Describe one straightforward method the student can use to check that the lens has focal length of $10\,\text{cm}$. A diagram may be included in your response.
On Fig. 1.1, indicate and label the lengths $u$ and $D$.
The distance $u$ is fixed at $85.0\,\text{cm}$ and the student measures $D$. He repeats the experiment and records the following values of $D$, in cm. $96.5,\;96.3,\;96.2,\;96.1,\;96.2$ Calculate $D_{av}$, the mean value of $D$. Give your answer to three significant figures.
State one precaution the student can take to make each measurement of $D$ accurate.
On Fig. 1.2, add your $D_{av}$ result for $u = 85.0\,\text{cm}$ from (b)(ii).
On Fig. 1.3, plot $D_{av} / \text{cm}$ against $u / \text{cm}$ with $D_{av}$ on the $y$-axis and $u$ on the $x$-axis. Begin your axes at $(0, 30)$. The graph indicates that $D_{av}$ reaches a minimum. Draw a smooth curve of best fit.
Use your graph to determine the minimum value of $D_{av}$.
Use your graph to determine $u_m$, the value of $u$ when $D_{av}$ is at its minimum.
Theory shows that the minimum value for $D_{av}$ occurs when $D_{av} = 4f$ and when $u_m = 2f$. Calculate $\frac{D_{av}}{4}$ and $\frac{u_m}{2}$ from the values you have given in (c)(iii). Comment on your answers.