Exercises

Equivalence of Points (Based on Exercise 3.1.)

Note that the thin lens model is similar since rays through the centre of the lens (optical centre) are not deflected, and thus serves the role of a pinhole.

(Exercise 3.2)

This initial figure is slightly inaccurate. Horizontal lines (object to lens, and lens to image point) delimit the region of interest. In reality it is the aperture that delimits the bundle of light that contributes to the image.

However it was my first impression of a possible solution, and if we just image that the aperture just happens to extend exactly to cover the rays drawn, then it is fine. Let’s redraw.

This figure shows the bundle of light emanating from the object point in the focus plane and passing through the apperture. Assuming that the aperture is is circular, the bundle is a skew cone, and the points contributing to the image point from the out-of-focus plane is a section of the skew cone.

Scale Ambiguity (Exercise 3.8).

Use the figure from Exercise 3.1. Ask if it does not suffice.

Exercise 3.3 Part 1-2.