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The sinking ship effect, often cited as evidence for Earth's curvature, refers to the observation that as a ship sails away from an observer on the shore, it gradually disappears from view, with the hull being the first part to vanish. This phenomenon is explained by the curvature of the Earth, as the ship moves farther away, eventually reaching a point where it becomes obstructed by the curved surface.

Regarding the use of high-powered telescopes, they can indeed bring distant objects back into view even when they are below the line of sight due to Earth's curvature. This effect is known as "bringing objects back over the horizon."

The reason high-powered telescopes can overcome the curvature of the Earth and bring distant objects back into view is due to the nature of optics and the refraction of light. The Earth's atmosphere is not completely uniform, and it has varying temperature and density profiles. These variations can cause the path of light to bend, a phenomenon known as atmospheric refraction.

Atmospheric refraction can have the effect of bending light rays downwards, which counteracts the Earth's curvature to some extent. This means that when using a high-powered telescope, the observer can potentially see objects that are technically below the line of sight due to this bending of light.

However, it's important to note that the extent to which atmospheric refraction can bring objects back into view depends on various factors, including the atmospheric conditions, the altitude of the observer, and the distance to the object. It is not a consistent or reliable phenomenon in all situations.

Furthermore, the sinking ship effect observed with the naked eye is still a valid demonstration of Earth's curvature, as it is a noticeable and consistent phenomenon that occurs over long distances. The use of telescopes and atmospheric refraction does not negate the overall evidence for the Earth's curved shape.

In summary, while high-powered telescopes and atmospheric refraction can sometimes bring distant objects back into view, they do not invalidate the evidence for Earth's curvature provided by the sinking ship effect and other observations.

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