A convex lens used as a magnifying glass has a focal length of f_e. Derive an expression for the angular magnification when the image is at the near point D.

The convex lens in (a) is used as the eyepiece of a compound microscope.

An object is placed 1.5 cm from the objective lens. The focal length f_o of the objective lens is 1.0 cm.

(i) Draw rays on the diagram to show the formation of the intermediate image.

(ii) Calculate the distance of the intermediate image from the objective lens.

Lenses used in the compound microscope are subject to spherical aberration and chromatic aberration.

Explain what is meant by

(i) spherical aberration.

(ii) chromatic aberration.

(angular magnification =linear magnification so) \(M = \frac{D}{u}\);
\(\frac{1}{u} + \frac{1}{D} = \frac{1}{f}\);
so \(\frac{D}{u} = \frac{D}{f} + 1 = M\);

(i) ray through centre of objective lens and ray through f_o;
to show formation of intermediate image;

(ii) \(\frac{1}{v} = \frac{1}{1} - \frac{1}{{1.5}}\);
v=3.0cm;
Award [2] for a bald correct answer.

(i) rays parallel to principal axis at edge of lens brought to different foci;
from those near to the centre of the lens;

(ii) different colours have different refractive indices/speeds;
different colour refracted at different amounts / image formed for each colour;