Which one of the following relation is CORRECT for refraction through…

The correct answer is Option (4) → \( A + D_m = 2i \)

At minimum deviation the ray passes through the prism symmetrically: the angle of incidence equals the angle of emergence (i = e), and the two refraction angles inside the prism are equal (\( r_1 = r_2 = r \)). For any ray through a prism,

    \( r_1 + r_2 = A \)
    \( i + e = A + D \)

Putting the symmetric values:

    \( 2r = A \Rightarrow r = A/2 \)
    \( 2i = A + D_m \)

So \( A + D_m = 2i \), which leads to the prism formula \( \mu = \sin\frac{A + D_m}{2} \big/ \sin\frac{A}{2} \).

NCERT (2026-27):
Refraction Through a Prism – “… At the minimum deviation \( D_m \), the refracted ray inside the prism becomes parallel to its base. We have

    \( \displaystyle \delta = D_m, \; i = e \)

which implies \( r_1 = r_2 \). Equation (9.34) gives

    \( \displaystyle 2r = A \ \text{or} \ r = \frac{A}{2} \qquad (9.36) \)

In the same way, Eq. (9.35) gives

    \( \displaystyle D_m = 2i - A, \ \text{or} \ i = (A + D_m)/2 \qquad (9.37) \)”