Final answer:
The angular magnification of the telescope is -0.0144. The angle subtended by a 25,000 km diameter sunspot is 8.37 x 10^-5 radians. The angle of the telescopic image is -1.21 x 10^-6 radians.
Step-by-step explanation:
(a) To find the telescope's angular magnification, we can use the formula: M = −fe/fo where fe is the focal length of the eyepiece and fo is the focal length of the objective. Plugging in the values, we get: M = −(0.036 m)/(2.5 m) = -0.0144. Therefore, the angular magnification of the telescope is -0.0144.
(b) The angle subtended by a 25,000 km diameter sunspot can be calculated using the formula: θ = (D/2) / d where D is the diameter of the sunspot and d is the distance between the sun and the observer. Plugging in the values, we get: θ = (25,000,000 m/ 2) / (1.496 x 10^11 m) = 8.37 x 10^-5 radians.
(c) The angle of the telescopic image can be found using the formula: θ' = M x θ where M is the angular magnification and θ is the angle subtended by the sunspot. Plugging in the values, we get: θ' = (-0.0144) x (8.37 x 10^-5 radians) = -1.21 x 10^-6 radians.