and μ 0 are small we may approximate their sines by their tangents and write tan μ = n tan μ 0 . Us this to substitute for tan μ in the expression for d 3 to obtain d 3 = nd 1 d 2 n ¡ d 2 = (1 : 33)(250 cm) + 2(200 cm) 1 : 33 ¡ 200 cm = 350 cm ; where the index of refraction of water was taken to be 1 : 33. 11 (a) The radius of curvature r and focal length f are positive for a concave mirror and are related by f = r= 2, so r =2(+12cm)=+24cm . 216 Chapter 34
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(b) Since (1 =p )+(1 =i )=1 =f ,whe re i is the image distance, i = fp p ¡ f = (12 cm)(18 cm) 18 cm ¡ 12 cm =36cm : (c) The magnification is m = ¡ i=p = ¡ (36 cm) = (18 cm = ¡ 2 : 0. (d) The value obtained for i is positive, so the image is real. (e) The value obtained for the magnification is negative, so the image is inverted. (f) Real images are formed by mirrors on the same side as the object. Since the image here is real it is on the same side of the mirror as the object. 9 (a) The radius of curvature r and focal length f are positive for a concave mirror and are related by f = r= 2, so r =2(+18cm)=+36cm . (b) Since (1 =p =i =f i is the image distance, i = p ¡ f = (18 cm)(12 cm) 12 cm ¡ 18 cm = ¡ 36 cm : (c) The magnification is m = ¡ i=p = ¡ ( ¡ 36 cm) = (12 cm = 3 : 0. (d) The value obtained for i is negative, so the image is virtual. (e) The value obtained for the magnification is positive, so the image is not inverted. (f) Real images are formed by mirrors on the same side as the object and virtual images are formed on the opposite side. Since the image here is virtual it is on the opposite side of the mirror from the object.
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This note was uploaded on 01/19/2009 for the course PHYS 171.102 taught by Professor Heckman during the Fall '98 term at Johns Hopkins.

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ssm_ch34 - Chapter 34 5 The light bulb is labeled O and its...

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