Both the statements provided in the question deal with the concept of refraction, which is the bending of light as it passes from one medium to another.

Statement I: When a person looks at a coin in a bucket of water, it appears lifted due to refraction. The light rays from the coin are bent or refracted as they move from the water (a denser medium) into the air (a less dense medium) which makes the coin appear closer than it actually is.

Statement II: Conversely, if a person is underwater and looking at a coin above the water surface, the light rays from the coin travelling from air (less dense medium) to water (denser medium) undergo refraction, and the coin appears to be at a higher level than it actually is.

So, both statement I and statement II are correct, making option 1 (I and II) the right answer.