1. **State the problem:** We want to determine the focal length $f$ of a given lens using the experiment described, to check if it can replace a damaged spectacle lens. 2. **Explain the setup:** The object distance $u$ is measured from the object to the lens, and the image distance $v$ is from the lens to the screen where a sharp image is formed. 3. **Measurements:** Values of $u$ are given as 20.0 cm, 30 cm, 40 cm, 50 cm, 60 cm, and 70 cm. Corresponding $v$ values are measured each time when a sharp image forms. 4. **Tabulate data:** For each pair $(u,v)$, calculate $\frac{1}{u}$ and $\frac{1}{v}$. 5. **Plot graph:** Plot $uv$ on the y-axis against $(u+v)$ on the x-axis, then find the slope $S$ of the best fit line. 6. **Determine focal length:** According to the experiment, the focal length $f = S$. 7. **Explanation:** This method relates to the lens formula $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$. The graph and slope method provide an experimental way to find $f$ without directly using the formula for each trial. 8. **Hypothesis:** The expected focal length $f$ ranges between 8.0 cm and 12.0 cm. 9. **Possible errors:** Parallax errors in measuring $v$, weak cells reducing light intensity, and environmental light affecting sharpness of image. **Final answer:** The focal length $f$ equals the slope $S$ of the graph plotted with coordinates $(u+v, uv)$, expected to be between 8.0 cm and 12.0 cm if the lens fits the hypothesis.