Problem 4 – Hint 5

Here are step-by-step instructions on how to construct the optical axis:

1. Construct the tangents of the ellipse OM and OL (note that M is the image of the point T mentioned in the earlier hints).
2. Construct the image of the farthest-from-O point on the circle (the point A from the earlier hints).
3. Construct the point V where all the rays parallel to t (the ray that touches the circle at the point A) converge after passing the lens.
4. Draw the image of the line AT.
5. Using the previous hints, draw a line u through O that is parallel to AT.
6. Hence find the point U where all the lines parallel to AT converge after passing the lens.
7. Hence find the focal plane and the optical axis.

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