Cambridge A Level Physics 9702 — 2018 May/June Paper 5 · Variant 2

1 A student is investigating the reflection of light from a compact disc (CD), as shown in Fig. 1.1. screen light h CD Fig. 1.1 The student observes on the screen a pattern of maxima and minima which is similar to that produced by a diffraction grating. The distance h is measured to one of the maxima. It is suggested that the relationship between h and the wavelength λ of the incident light is nλ h = + B d where n is the order of the maximum and d and B are constants. Design a laboratory experiment to test the relationship between h and λ. Explain how your results could be used to determine values for d and B. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken. 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Mark scheme: 1 Defining the problem λ is the independent variable and h is the dependent variable or vary λ and measure h 1 keep angle of incidence of light on to CD constant 1 Methods of data collection labelled diagram of workable experiment including: • light source, CD and screen • method to support light source • light source labelled and at least one other label 1 method to change wavelength, e.g. use filters, different lasers/LEDs 1 method to determine λ e.g. read from filter/label or experiment e.g. Young’s slits, diffraction grating 1 measure h with a rule or labelled rule shown in diagram close to screen with h indicated 1 Method of analysis plot a graph of h against λ or plot a graph of h against nλ 1 d = n / gradient or d = 1 / gradient (consistent with graph) 1 B = y-intercept 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 safety precaution linked to exposure of eyes to (intense) light, e.g. avoid looking (directly) at the (intense) light source or wear dark glasses or wear goggles to protect eyes from light D2 keep distance from CD to screen constant D3 keep n constant D4 method to identify same order, e.g. identify the zero order and count the number of maxima to where h is measured D5 equation to determine λ e.g. Young’s slits/diffraction grating formula with λ as subject D6 use intense light source/collimated light source D7 perform experiment in a dark room D8 clean surface of CD/check that there are no scratches D9 detail on measuring h (e.g. measure to the top and bottom of the maximum and average) D10 relationship valid if a straight line (with a y-intercept)

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2 A student is investigating the charging of a capacitor. A circuit is set up as shown in Fig. 2.1. E C P Q V Fig. 2.1 The capacitor is initially discharged. A resistor of resistance R is connected between P and Q. When the switch is closed, the time t for the voltmeter reading to increase to a specific value V is measured. The capacitor is then discharged. The experiment is repeated with a different number n of resistors each of resistance R connected in series between P and Q. It is suggested that t and n are related by the equation J t N OO - KK V nRC L 1 - = e E P where E is the electromotive force (e.m.f.) of the power supply and C is the capacitance of the capacitor. (a) A graph is plotted of t on the y-axis against nR on the x-axis. Determine an expression for the gradient. gradient = .......................................................... [1] (b) Values of n and t are given in Fig. 2.2. Each resistor has a resistance R of 4.7 kΩ ± 10%. n t / s 1 15.8 2 34.8 3 50.8 4 66.8 5 83.8 6 97.2 Fig. 2.2 Calculate and record values of nR / 103 Ω in Fig. 2.2. Include the absolute uncertainties in nR. [2] (c) (i) Plot a graph of t / s against nR / 103 Ω. Include error bars for nR. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = .......................................................... [2]

Mark scheme: 2(a) gradient = ln 1 ln V E C C E E V     − −     −     or 1 2(b) nR / 103 Ω absolute uncertainty in nR 4.7 or 4.70 0.5 or 0.47 9.4 or 9.40 0.9 or 0.94 14 or 14.1 1 or 1.4 or 1.41 19 or 18.8 2 or 1.9 or 1.88 24 or 23.5 2 or 2.4 or 2.35 28 or 28.2 3 or 2.8 or 2.82 First mark for correct column heading and values of nR. Second mark for absolute uncertainties in nR. Allow a mixture of significant figures. 2 2(c)(i) Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in nR plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Upper end of line should pass between (25, 90) and (26, 90) and lower end of line should pass between (10.5, 40) and (11.5, 40). Do not allow line from top point to bottom point unless points are balanced. 1 Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted. 1 Question Answer Marks 2(c)(iii) Gradient determined with clear substitution of points from the line of best fit into ∆y / ∆x. Distance between points must be at least half the length of the drawn line. 1 Gradient of worst acceptable line determined. uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(d)(i) C determined using gradient and given to 2 or 3 significant figures. 1 C determined using: ( ) gradient (c)(iii) (c)(iii) ln 0.2 1.609438 ln 1 C V E − − − = = = −   −     1 C determined correctly using gradient and with unit (F or s Ω–1) and correct power of ten. 1 2(d)(ii) % uncertainty in C = % uncertainty in gradient. 1 Question Answer Marks 2(e) K determined using C. Correct substitution of numbers must be seen. ( ) 300 300 130.3 ln 1 0.9 2.30 (d)(i) (d)(i) K C − − = = = − × − × 1 Absolute uncertainty in K determined. Correct substitution of numbers must be seen. gradient uncertainty gradient C K K C   ∆ ∆   = × = ×         Maximum/minimum methods: 130.3 130.3 1.609 209.69 max min (d)(i) min gradient min gradient K − − × − = = = 130.3 130.3 1.609 209.69 min max (d)(i) max gradient max gradient K − − × − = = = 1

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