About absolute error calculation

Question

Given a prism immersed in the air with an opening angle equal to $\alpha = \bar{\alpha} \pm \Delta\alpha = 60° \pm 1°$ and $\delta = \bar{\delta} \pm \Delta\delta = 45° \pm 2°$ is the angle of minimum deviation. From the theory it is known that $n(\alpha,\,\delta) = \frac{\sin\left(\frac{\alpha+\delta}{2}\right)}{\sin\left(\frac{\alpha}{2}\right)}$, then $\bar{n} = n(\bar{\alpha},\,\bar{\delta}) \approx 1.58671$ (first question: what are the significant digits of $\bar{n}$?), but as far as the absolute error $\Delta n$ I am in trouble. In fact, I don't understand if: $$\Delta n = \sqrt{\left(\frac{\partial n(\bar{\alpha},\,\bar{\delta})}{\partial\alpha}\,\Delta\alpha\right)^2 + \left(\frac{\partial n(\bar{\alpha},\,\bar{\delta})}{\partial\delta}\,\Delta\delta\right)^2} \approx 1.43811 $$ or $$\Delta n = \left|\frac{\partial n(\bar{\alpha},\,\bar{\delta})}{\partial\alpha}\right| \Delta\alpha + \left|\frac{\partial n(\bar{\alpha},\,\bar{\delta})}{\partial\delta}\right| \Delta\delta \approx 1.98289$$ or whether to refer to the propagation of the maximum or statistical error. If it is correct that the second option would make sense that $\bar{n} < \Delta n$? Thanks a lot to everyone!!

Answer 1

You have to calculate the error in rad. Other then that, I would always use gaussian error propagation, unless there is a special reason.