A parallel beam of light is incident on a glass cylinder of elliptical cross-section with refractive index $n$ that makes an angle $\delta$ with the major axis of the ellipse.

1 Calculate and plot the caustics of the refracted rays inside the glass block.

2 Find the part of the incident light beam that is involved in the formation of the caustics inside the glass. Give the boundaries of this part of the beam.

Draw figures and investigate the phenomenon for different values of the refractive index $n$, the eccentricity of the ellipse $\varepsilon$ and the angle $\delta$.

Hint: use the parametric equation of the ellipse $x = a \cos t$, $y = b \sin t$, calculate the points of the caustics and find the boundaries of the incident beam in question 2 in terms of the parameter $t$.