An astronomical refracting telescope will have large angular magnification and high resolution, when it has an objective lens of:
A. Large focal length and large diameter
B. Small focal length and large diameter
C. Small focal length and small diameter
D. Large focal length and small diameter

Hint: The formula for angular magnification is: $ - \dfrac{{{f_ \circ }}}{{{f_e}}}$. In case of focal length, consider both large and smaller one and in case of diameter consider both large and smaller one and derive it.

Complete step by step solution:
The difference between a refracting telescope and a reflecting telescope is the use of mirrors and lenses.
A reflecting telescope uses a mirror and a refracting telescope uses lenses.
Astronomers use refracting telescopes instead of reflecting because refracting telescopes makes distant objects appear larger, distinct and magnified.
Also astronomical refracting telescopes have large angular magnification. Refracting telescopes uses two main lenses. The lens with larger size is called the objective lens and the lens with small size is considered the length of the eyepiece.

The formula for angular magnification is: $ - \dfrac{{{f_ \circ }}}{{{f_e}}}$, where ${f_ \circ } = $ focal length of objective, ${f_e} = $ focal length of earpiece.
The negative sign indicates that the image is inverted.
A refracting telescope’s magnification is equal to the intended focal length measured by the eyepiece focal length.

The longer the focal length of the telescope, the greater is the image.
A telescope’s diameter is directly equivalent to the telescopic resolution.
The larger the diameter, the better the telescopic resolution and vice versa.
So, it can be concluded that an astronomical refracting telescope will have large angular magnification and high clarity, when it has an objective lens of large focal length and large diameter.

Hence, option A is correct.

Note: We should remember that angular magnification is different from linear magnification. And there may be confusion between reflecting and refracting telescopes. The conditions are different for both the type of telescopes.