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2008SFinalSol

# 2008SFinalSol - F Phys;cs 202 I 1'1 Sf 1> 2i 8 Name r e~ E...

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Phys;cs 202/ Sf/"; 1>} 2°i?, 8 F . I E Name: r\ e ~ 1;')'1 Xa~ 1. [6 points] The claddingof an optical fiber has refractive index nc = 1.20. Light rays in the fiber core that make an angle of 30° or less with the fiber's central axis are reflected from the fiber core-cladding boundary without any loss in intensity; rays that make a larger angle with the axis decrease in intensity each time they reflect. What is the index of refraction of the fiber core? cladding, nc = 1.20 fiber core, nf central - - - - - - - - --- ~- ~ -3-00-- - - ~axis - - - - - -- - - -- e I e ::= 90° - f. W h e YI i> .::::;. 30: e ~ ec / fh e c ,.;f; C-4( Q."", / ~ to Y" +~+«. ( ; VI tel""~ { ,... ef/-e c f;o ~ (TI~) Q + +~e tl>vnJ~",y be:.tlA/ee'1r fhe f;ber Core a"J fA~ c(QJJ;j't'j. ec; -= 100 - 30° = 60°- Sin e =- nc C -' f\f n -:: nc - 1.20 - /J Q ~ - - -- - I S;'1 ec. s;~ tOo nf = I. 3 Cj. 1

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Name: f( e. ~ 2. [6 points] Two laser beams, both of wavelength A = 500 nm, are incident on a converging lens of focal length f = 25.0 cm and radius 5.0 cm. The beams are incident parallel to the central axis of the lens. One beam hits the center of the lens and and passes straight through, as shown. The other beam hits the lens offset from its center by 4.0 cm and is deflected by the lens; the deflected ray is not shown. A screen is 80.0 cm behind the lens. : scree : 4.0cm . : : ~ ! L 0 0 ; 80cm I 0 0 How far apart are the centers of the two laser spots on the screen? h -=. Lf.O CM fol' offset bect:/I"'1. T~ e Je .{Iec-f; D" aV'\fl-c 0 f fA;)'" 6elt--"1 if r;( = - Ph -:::: :11. d\ ::=. - O. I h raJia"j ( - 11~o ~ -= - 1. z 0 - f rr r~J:~...J' ) I h ; J b e ct: "'" h ; f J + h ~ .J" C r ~ ~ ,., IJ/ ;5 I' I ~ c. e: 0( J c ~ "'" b.7 ~"" ~"",o"",f L:J)(' -:=: (30C-fNI) +~f'\ ~ =:- - /2.1ct"1 dJ f J = I A + ~ X I = ( ~. 0 c,..., - /2. q c ~ I 6 e '" ee" ',.t) d - g.1c~ between spots -. 2 !
Name: K e ~ ~-- 3. [14 points] An object is placed a distance p = 0.50t in front of an ideal, thin converging lens of focal length t. (a) On the diagram below, carefully draw three rays from the upper tip of the object and use them to locate the corresponding image point. ; : I , --- I " ~ '"'" -- '0 -"--"""--~ F1 (b) What is the image distance i in terms of t (include correct algebraic sign)? I = , t- I J"=: I - I - - . - - -. f "fL T .; f fL -L= L..=.£. .i,=._~.£.- -:=. IJ-sof"l. - O.SIJf - - - - ~ f fl 'fJ- -I' /)-50.,[' - f -0 -s () i= -f (c) Is the image real or virtual? Please explain. rh~ I'/{l\$ J",'f- ac/-"4/'y Cool"\~ I""",, f-h~ coi',.e.r,~"J.:f'l1 J"~ {)J- If" rhe. ; "",a,e. Image type: Vif'+C.I~( . : , (Continued on the next page.) 3

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Name: f( -e r (d) What is the lateral magnification? Y'Y\= -~ = L- =- 2.1J f 0.50;(' m= 2.0 ! , i ! ; j i + l" ; 't' t" 4 1
Name: K e,Y 4. [8 points] Due to a mistake by the manufacturer, the antireflection coating on a lens is 180 nm thick- twice as thick as intended. Also, the wrong material . 1 00 was appliedas the coating; the indices of refraction air (nair =. ) of the coating used and the glass are ncoating = 1.60 and ng1aSS = 1.50, respectively. The lens is surrounded by air (nair = 1.00). (a) What wavelengths in air in the visible range (400 nm to 700 nm), if any, are strongly reflected due to constructive interference? L = /30,.,...,- £) { '- f " '- 1 /'_.. ~ '""e. f~ ,.ef/ec.+.~" ..I,..e ;.rl:..

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2008SFinalSol - F Phys;cs 202 I 1'1 Sf 1> 2i 8 Name r e~ E...

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