Final answer:
The power of a lens is inversely proportional to its focal length. Given a power ratio of 1:4 between two lenses, the ratio of their focal lengths is 4:1, matching option D.
Step-by-step explanation:
The power of a lens (P) is the inverse of its focal length. We have a ratio of powers P1 to P2 as 1:4, meaning if P1 is 1 diopter, then P2 is 4 diopters.
Using the formula P = 1/f, the power is inversely proportional to the focal length, so if one lens is four times as powerful as the other, its focal length must be one-fourth that of the less powerful lens.
Therefore, the ratio of focal lengths of L1 to L2 would be 4:1, which corresponds to option D. 4:1.