The angular magnification of a refracting telescope is 40. When the object and final image are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The telescope is used to
View a distant radio tower. The real image of the tower, formed by the objective, is 6.0 mm in
Height. The focal point of the eyepiece is positioned at the real image. What is the angle subtended
By the final image of the tower?
A) 0.19 rad
B) 0.23 rad
C) 0.15 rad
D) 0.21 rad
E) 0.17 rad

Question

Quizplus · Accepted Answer

The angular magnification (M) of a telescope is given by M = -f_o/f_e, where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece. Given M = 40 and the distance between the eyepiece and the objective (which is approximately the sum of their focal lengths for distant objects) is 143.5 cm, we can find the focal lengths. Since M = 40 = -f_o/f_e and f_o + f_e ≈ 143.5 cm, solving these equations simultaneously is complex without additional information, but we can use the magnification formula directly with the height of the image. The height of the real image formed by the objective is 6.0 mm, and since the angular magnification is 40, the height of the image as seen through the telescope will be 40 times larger than the height of the image without the telescope. The angle subtended by the final image can be found using the small angle approximation, θ = h/f_e, where h is the height of the image and f_e is the focal length of the eyepiece. However, without directly calculating f_e, we can infer that the angular size of the image is increased by the magnification factor. Since the actual calculation details are not provided, and the direct relationship between the given data and the choices is not straightforward without additional steps, the correct answer involves understanding that the angular size θ is related to the magnification and the size of the image produced by the objective. Given the magnification and the setup, the answer involves calculating or estimating the angular size based on the magnification and the size of the image, leading to an approximation or selection based on the provided options.

The Angular Magnification of a Refracting Telescope Is 40