How does the minimum deviation change with the prism angle? [duplicate]

I tried approaching it from the equation $$n=\frac{\sin(\frac{A+D}{2})}{\sin(A/2)}$$ I got to this equation $$n= \cos(D/2)+ \cot(A/2)\sin(D/2)$$ and i tried to see how D(minimum deviation) changes with A(prism angle) but i couldn't figure it that way.

I did have a simple thought experiment were if i decrease the prism angle to a point where the prism angle is close to 0° the minimum deviation would be close to 0° too. So i have a feeling that the minimum deviation would increase as the prism angle increases. I'm not sure if I'm correct on that please help me clarify it

• @Frobenius yes the graph in the duplicate 2 question is what i was looking for thank you Jul 29, 2021 at 1:43

Assuming the formula you cite: n sin(A/2) = sin[(A + D)/2] is correct, then use differentials:

n (dA/2) cos(A/2) = [(dA + dD)/2] cos[(A + D)/2] and solve for dD/dA

• I don't think the use of differentials is necessary. Look equation (12) in the Duplicate here Analytic solution for angle of minimum deviation? Jul 28, 2021 at 22:17
• I only know limits in calculus for now so i don't know how to do that. edit- Jul 29, 2021 at 1:47
• Frobenius linked a already answered question that solved my issue :) Jul 29, 2021 at 1:53