Law of reflection: ${\theta }_{\text{r}}={\theta }_{\text{i}}$

Reflection can be specular (mirror-like) or diffuse (from rough surfaces).

Plane mirrors: A virtual image is formed at $\text{P}\prime$ with $s\prime =s$.

Snell’s law of refraction:

Index of refraction is $n=c/v$.

The ray is closer to the normal on the side with the higher index of refraction.

If $n_2<n_1$, total internal reflection (TIR) occurs when the angle of incidence ${\theta }_1\ge {\theta }_{\text{c}}={\text{sin}}^{-1}(n_2/n_1)$.

Light travels along straight lines, called light rays, at speed $v=c/n$.

A light ray continues forever unless an interaction with matter causes it to reflect, refract, scatter, or be absorbed.

Light rays come from objects. Each point on the object sends rays in all directions.

The eye sees an object (or an image) when diverging rays are collected by the pupil and focused on the retina.

Ray optics is valid when lenses, mirrors, and apertures are larger than $\approx 1\text{mm}$.

If rays diverge from P and interact with a lens or mirror so that the refracted/reflected rays converge at $\text{P}\prime$, then $\text{P}\prime$ is a real image of P.

If rays diverge from P and interact with a lens or mirror so that the refracted/reflected rays diverge from $\text{P}\prime$ and appear to come from $\text{P}\prime$, then $\text{P}\prime$ is a virtual image of P.

Spherical surface: Object and image distances are related by

Plane surface: $R\to \text{∞}$, so $s\prime =-\left(n_2\text{/}{n}_1\right)s$.

3 special rays in 3 basic situations:

Magnification: $m=-{\displaystyle \frac{s\prime }{s}}$

$m$ is $+$ for an upright image, $-$ for inverted.

The height ratio is $h\prime /h=\left|m\right|$.

The image and object distances are related by

where the focal length is given by the lens maker’s equation:

The image and object distances are related by

Focal length $f=R/2$