A larger objective gives better resolution — option 3.

The physics. Even a perfect lens cannot form a point image of a point source, because light diffracts at the aperture. A star is imaged as a small disc surrounded by faint rings — the Airy pattern. Two stars can be told apart only if their discs are far enough apart, and by the Rayleigh criterion the smallest angle that can be resolved is

\(\theta=\dfrac{1.22\lambda}{D}\)

where λ is the wavelength and D the diameter of the objective. The resolving power is the reciprocal of that angle :

\(\text{R.P.}=\dfrac{D}{1.22\lambda}\)

which is directly proportional to D. Doubling the diameter halves the smallest resolvable angle and doubles the resolving power.

Why option 2 is the trap. Focal length governs magnification, not resolution. Magnifying an image beyond the resolution limit gives a bigger but no clearer picture — “empty magnification”. Resolution is set by the aperture alone, which is why astronomical telescopes are described by their diameter, not their length: the Giant Metrewave Radio Telescope, the 8-metre class optical telescopes, the 6·5-metre James Webb.

The same principle elsewhere. A microscope’s resolution improves with the numerical aperture and worsens with wavelength, which is why oil-immersion objectives are used and why the electron microscope — using electron waves of far shorter wavelength — resolves detail a light microscope never can.

A practical bonus : a bigger objective also collects more light, as the square of the diameter, so a large telescope is both sharper and able to see fainter objects.

Hence, the resolution increases.