Step 1: Understanding power of a lens.
The power of a lens is defined as the reciprocal of its focal length (in meters).
\[
P = \frac{100}{f \, (\text{in cm})} = \frac{1}{f \, (\text{in m})}
\]
Step 2: Unit of power.
Since focal length is measured in meters, the unit of power is \( m^{-1} \). This unit is given a special name "Dioptre (D)".
Step 3: Conclusion.
Therefore, the SI unit of power of a lens is Dioptre.