Concept:
Different microscopes are designed with specific optical arrangements to serve distinct purposes in scientific and forensic investigations.
Step 1: Compound Microscope (A).
A compound microscope uses two convex lenses (objective and eyepiece) to magnify objects.
Thus, A $\rightarrow$ IV.
Step 2: Stereo Microscope (B).
A stereomicroscope allows viewing of objects in three dimensions and can observe multiple features simultaneously.
Thus, B $\rightarrow$ II.
Step 3: Comparison Microscope (C).
A comparison microscope enables side-by-side viewing of two specimens (e.g., bullets), effectively comparing them. It also maintains sufficient working distance.
Thus, C $\rightarrow$ III.
Step 4: Polarizing Microscope (D).
This microscope contains a polarizer and analyzer to study birefringent materials.
Thus, D $\rightarrow$ I.
Step 5: Final matching.
\[
A-IV,\quad B-II,\quad C-III,\quad D-I
\]
Final Conclusion:
Hence, the correct answer is option (1).