PS10_2005 - OPTI 201R, Fall 2005 Problem Set X 1 X .1 For a...

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X .1 For a concave mirror, radius of - 20 cm, with a diameter of 4 cm : H a L Find the power in diopters if used in air. f= n' - n ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ R = - 1 - 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ - .2 = 10 D H b L What is the H F ê # L in air? f eff = 1 ÅÅÅÅÅ f =- f ÅÅÅÅÅ n = f * ÅÅÅÅÅÅ f ê # = f eff ÅÅÅÅÅÅÅÅÅÅ D en = 1 ê f ÅÅÅÅÅÅÅÅÅÅÅ D en = 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅ 10 μ 0.04 = 2.5 H c L Make a sketch showing the cardinal points. HN êêêêê = H * N * êêêêêêêê = f + f * 2 f R C.C N, N* f f* HH* 10 cm H d L What is the power H diopters L if the mirror is submerged in water? H n = 4 ê 3 L - 4 ÅÅÅÅÅÅ 3 - 4 ÅÅÅ 3 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅ - .2 = - 1 - 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ - .2 = 13.33 D H f L What is the focal lengths H f, f * L in water? f n o ÅÅÅÅÅÅ f 4 ê 3 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ 13.33 0.1 f * = n i ÅÅÅÅÅ f = - 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ 13.33 0.1 Both focal points are 10 cm to left of vertex. Notice that the power changes, but rear and front focal lengths do not. OPTI 201R, Fall 2005 Problem Set X 1
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X .2 A concentric lens of index 1.5 with radii of - 5 and - 8 cm is aluminizedon the 8 cm surface as shown below. H a L What is the total power of the lens? Radius ÿ R 1 =- 0.05 ÿ R 2 0.08 ÿ R 3 0.05 ÿ index n 0 = 1 ÿ n 1 = 1.5 ÿ n 2 1.5 ÿ n 3 1 thickness ÿÿ t 1 = 0.03 ÿ t 2 0.03 power ÿ- 10 ÿ 37.5 10 ÿ f 1 = n 1 - n 0 ÅÅÅÅÅÅÅÅÅÅÅÅ R 1 = 1.5 - 1 ÅÅÅÅÅÅÅÅÅÅÅÅ - 0.05 10 f 2 = n 2 - n 1 ÅÅÅÅÅÅÅÅÅÅÅÅ R 2 = - 1.5 - 1.5 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ - 0.08 = 37.5 f 3 = n 3 - n 2 ÅÅÅÅÅÅÅÅÅÅÅÅ R 3 = - 1 + 1.5 ÅÅÅÅÅÅÅÅÅÅÅÅÅ - 0.05 10 f 12 =f 1 +f 2 - f 1 f 2 t 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ n 1 10 + 37.5 - H - 10 L H 37.5 L H 0.03 L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅ 1.5 = 35 D d 12 = n 0 f 2 t 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ f 12 n 1 = 1 H 37.5 L H 0.03 L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ H 35 L H 1.5 L = 0.0214 = 2.14 cm d 12 * n 2 f 1 t 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ f 12 n 1 H - 1.5 L H - 10 L H 0.03 L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ H 35 L H 1.5 L 0.008571 0.8571 cm t 12 = t 2 -d 12 * 0.03 + 0.008571 0.021429 f 123 12 3 - f 12 f 3 t 12 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅ n 2 = 30 D Null OPTI 201R, Fall 2005 Problem Set X 1
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H b L Where is the back focal point located? d 123 * =- n 3 f 12 t 12 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ f 123 n 2 = 0.016667 = 1.6667 cm efl = 1 ÅÅÅÅÅÅÅÅÅÅÅ f 123 = 0.03333 m and elf = f * ÅÅÅÅÅÅ n' f ÅÅÅÅ n f = f * 0.03333 m BFD = f * +d 123 0.03333 + 0.016667 0.016667 m In the real space, F * is located 1.66 cm to left of front vertex.
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PS10_2005 - OPTI 201R, Fall 2005 Problem Set X 1 X .1 For a...

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