Unable to recreate raytracing math.

[shihanqu]

Aight I've spent all my GPT o1-preview tokens, and I still can't figure out how exactly this simulator is calculating rays.

The lens equation isn't complicated, yet I'm not able to recreate the same path as the simulator using Snell's law or Optical Path Length difference calculations. Can any wizards of this simulator explain what magical alternative math the sim is doing?

For an example ray that enters at (−0.5,0.5), here's the math:
https://chatgpt.com/share/67102882-4a88-800b-9f70-1b5f7ac80506

Here's the link to the simulation:

https://phydemo.app/ray-optics/simulator/#XQAAAAJcAQAAAAAAAABGKcrGU8hqLFnpmU9EnTFrVnU9-XiP9Y4PK0-OC-ZDOxusqN6WKrxeSrcZXzQ6eHnjYeKlDDNv7IUWaCQxAjcUR_xDC-xo23up4Cc8GD2dKFplxvlPl8Y75P9gJplTAvLcrevP87fJW8pYf_3j2ue5DSEK52d7fsgYuMMQ2G-zYO72HCoXt0zoY5vslOb3cUGc0a9zEboH9a9c_RX38DjRM6yE4-bKgB2gRLMsD0EBy16Fh98zJvNDIEMMMMtaO6mfBAzYVYRenIEbrezDif_GH4evqM9jL2ZAb_PneRvF6bjvi3kGqPnrabrsUdTl3LVHTCey_gAMQA