Let us consider the air with the index 1 and the lucite with index 2. Using the Snell's Secound Law, we have:
\(\frac{sen\O_{2}}{sen\O_{1}} = \frac{n_{2}}{n_{1}} \\ sen\O_{2}= \frac{n_{2}*sen\O_{1}}{n_{1}}\)
Entering the unknowns, remembering that the air refrective index is 1 and the lucite refrective index is 1.5, comes:
\(sen\O_{2}= \frac{n_{2}*sen\O_{1}}{n_{1}} \\ sen\O_{2}= \frac{1.5* \frac{1}{2} }{1} \\ sen\O_{2}=0.75\)
Using the arcsin properties, we get:
\(sen\O_{2}=0.75 \\ arcsin(0.75)=\O_{2} \\ \boxed {\O_{2}=48.59^o}\)
Obs: Approximate results, and the drawing is attached
If you notice any mistake in my english, let me know, because i am not native.
