Final answer:
The magnification power of an astronomical telescope with focal lengths of 100cm for the objective lens and 10cm for the eyepiece lens is 10 when the final image is formed at the least distance of distinct vision.
Step-by-step explanation:
The magnification power of a telescope is given by the ratio of the focal length of the objective lens to the focal length of the eyepiece lens. In this case, the telescope has an objective lens with a focal length of 100cm and an eyepiece lens with a focal length of 10cm.
When the final image is formed at the least distance of distinct vision (generally taken as 25cm), the magnification power (M) can be calculated.
To find the magnification power of the telescope, we use the formula:
M = (focal length of objective) / (focal length of eyepiece)
So, substituting the given focal lengths into the formula we get:
M = 100cm / 10cm
This simplifies to:
M = 10
Therefore, the angular magnification power of the telescope, with the final image at the least distance of distinct vision, is 10.
The correct answer is (c) 10 cm.