A student investigates the image formed by a converging lens. (a) The student: • arranges the apparatus as shown in Fig. 3.1 [Figure 3.1] • places a white screen approximately 30 cm from the lens • adjusts the position of the screen until a sharp image of a window in the laboratory, a few metres distant from the lens, is formed on the screen.

1. (a)(i)Measure and record, in centimetres to the nearest 0.1 cm, the distance x on Fig. 3.1 from the lens to the screen. x =[1]
2. (a)(ii)The distance x shown on Fig. 3.1 is drawn to a scale of one-third full size. Use your answer from (a)(i) to calculate the actual distance from the lens to the screen. This distance is the focal length f of the lens. f=[1]
3. (b)The student: • rearranges the apparatus as shown in Fig. 3.2 [Figure 3.2] • switches on the lamp • places the lens a distance u = 20.0 cm from an illuminated triangular object • adjusts the position of the screen until a sharp image of the triangular object is formed on the screen • measures the image distance v from the lens to the screen. v = 60.5 cm Calculate the values of (u + v) and uv. Record your values of (u + v) and uv to an appropriate number of significant figures on the answer lines and in the first row of Table 3.1. (u + v) = uv =[1]
4. (c)The student repeats (b) for values of u between u = 25.0 cm and u = 55.0 cm. The student's results are shown in Table 3.1. Add appropriate units to the headers of the last two columns. [Table 3.1][1]
5. (d)On the grid provided in Fig. 3.3, plot a graph of uv on the y-axis against (u + v) on the x-axis. You do not need to start either axis from the origin (0, 0). Draw the straight line of best fit. [Figure 3.3][4]
6. (e)Calculate the gradient of the line. Indicate on the graph the points you use. Show all your working. gradient =[2]
7. (f)Two quantities can be considered to be the same within the limits of experimental accuracy if their values are within 10% of each other. The gradient of your line calculated in (e) is numerically equal to the focal length f of the lens in cm. Compare your value of f obtained in (a)(ii) with the value of the gradient obtained in (e). State if your two values can be considered to be the same. Support your statement with a calculation. calculation statement[2]
8. (g)(i)When measuring the object and image distances with a metre rule, it is important to avoid line-of-sight (parallax) errors. State how the student avoids parallax errors when doing the experiment.[1]
9. (g)(ii)Describe a technique that the student uses to make sure that the image on the screen is as sharply focused as possible.[1]

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