AP* Optics Free Response Questions KEY - AP Physics B

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AP* Optics Free Response Questions KEYMIRRORS1978 Q5(1) AP is a registered trademark of the College Board. The College Board was not involved in the production of and does not endorse this product. (2) Test Questions are Copyright 1984-2008 byCollege Entrance Examination Board, Princeton, NJ. All rights reserved. For face-to-face teaching purposes, classroom teachers are permitted to reproduce the questions. Web or Mass distributionprohibited.1

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AP PHYSICS B2002 SCORING GUIDELINESQuestion 415 points total(a)Distribution ofpoints4 pointsFor any two correct rays through the lensTwo of the three principal rays shown on the diagram above were expected.One point was subtracted for additional incorrect rays. No credit was awarded forreflected rays.For correct extension of the rays backwardFor showing the image with correct size, position, and orientation(b)1 point1 point2 pointsFor stating that the image is virtual, or for stating a choice consistent with the raydiagram in part (a)If there were no supporting diagrams or calculations, virtual was the onlyaccepted answer.For a correct explanation consistent with the choice given, such as:The light rays diverge on the left side of the lens, but appear to come from a pointbehind the object. OR The image is on the same side of the lens as the object.OR The object is placed between the converging lens and the focal point.This point was not awarded if additional wrong statements were part of the response.(c)2 points1 point1 point3 pointsFor the lens equation OR for the lens equation with substituted quantities11 1111 ORsosifsi 10 cm6 cmFor the correct solutionsi -15 cm (Minus sign was not necessary to receive full credit.)Only 1 of the 2 answer points was awarded for the correct number without units.1 point2 pointsCopyright 2002 by College Entrance Examination Board. All rights reserved.Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.1119

AP PHYSICS B2002 SCORING GUIDELINESQuestion 4 (cont’d.)Distribution ofpoints(c)continuedAlternate SolutionLet xo distance from object to focal point and xi distance from image to focal point.For the correct formulaxif fxoFor correct substitutionsxi10 cm 10 cm 10 cm - 6 cm(10 1 point1 point2 pointsFor the correct image size to object size ratio with no units, or with units that cancelhis 15 cm 5 i 6 cm 2ho soNotes:Students could use either a calculation or a ray diagram to arrive at the final answer.1 point only was awarded if the correct ratio was imbedded in extra calculations or ifunits were provided for the answer (for example, 2.5 cm).No points were given for giving the object size to image size ratio.(e)1 point2cm )xi 25 cm4 cmsi 25 cm - 10 cmFor the correct answersi 15 cm(d)Alternatepoints2 points4 pointsSince the question asked for a description, a verbal response was expected, althoughthe image position, size, and orientation could be determined from either a calculationor a ray diagram.For the correct position:Image on the opposite side of the lens from the objectDistance from the image to the lens in the range 20 cm 3 cmFor the correct size: image size same as object size, or for size consistent with valuefor positionFor the correct orientation: image is inverted1 point1 point1 point1 pointCopyright 2002 by College Entrance Examination Board. All rights reserved.Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.1220

AP* Optics Free Response Questions KEYINDEX OF REFRACTION1979 Q621

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AP PHYSICS B2006 SCORING GUIDELINESQuestion 415 points total(a)Distributionof points2 pointsTrialqi130o20240o35045qrsinqisin o40o0.940.64For identifying that both quantities to be graphed are the sines of the anglesFor correctly calculating the sines using degrees(b)1 point1 point4 pointsExample:For correctly labeling both axes with the sines of the anglesFor correctly labeling both axes with appropriate numerical scalesFor plotting the five pointsFor correctly drawing a best fit line that includes the entire range of data points and mayextend beyond them1 point1 point1 point1 point 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).3110

AP PHYSICS B2006 SCORING GUIDELINESQuestion 4 (continued)Distributionof points(c)(d)4 pointsFor a statement or implicit use of Snell’s Lawn1 sin qi n2 sin qr (or sin qi n2 sin qr since n1 nair 1 )1 pointFor indicating that the index of refraction n can be obtained from the slope or inverseof the slope depending on choice of variable plotted on each axisExample using graph abovesin qi1n sin qrslopeFor using two sets of points directly from the line to find the slope0.53 - 0.41 0.67slope 0.78 - 0.60For a correct calculation of the index of refraction consistent with the slope of the graphn 1 0.67 1.51 point1 point1 pointFor checking “The air-oil interface only”(e)1 point1 point4 pointsFor indicating that the optical path difference between the waves reflecting off the air-oilinterface and the oil-water interface is one-half wavelengthDA l 2For indicating that the wave reflecting off the oil-water interface travels a distance equalto twice the thickness of the oilDA 2 tFor indicating that the wavelength of the light in the oil film is different from thewavelength of the light in airl film lair n film1 point1 point1 pointThe three equations above are combined to relate the film thickness to the wavelength.2t l film 2 lair 2 n filmt lair 4n filmt 6.0 10 -7 m 4(1.43)For the correct answer with appropriate units1 point-7t 1.05 10 m 105 nmNotes:A student who checked “The oil-water interface only” in part (d) and then correctlycalculated a wavelength of 105 nm for the thickness of the oil was awarded full credit.A student who checked “Both interfaces” or “Neither interface” in part (d) and thencorrectly calculated a wavelength of 210 nm for the thickness of the oil was awardedfull credit. 2006 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).3211

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AP* Optics Free Response Questions KEYDOUBLE SLIT1991 Q640

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AP* Optics Free Response Questions KEY1996 Q3Question 3 (15 points)(a) 2 pointsFor indicating that interference demonstrates the waveproperty of light or diffraction, or constructive anddestructive interference(b) 3 pointsFor realizing that the distance of point P from the centerof the in terference pattern is 3/2 the spacing of thepattern, and indicating that the path difference is 3/2 λDistributionof points2 points3 pointsNote: An answer of simple 3/2 was awarded 2 points.(Alternate solution 1)(Alternate points)For a diagram showing the path difference1 pointPath difference mλ dsinθFor using sinθ tanθ x / LPath difference dx / L (2 x 10 -3 m)(18. x 10 -3 m) / (5m)For the correct answerPath difference 7.2 x 10 -7 m1 point1 point(Alternate solution 2)(Alternate points)For using the Pythagorean theorem1 pointUsing the geometry shown abovea (0.8mm) 2 (5000mm) 2 25,000,000.64 mm(1) AP is a registered trademark of the College Board. The College Board was not involved in the production of and does not endorse this product. (2) Test Questions are Copyright 1984-2008 byCollege Entrance Examination Board, Princeton, NJ. All rights reserved. For face-to-face teaching purposes, classroom teachers are permitted to reproduce the questions. Web or Mass distributionprohibited.42

AP* Optics Free Response Questions KEYb ( 2.8 mm) 2 (5000 mm) 2 25,000,007.84 mmFor subtracting the two lengthsPath difference b aFor the correct answerPath difference 7.2 x 10 -7 m1 point1 point(c) 4 pointsThere are two methods for this solution corresponding togiving an answer of 3/2 λ in part (c).Method 1Path difference mλ dsinθMethod 2 ఒ ݔ ൎFor correct substitutionUsing sinθ or tanθ x / LFor correctly substitutingL, d, a value of x thatcorresponds to amaximum or minimum inthe interference pattern,and whole of half integernumber for mSubstituting the correctvalue of m correspondingto the value of xSubstituting the correctvalue of m correspondingto the value of xλ λ dxmLChoosing to make thesubstitutions for point Pλ ( 2 x 1 0 - 3 m ) ( 1 .8 x 1 0 - 3 m )(3 / 2 )(5 m )For a correct answer, inwhich the units match themagnitude λ 4.8 x 10 -7 m1 pointௗdxmLChoosing to make thesubstitutions for point Pλ ( 2 x 1 0 - 3 m ) ( 1 .8 x 1 0 - 3 m )(3 / 2 )(5 m )For a correct answer inwhich the units match themagnitude λ 4.8 x 10 -7 m1 point(Alternate solution)(Alternate points)For setting a numerical answer to part (b) (or a newlycalculated value) equal to 2/3 λFor a correct answer, in which the units match the magnitude3 points1 point(d)i.2 pointsFor indicating that the interference pattern will be compressedtoward the central maximum1 point43

AP* Optics Free Response Questions KEYii.2 pointsFor indicating that there will be a spreading of the pattern, or alarger central maximum in the patternFor indicating that the new pattern is a one-slit diffractionpattern.iii.1 point1point2 pointsFor indicating that the interference pattern will be compressedtoward the central maximum1 point ఒ For referring to the equation ݔ ൎ, and indicating that as dௗincreases the pattern in compressed1 pointNote: Allowance was made in all calculations for the smalldiscrepancies in the reading values from the graph44

AP PHYSICS B 2006 SCORING GUIDELINES Question 4 15 points total D

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