An IGCSE physics class is carrying out an experiment to determine the focal length of a converging lens.
A student measures the object distance u u\,u and image distance v v\,v from a diagram drawn to 14\displaystyle \frac{1}{4}41th full size.
On this diagram, the measured distances are:
(i) Determine the actual values, in metres, of u u\,u and v v\,v for this measurement.
(ii) Calculate the corresponding values of 1u\displaystyle \frac{1}{u}u1 and 1v\displaystyle \frac{1}{v}v1 in m−1\text{m}^{-1}m−1.
Four more object distances are set up and these and the corresponding image distances are recorded in Table 4.1.
Table 4.1
| u / mu\ /\ \text{m}u / m | 1u / m−1\displaystyle \frac{1}{u}\ /\ \text{m}^{-1}u1 / m−1 | v / mv\ /\ \text{m}v / m | 1v / m−1\displaystyle \frac{1}{v}\ /\ \text{m}^{-1}v1 / m−1 |
|---|---|---|---|
| 0.200 | 5.00 | 0.400 | |
| 0.250 | 4.00 | 0.286 | |
| [Row 3] | |||
| 0.500 | 2.00 | 0.182 | |
| 0.800 | 1.25 | 0.160 |
Complete Table 4.1 by entering the values from part (a) in Row 3 and calculating the values of 1v\displaystyle \frac{1}{v}v1 for the other rows.
A graph of 1v\displaystyle \frac{1}{v}v1 (yyy-axis) against 1u\displaystyle \frac{1}{u}u1 (xxx-axis) is plotted. Both axes begin at the origin (0,0)(0, 0)(0,0).
(i) From the graph, determine the value p p\,p of 1u\displaystyle \frac{1}{u}u1 when 1v\displaystyle \frac{1}{v}v1 is zero (the xxx-intercept).
(ii) From the graph, determine the value q q\,q of 1v\displaystyle \frac{1}{v}v1 when 1u\displaystyle \frac{1}{u}u1 is zero (the yyy-intercept).
(i) Calculate zzz, where z z\,z is the average value of p p\,p and qqq.
(ii) Calculate the focal length f f\,f of the lens where f=1z\displaystyle f = \frac{1}{z}f=z1.
56 exam-style questions on CIE IGCSE Physics 3.2.3a Converging and diverging lenses. Each one has a worked solution and a mark scheme showing where the marks go.