Geometric Optics: Reflection and Refraction

A straw in a glass of water looks broken because your brain insists light travels in straight lines — it traces the bent rays backwards and hallucinates the straw where they seem to come from. All of geometric optics is this one game: follow rays that bend at surfaces, then ask where the brain would put the image.

When light encounters a boundary between media, it can be reflected and refracted.

Law of reflection:

$$\theta_i = \theta_r$$

Snell's law of refraction:

$$n_1\sin\theta_1 = n_2\sin\theta_2$$

where $n = c/v$ is the refractive index of the medium.

Total internal reflection occurs when light travels from a denser medium ($n_1 > n_2$) and:

$$\theta_1 > \theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$$

Thin lens equation:

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

Magnification:

$$m = -\frac{d_i}{d_o}$$

Mirror equation has the same form, with $f = R/2$ for a spherical mirror of radius $R$.

Tip: Always draw a ray diagram with at least two principal rays. The diagram catches sign errors and gives physical intuition about image location.

Common pitfall: Total internal reflection happens only when light tries to leave a slower (denser) medium for a faster one, beyond the critical angle. Going the other way — air into glass — light always enters, no matter the angle.