In the case of minimum deviation, the refracting angles at two surfaces are equal. Then the ray inside the prism should be parallel to the base only if it is isosceles triangular prism. But everywhere I read they haven't mentioned this condition. Is this correct ?
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1$\begingroup$ You are correct - the theorem assumes an isosceles prism, with the base at having the same angles with both of the sloping sides. It is usually apparent in the diagram. $\endgroup$– Peter DiehrCommented Mar 3, 2016 at 18:42
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If the angle of the ray to each of the two surfaces of the prism is the same, it follows from symmetry that you should be able to flip the scenario left-right about an axis that bisects the angle connecting the surfaces, and have the same exact picture.
But this implies that the ray inside the prism must be perpendicular to that axis, which would put it horizontal to the base of the prism if, and only if, it is isosceles.
You are right, if you want to claim that the ray is parallel to a surface it is not interacting with, then you need to specify the relationship of that surface to the other surfaces..
