Construct rays on the diagram to show how the final image is formed.

The intermediate image forms 14.8 cm from the objective lens. The distance between the lenses is 18.1 cm. The focal length of the eyepiece lens is 3.8 cm.

(i) Determine the distance of the final image from the eyepiece lens.

(ii) The angular magnification of the objective lens is ×6. Calculate the angular magnification of the microscope.

Outline how the effects of chromatic aberration in the microscope eyepiece can be reduced by illuminating the object with light that has a narrow range of wavelengths.

at least two rays from O correctly refracted at eyepiece;
completed extrapolation of these rays to form a virtual image;
Ignore rays refracted by the objective lens.
Award [1 max] ECF in second marking point.
Allow virtual image positions to be either side of objective lens.
Award [0] for formation of a real image.

(i) u=(18.1-14.8=)3.3 (cm);
\(\frac{1}{v} = \frac{1}{{3.8}} - \frac{1}{{3.3}}\);
(–)25.1(cm);
Award [2 max] ECF for wrong u value (eg. 14.8 (cm) giving an answer of v=5.1(cm).
Award [1 max] if positive sign appears in second term in right-hand side of equation.
Award [3] for a bald correct answer.

(ii) \({M_{eye}} = \left( {\frac{D}{f} + 1 = \frac{{25.1}}{{3.8}} + 1 = \frac{{25.1}}{{3.3}} = } \right)7.6\);
overall magnification=(6×7.6=)46;
Award [2] ECF from (b)(i).
Award [1 max] ECF from first to second marking point.
Award [2] for a bald correct answer.

each colour/wavelength has a different refractive index / OWTTE;
a range of wavelengths focuses different colours/wavelengths at different points/distances;
reducing the range of wavelengths reduces the range of image distances/reduces the coloured edging to images/reduces dispersion;