Concept:
Different optical mineral properties are observed under different light conditions in a polarizing microscope.
Step 1: Match Cleavage.
Cleavage is commonly observed in plane polarized light.
\[
A\rightarrow I
\]
Step 2: Match Twinkling.
Twinkling is observed in ordinary light conditions in optical mineralogy.
\[
B\rightarrow II
\]
Step 3: Match Twinning.
Twinning is clearly observed under crossed nicols because different twin lamellae show different extinction positions.
\[
C\rightarrow III
\]
Step 4: Match Dispersion.
Dispersion is studied with convergent light in interference figures.
\[
D\rightarrow IV
\]
Therefore, the correct matching is:
\[
A-I,\ B-II,\ C-III,\ D-IV
\]
\[
\therefore \text{Correct Answer is (A)}
\]