Final answer:
The power of the lens is 0.1 diopters.
Step-by-step explanation:
The power of a lens can be calculated using the formula:
Power (P) = 1 / focal length (f)
Given that the magnification (m) of the object is 2, we can use the formula:
m = image distance / object distance
Since the object is placed 20 cm away from the lens, the image distance is also 20 cm. Using the magnification formula, we can find the object distance: 2 = 20 / object distance. Solving for the object distance, we get object distance = 10 cm. Now, we can find the power of the lens using the formula for magnification: Power = 1 / focal length = 1 / object distance = 1 / 10 cm = 0.1 diopters.