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How can I find the focal length of a thick lens by the method of ray tracing ? I know the ray matrix method but by ray tracing I don't get to an answer.

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closed as off-topic by John Rennie, GiorgioP, FGSUZ, Aaron Stevens, Kyle Kanos Apr 8 at 12:17

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  • $\begingroup$ What do you mean by "the ray tracing method"? $\endgroup$ – Farcher Apr 6 at 9:47
  • $\begingroup$ Use the dioptre equations twice. $\endgroup$ – FGSUZ Apr 7 at 19:13
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The focal length for a thick lens is the distance between its focal and principal planes.

To find the principal planes, I am following the idea I found in a website on optics (http://www.optique-ingenieur.org/en/courses/OPI_ang_M03_C01/co/Contenu_26.html, by Jacques Sabater), referring to the figure below:

Optical system with focal and principal planes

Let us take an optical system and let us admit that we know how to trace rays. We then first trace a ray which, in object space, is parallel to the optical axis (the red ray in the image); this will meet the optical axis in image space in a point which is the focal point (in image space; it is point F' in the image). Let us consider the portion of the ray in image space; we mark the point at which the ray has the same height in image space as it had in object space with the letter I' We do the same for a ray that is parallel to the optical axis in image space (the blue ray in the image) and has in image space the same height as the first ray had in object space. With its help we define two points in object space, the focal point (in object space, F) and the point I, where the ray in object space has the same height as in image space.

The points I and I' are conjugate with respect to each other: we have traced two rays which both pass through I and I', all other rays which pass through one point will pass through the other.

In conclusion, we have found two points which are conjugate with respect to each other and have the same height. The same condition will be true for all points which lie in the planes perpendicular to the optical axis passing through I and I': so we have found the principal planes.

Using the principal and the focal planes, we calculate the focal length.

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