A student measures the focal length of a lens. Fig. 3.1 shows the apparatus she uses and the position of the lens when a clearly focused image is formed on the screen. [Figure 3.1 (one fifth full size)] The student: • places the screen a distance D = 60.0 cm from the illuminated object • places the lens between the object and the screen so that the lens is very close to the illuminated object • moves the lens slowly away from the illuminated object until a clearly focused image is formed on the screen.

1. (a)(i)Measure and record distance x on Fig. 3.1. x = ................................................................ cm[1]
2. (a)(ii)Fig. 3.1 is drawn to a scale of one fifth full size. Use your answer to (a)(i) to calculate the actual object distance u from the lens. u = ................................................................ cm[1]
3. (a)(iii)Deduce the image distance v, the distance from the lens to the screen when a clear image is seen. v = ................................................................ cm[1]
4. (b)Fig. 3.2 shows the shape of the illuminated object and Fig. 3.3 shows the image seen on the screen. [Figure 3.2] [Figure 3.3] Describe two differences between the illuminated object and its image on the screen.[2]
5. (c)(i)The student moves the screen away from the illuminated object and repeats the procedure for values of D = 70.0 cm, 80.0cm, 90.0cm and 100.0 cm. Table 3.1 shows the values recorded. Add your values for u and v from (a)(ii) and (a)(iii) to Table 3.1 on page 12. Complete Table 3.1 by calculating the value of (u × v) for each value of D. Give your answers to 3 significant figures.[2]
6. (c)(ii)Use the grid provided in Fig. 3.4 on page 13 to plot a graph of (u × v)/cm² on the y-axis against D/cm on the x-axis. You do not need to start your axes at the origin (0,0). Draw the straight line of best fit.[4]
7. (c)(iii)The focal length f of the lens is numerically equal to the gradient of the line. Calculate the gradient of the line. Show all working and indicate on your graph in Fig. 3.4 the values you use. f = .............................................................. cm[2]
8. (d)The lens manufacturer states that the focal length of the lens is 15.0cm ± 10%. Decide, with a calculation, whether your value of f agrees with this statement and tick the box that shows your answer. calculation: My value for f agrees with the manufacturer's statement. My value for f does not agree with the manufacturer's statement.[1]

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