The optician prescribes a power of -0.5 dioptre, which means that the lens should have a focal length of -2 m.
Option 1: A convex lens of focal length 2 m. Convex lenses have positive focal lengths, so this option is incorrect.
Option 2: A convex lens of focal length 50 cm. The focal length should be -2 m, so this option is incorrect.
Option 3: A concave lens of focal length 2 m. Concave lenses have negative focal lengths, so this option is correct.
Option 4: A concave lens of focal length 50 cm. The focal length should be -2 m, so this option is incorrect.
The correct answer is option 3 because a concave lens with a focal length of -2 m is required to produce a power of -0.5 dioptre.