Final answer:
Changing a telescope's eyepiece indeed changes the magnification, as magnification is determined by the focal lengths of the telescope's eyepiece and objective lens.
Step-by-step explanation:
It is true that changing a telescope's eyepiece changes the telescope's magnification. The eyepiece of a telescope magnifies the first image created by the objective lens. The angular magnification, or the ratio of the angle subtended by the telescope image to the angle subtended by the unaided eye, is dependent on the focal lengths of the objective lens and the eyepiece. Thus, to achieve a higher angular magnification, one typically uses an objective with a long focal length and an eyepiece with a short focal length. As a practical matter, eyepieces come in various focal lengths and can be interchanged to provide different magnifications, offering flexibility in viewing astronomical objects. However, excessive magnification can cause the image to shimmer or shake due to atmospheric turbulence, so there is a limit to useful magnification.