How does the minimum deviation change with the prism angle?

Question

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 — Ranidu Lakshan, Jul 29 '21 at 01:43

score 0 · Answer 1 · answered Jul 28 '21 at 18:51

0

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

answered Jul 28 '21 at 18:51

R.W. Bird

12,139

I don't think the use of differentials is necessary. Look equation (12) in the Duplicate here Analytic solution for angle of minimum deviation? – Frobenius Jul 28 '21 at 22:17
I only know limits in calculus for now so i don't know how to do that. edit- – Ranidu Lakshan Jul 29 '21 at 01:47
Frobenius linked a already answered question that solved my issue :) – Ranidu Lakshan Jul 29 '21 at 01:53

How does the minimum deviation change with the prism angle?

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