Physics / core
Rays, images, and optical instruments
Build ray optics from optical path length, then analyze imaging systems, apertures, aberrations, and the boundaries of the ray approximation.
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Module 01 core
Rays, images, and optical instruments
Build ray optics from optical path length, then analyze imaging systems, apertures, aberrations, and the boundaries of the ray approximation.
- 01
Fermat’s principle and optical path
Derive ray directions from stationary optical path while distinguishing phase, travel time, and a true minimum.
24 min - 02
Snell refraction and total internal reflection
Track frequency, angle, and critical conditions at a dielectric interface without confusing ray directions with energy fractions.
23 min - 03
Paraxial rays and ABCD matrices
Build first-order ray transport from a declared reduced-angle vector, signed distances, and ordered matrix multiplication.
25 min - 04
Thin and thick lens imaging
Use conjugate distances consistently and distinguish effective focal length from vertex-based focal distances in a thick lens.
25 min - 05
Aperture stops and field of view
Separate the admitted cone from the admitted scene, identify pupils, and calculate simple camera aperture and field limits.
24 min - 06
Optical invariants and étendue
Connect ray phase-space preservation with the trade between beam area, angular spread, and passive radiance limits.
26 min - 07
Spherical and chromatic aberration
Explain how aperture and wavelength produce different focus errors, then balance geometric blur against diffraction.
25 min - 08
Microscopes, telescopes, and angular resolution
Relate angular magnification to objective and eyepiece geometry, then separate image enlargement from resolved detail.
25 min - 09
Graded-index rays and fiber guiding
Derive smooth ray bending in a quadratic index profile and contrast it with the acceptance geometry of a step-index fiber.
26 min - 10
The eikonal equation and the ray limit
Derive phase geometry and amplitude transport from a high-frequency wave ansatz, then identify where the ray approximation fails.
27 min