Geometric Optics: Reflection and Refraction

Bending Light at Boundaries

A straw in a glass of water looks broken because your brain traces bent light rays backwards to a false location. All of geometric optics follows rays reflecting and refracting at surfaces to find where images appear.

When light strikes a boundary, it follows two core rules:

Law of reflection: $\theta_i = \theta_r$, where angles are measured from the surface normal.

Snell's law of refraction: $n_1\sin\theta_1 = n_2\sin\theta_2$, where refractive index $n = c/v$ measures how much a medium slows light down.

Total internal reflection occurs when light travels from a denser medium ($n_1 > n_2$) at an angle exceeding the critical angle $\theta_c = \arcsin(n_2 / n_1)$.

Common pitfall: Total internal reflection happens only when light leaves a slower, denser medium for a faster one. Going from air into glass, light always refracts regardless of the angle.

Lenses, Mirrors, and Images

Lenses and spherical mirrors locate images using standard equations and sign conventions. The thin lens equation and the mirror equation share the same mathematical form:

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

where $f = R/2$ for spherical mirrors. Magnification is given by $m = -d_i / d_o$.

Tip: Always draw a ray diagram with at least two principal rays to catch sign errors and build physical intuition.