The formula that you gave, namely
(1) ..... n = { sin[(A + D)/2] }/sin(A/2)
is true only for the angle of incidence θ that gives an angle of refraction α such
that α = A/2 , so that the light ray passes symmetricall through the glass prism.
In that case (when the light ray passes symmetricall through the prism), (1) holds
true and the angle D in (1) is called the angle of minimum deviation. Perhaps it
would be better to denote this angle by Dmin in order not to confuse it with the
general angle of deviation D which is not equal to Dmin. In that case, we can
rewrite (1) as
(2) ..... n = { sin[(A + Dmin)/2] }/sin(A/2)
For a given glass prism with a particular value of the index of refraction n
and a specific value of the prism angle A, there is only one minimum angle
of deviation Dmin. That is why n in (2) is a constant.
But the general angle of deviation D is in general different from the minimum
angle of deviation Dmin. That occurs when the angle of incidence θ makes
the light ray pass through the prism unsymmetrically so that the angle of
refraction α is no longer equal to A/2. And that is also the angle referred to
(not Dmin) in yourphysics book, the angle of deviation D that first decreases
until it reaches a minimum value (that is now Dmin) and then starts increasing
afterwards, when the angle of incidence is increased first from a small value.
Now, if you want to understand why the angle of deviation D (not Dmin) first
decreases and then increases only later, that has something to do with the
double refraction encountered by light in passing through the glass prism.
The first refraction (from air to glass) is from a lighter to a denser medium,
n1 < n2 , so that θ1 > θ2 in the law of refraction, and light is bent TOWARDS the
normal, AWAY from the initial direction of incident light. But as`θ1 increases,
θ2 also increases, and that brings the refracted light TOWARDS the initial direction
of the incident light.
The second refraction (from glass back to air) is from a denser to a lighter medium,
n1 > n2 , so that θ1 < θ2 in the law of refraction, and light is bent AWAY from the
normal, also AWAY from the initial direction of incident light. As`θ1 increases,
θ2 also increases, and that brings the refracted light FARTHER AWAY from the initial
direction of the incident light.
Starting from a small value of angle of incidence, the CHANGE TOWARDS the initial
direction of the incident light in the first refraction is GREATER than the change
FARTHER AWAY from the initial direction of the incident light in the second refraction,
so that theangle of deviation D decreases at first. But after reaching D = Dmin, the
CHANGE TOWARDS the initial direction of the incident light in the first refraction
BECOMES SMALLER than the change FARTHER AWAY from the initial direction of
the incident light in the second refraction, so that the angle of deviation D finally
increases.