Final answer:
For relaxed vision in a telescope with powers of 1.25 D for the objective and 20 D for the eyepiece, the length of the telescope would be slightly less than 85 cm, and the magnification decreased compared to a system with lower power in the objective and higher power in the eyepiece.
Step-by-step explanation:
In a telescope, the powers of an objective and eye lens are 1.25 D and 20 D, respectively, which translates to focal lengths of 80 cm (1 m/1.25 D) for the objective and 5 cm (1 m/20 D) for the eyepiece. For relaxed vision, where the image is at infinity, the length of the telescope is slightly less than the sum of the focal lengths of the objective and the eyepiece. This would result in the distance between the objective and the eyepiece being slightly less than 80 cm + 5 cm = 85 cm. The magnification of a telescope is the product of the magnifications due to the objective and the eyepiece. Since the focal length of the objective is larger for lower power and that of the eyepiece is smaller for higher power, to achieve a high magnification, it is ideal to have a long focal length for the objective and a short focal length for the eyepiece.
Thus, with the given powers, the length and magnification of the telescope for relaxed vision would see the length decreased from the theoretical maximum, and the magnification would also be decreased compared to a system with a lower power objective and a higher power eyepiece, which would result in a higher magnification overall.