The power of a lens is -2.0 D. Here 'D' stands for:

dioptre

The correct answer is option 2. dioptre.

In optics, the power of a lens refers to its ability to converge or diverge light rays. It is a measure of how strongly the lens bends or refracts light. The unit used to express the power of a lens is called the dioptre (symbol: D).

The power of a lens (P) is defined as the reciprocal of its focal length (f) in meters. Mathematically, it is expressed as:

\[ P = \frac{1}{f} \]

where:

\( P \) is the power of the lens in dioptres (D).

\( f \) is the focal length of the lens in meters.

A positive power indicates that the lens is converging (convex lens), meaning it can focus parallel rays of light to a point. A negative power indicates that the lens is diverging (concave lens), meaning it causes parallel rays of light to spread out.

In the given scenario, the power of the lens is stated as -2.0 D, where the negative sign indicates that the lens is diverging (concave lens). This means that the lens has a focal length such that parallel rays of light passing through it appear to diverge from a point 0.5 meters behind the lens.

So, in summary, 'D' in this context stands for dioptre, which is the unit used to measure the power of a lens.