Question

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

• A. small focal length and small diameter
• B. small focal length and large diameter
• C. large focal length and large diameter
• D. large focal length and small diameter

Answer 1

The Correct Option is C

The question pertains to the design of an astronomical refracting telescope, focusing on how to achieve large angular magnification and high angular resolution. To understand which option is correct, let’s break down the concepts involved:

1. Angular Magnification: The angular magnification \( M \) of a telescope is given by the formula: M = \frac{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. To maximize magnification, a large focal length for the objective lens (f_o) is preferred.
2. Angular Resolution: Angular resolution determines how well a telescope can distinguish two close objects. It is largely dependent on the diameter of the objective lens according to the formula: \theta = \frac{1.22 \lambda}{D} where \(\theta\) is the angular resolution, \(\lambda\) is the wavelength of light, and \(D\) is the diameter of the objective lens. A larger diameter (\(D\)) reduces \(\theta\), thus improving resolution.
3. From the above points, for large angular magnification, a large focal length of the objective lens is needed. For high angular resolution, a large diameter of the objective lens is important.

Therefore, the correct answer is having an objective lens with large focal length and large diameter.

Thus, the given option “large focal length and large diameter” is the appropriate choice as it fulfills both requirements for enhancing the telescope's performance in terms of angular magnification and resolution.