What is Normal and angle of incidence?

Example 3.3 (Reading angles correctly)

A laser beam strikes a mirror “at $35^\circ$” — measured from the mirror’s surface, as beams are often described. The angle of incidence is $90^\circ - 35^\circ = 55^\circ$, so the reflected ray also leaves at $55^\circ$ from the normal, and the beam turns by $180^\circ - 2 \times 55^\circ = 70^\circ$. Forgetting the normal convention is the most common error of this chapter; it costs $90^\circ$ every time.

Example 3.9 (Air to water)

A ray hits a calm pond at $i_1 = 30^\circ$. With $n_1 = 1.00$ and $n_2 = 1.33$:

The ray bends toward the normal, as it always does when entering a slower medium ($n_2 > n_1$). Leaving the water, the same computation runs backwards and the ray bends away from the normal.

Example 3.18 (Three critical angles)

Toward air: for water, $\sin i_c = 1/1.33 = 0.752$, so $i_c = 48.8^\circ$; for glass, $\sin i_c = 1/1.50$, so $i_c = 41.8^\circ$; for diamond, $\sin i_c = 1/2.42 = 0.413$, so $i_c = 24.4^\circ$. The higher the index, the narrower the escape cone: in diamond, any ray more than $24.4^\circ$ off a facet’s normal is trapped — the secret of its sparkle, dissected in Problem 3.1.