| Date | May 2014 | Marks available | 6 | Reference code | 14M.3.SL.TZ1.18 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Construct, Deduce, Define, Estimate, Label, and Outline | Question number | 18 | Adapted from | N/A |
Question
This question is about a compound microscope.
The diagram below shows two thin converging lenses in a compound microscope. The focal length of the objective lens is fo. The object O is placed at a distance u from the objective lens.
(i) On the diagram above, construct a ray diagram to locate the position of the image formed by the objective lens. Label this image I.
(ii) Outline whether the image I is real.
The compound microscope in (a) is in normal adjustment so that the final image is formed at the near point of an unaided eye. The position of the near point of the eye is located at N.
(i) Define near point.
(ii) Deduce that the focal length of the eyepiece is around 10.7 cm.
(iii) Estimate the total linear magnification of the microscope.
Markscheme
(i) any two standard rays out of the three shown below;
converging to locate the image;
(ii) (image is real) because rays of light/energy pass through it;
(i) the closest distance the unaided human eye can focus (without undue strain);
Do not accept 25cm without explanations.
(ii) standard ray through the center of the eyepiece to locate point A;
standard ray through points A and B;
extrapolated to the principal axis to locate the focus F, 10.7cm from the eyepiece; } (allow focal lengths between 9 cm and 12.5 cm if the two standard rays are clearly identified)
or
v=-25cm;
u=+7.5cm;
\(f = {\left[ {\frac{1}{u} + \frac{1}{v}} \right]^{ - 1}}\left( { = 10.7{\rm{cm}}} \right)\);
(iii) counting small squares, size of final image=33.3 and size of object=10;
\(m = \frac{{33.3}}{{10}} = 3.3\);
or
\({m_1} = 1\) and \({M_2} = \left( {\frac{{25}}{{7.5}} = } \right)3.3\);
\(M = \left( {{m_1} \times {M_2} = } \right)3.3\);
Examiners report
This question was relatively well answered. In (a), the majority of candidates proved that they are able to use standard rays to find the position of the image, although too many candidates were not able to outline clearly enough whether the image is real.
There were many correct answers to (b)(i), despite the general tendency for a lack of clarity in the answers to “define” questions. (b)(ii) and (iii) were well answered by the more able candidates. Generally the answers lacked clarity, explanation of formulas used and clarity of layout of working. More alternative solutions were accepted if clearly explained. Only a few construction based solutions was found, although this is by far the more understandable approach to the problem.
