3.4b Specular and Bessel labs

Source: Lab ideas from Computational Physics (Landau, Páez, Bordeianu), §§3.3.2–3.4.2. Rewritten as original drills. Continues 3.4 Specular reflection and Bessel theory. Next: 4.1 Monte Carlo — random numbers.

Two tracks in one activity set: specular rays ($\theta\leftarrow\theta+2\phi$) and spherical Bessel $j_\ell(x)$ (upward vs Miller downward). Stubs fail until you write the logic. Explorers live at the bottom for reference while you work.

Labs

Activity: Specular path

Unit circle, start at $\theta=0$. Each bounce: $\theta\leftarrow\theta+2\phi$. Print the hit points $(\cos\theta,\sin\theta)$ including the start.

Input: phi_rad bounces (floats / int). Output: bounces+1 lines, each x y with 6 decimals.

0/4 solved

3.4b.S1

Using “rational” and “close”, explain:

When does a specular ray with step $2\phi$ on a circle close into a finite figure?

Minimum 3 words. Your answer must include: “rational”, “close”.

0 words/ 3 min

Meet the writing requirements, then you can open the model answer.

Next: 4.1 Monte Carlo.