A prism of glass (n = 1.50) has angles 45°, 45° and 90°…

Step 1. In air. $\sin C = \dfrac{1}{1.50} = 0.667$, so $C = 41.8°$. Since $45° > 41.8°$, the ray is totally reflected and the prism turns it through $90°$.

Step 2. In water. $\sin C = \dfrac{1.33}{1.50} = 0.887$, so $C = 62.5°$.

Step 3. The ray in water. Now $45° < 62.5°$, so total internal reflection fails and the ray refracts out. $1.50 \times \sin 45° = 1.33 \times \sin\theta_2$, so $\sin\theta_2 = \dfrac{1.50 \times 0.707}{1.33} = 0.798$ and $\theta_2 = 52.9°$.

Step 4. The smallest index in air. The ray is just totally reflected when $C = 45°$. Then $n = \dfrac{1}{\sin 45°} = \sqrt{2} = 1.41$.