What type of eyepiece compensates for the upside down and backwards image of a telescope?

The correct choice is an erecting eyepiece, which is specifically designed to correct the orientation of the image seen through a telescope. Telescopes typically produce images that are flipped both vertically and horizontally due to the way light is refracted through their lenses. An erecting eyepiece counteracts this inversion and provides a right-side-up and correctly oriented image.

This type of eyepiece uses additional optical elements to achieve the desired view, making it particularly useful for terrestrial observations where a correctly oriented image is essential for navigation or identifying objects. For example, if a user was observing a distant landscape, an erecting eyepiece would allow them to easily recognize features without the confusion of viewing an inverted image.

Understanding the specific role of an erecting eyepiece helps clarify the purpose of different types of eyepieces and their applications in various observational settings.