Deep Physics: Geometric Optics for Talented High Schoolers
Real geometric optics, taught from rays, mirrors, and lenses through aberrations, photometry, and modern applications from fiber optics to lasers. For talented high schoolers.
Online for homeschool families anywhere · or in-person in Princeton, NJ
A World Through the Lens of Geometric Optics
Light is the everyday signal we read the world by. When wavelengths are small compared with the apparatus, light travels in rays, and the geometry of those rays builds every image we ever see: in a mirror, through a lens, on a screen, across a fiber.
A pencil in a glass of water looks broken at the surface. The pencil is straight. The light is what bends.
A magnifying glass held in sunlight focuses to a point hot enough to burn paper. Move the same glass back from a window, and an upside-down image of the window appears on a wall.
A single strand of fiber thinner than a human hair carries a phone call under the Atlantic Ocean. Light bouncing off the inner walls of the fiber never escapes, no matter how the cable bends.
The sky turns red at sunset. Sunlight grazes through hundreds of kilometres of atmosphere, the shorter blue wavelengths scatter away, and only the red survives the journey.
Light as a ray is enough for almost every optical instrument ever built: mirrors, lenses, telescopes, microscopes, cameras, fiber-optic networks. The geometry of how rays bend at boundaries and converge at focal points predicts every image, every focal length, every angle of view.
You will:
- Trace any ray through a system of lenses and mirrors and predict the image it forms.
- Use Snell’s law to predict refraction at any boundary, and find the critical angle for total internal reflection.
- Identify the type of aberration in a real optical system and choose a correction (achromatic doublet, aspheric surface, multi-element design).
- Predict the illuminance on a surface from the luminous intensity of a source and the geometry between them.
What You Will Actually Understand
1. Reflection and Mirrors
How light bounces, and how mirrors form images. The law of reflection. Image formation by plane mirrors. Spherical mirrors, concave and convex. Focal length, the mirror equation, magnification. Ray tracing as the universal tool.
2. Refraction and Snell’s Law
How light bends at a boundary, and what the bending lets us build. Index of refraction. Snell’s law. Total internal reflection and the critical angle. Optical fibers, prism dispersion, and the geometry behind a rainbow.
3. Lenses and Image Formation
From a single lens to the equation that governs them all. Thin lenses, converging and diverging. The thin-lens equation. Image construction by ray tracing. Sign conventions. Real and virtual images. Combined lens systems.
4. Optical Instruments
What lenses combine to do. The human eye and accommodation, the near point, the far point, and common refractive defects. The simple magnifier. The compound microscope: magnification and numerical aperture. The astronomical telescope: refractor versus reflector, and the design choice behind each. The camera: aperture, depth of field, exposure.
5. Aberrations and Lens Design
Where the ideal lens equation stops being enough. Chromatic aberration, spherical aberration, coma, astigmatism, and distortion. Achromatic doublets and the philosophy of modern lens design. Diffraction-limited resolution as the point where the ray picture finally runs out.
6. Photometry, Color, and Where Geometric Optics Ends
How much light, what colour, and the modern instruments that sit at the boundary between geometric optics and what lies past it. Photometric quantities: luminous flux, intensity, illuminance, luminance, and the candela. Color science: trichromacy, RGB, the CIE chromaticity diagram. Fiber optics in depth, with numerical aperture and propagation modes. Then a short survey of three modern instruments whose full theory lives past geometric optics: the laser, and holography as a reconstruction of wavefronts. Adaptive optics, which corrects atmospheric distortion and stays squarely inside geometric optics.
The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and certificates apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Geometric Optics is one of six classical core courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ. Students earning the Mastery in Classical and Modern Physics complete the six classical core courses plus any two of the four modern electives.
Classical core: Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Geometric optics.
Modern electives: Special Relativity. Quantum mechanics. Nuclear and particle physics. Astronomy and cosmology.
The Lyceum is built on the Deep Physics methodology.