open science ftw
(when winning means we save Earth and learn awesome things!)
Optics is the study of light.
There is a value that measures the ratio, n, between the speed of light in a vacuum, c, to the speed of light in a medium, v, particular for various mediums.
Arguably one of the most important laws in optics, especially geometric optics, is Snell's Law, or the Law of Refraction. It defines how light hitting a surface changes angle behind the surface. More specifically, the product of the indicent light's angle to the surface normal, θ, and the index of refraction of the first medium, n, is equal to the product of the outward light's angle to the surface normal, θ', and the index of refraction of the medium incident upon, n'.
There's many reasons to like Snell's Law. For one, it produces extremely cool effects in our everyday life like the famous "Snell's Window" in pools of water.
I like Snell's Law because I imagine that a snail invented it 🐌
Total Internal Reflection:
Lenses are optical elements made of surfaces of glass which bend light across a front surface into its own material, often glass, and then through a second surface. The surfaces are often made with precise curvature to
In all optical elements, there are a set of characteristic points that we can measure to define a model of a system. These will be discussed in further detail later on.
Moving beyond the thin lens approximations, we can start analyzing systems taking into account the ray bending and transfer happening within the sag of lenses or other optical elements. This is extremely useful for building models of complex systems into
Any imaging system can be broken down into a few charactistic points known as cardinal points, which provide us reference points for things we want to image from object space into image space, using our imaging equations. There are six to be aware of:
And their conjugate rear versions, for image space:
The principal planes of an optical system represent the
When we imagine everything in front of a lens as the "object space" of that system and every ray of light that propogates through the lens, cumulatively known as the ray bundle, as the "image space" of that system, we are able to consider the mathematics for imaging object space onto image space.
When an object is a distance away from the front principal plane of a system (measured negative if in opposite direction of light; a vector measurement), it is imaged through a system with focal length f, to a distance away from the rear principal plane of the system
The optical "power" of an element is defined as the inverse of its focal length, often measured in mm^-1 known as diopters to opticians. It is represented by the symbol Φ
It is useful in many applications to trace a "ray" through an optical system to understand where key objects are being imaged or even occluded by objects in a system.
For convenience when doing raytrace calculations, we will denote the "optical angle" of a ray, the product of the index, n, and angle relative to the optical axis, u, as the optical angle, ω.
Transfer:
Refraction:
Reduced thickness.
Reduction of power between refractive surface 1, with power , and refractive surface 2, with power , and a reduced thickness between the surfaces to find the system power Φ
By def
Any optical system collects a limited amount of light, often restricted by a
There are two characteristic pupils
The f/# of a system is a characteristic yadayada
I'm still learning 😀