The power of a lens is calculated using the formula P = 1/f, where f is the focal length in meters. Given that the object distance (u) is 50 cm and the linear magnification (m) is 2, the image distance (v) can be determined using the magnification formula m = v/u, leading to v = 100 cm. The lens formula 1/f = 1/v - 1/u allows for the calculation of the focal length, which results in a power of 10 dioptres.