1.
[tex]$3 \cdot 10^{-12} = \frac{c}{\lambda} \rightarrow \lambda = \frac{c}{3 \cdot 10^{-12}} = \frac{3 \cdot 10^8}{3 \cdot 10^{-12}} = 10^{20} \text{m} = 1 \text{nm}$[/tex]
2.
[tex]$\lambda = 240 \text{nm} \rightarrow \frac{c}{\lambda} = \frac{3 \cdot 10^8}{240 \cdot 10^{-9}} = 1,25 \cdot 10^{14} \text{Hz}$[/tex]
3.
[tex]$n = \frac{\sin \theta_2}{\sin \theta_1} \rightarrow \sin \theta_1 = \frac{\sin \theta_2}{n} \rightarrow \theta_1 = \arcsin \left( \frac{\sin \theta_2}{n} \right)$[/tex]
4.
[tex]$\tan \theta = \frac{H}{2 \cdot r} \rightarrow \tan \theta = \frac{H}{2 \cdot 4} \rightarrow H = \tan \theta \cdot 8 = \tan 40^{\circ} \cdot 8 = 1,33 \cdot 8 = 10,66 \text{m}$[/tex]