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Solutions/Image Formation

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title: Solutions for Image Formation
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# Exercises

## Equivalence of Points (Based on Exercise 3.1.)

![Pinhole Model](wk5-1.png)

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)

![Initial Model](wk5-2.png)

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.

![Second Model](wk5-2b.png)

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.