Final answer:
The statement is true; a smaller target angle leads to a smaller effective focal spot, improving resolution in optical systems. This principle is reflected in the design of microscopes and telescopes, as well as the characteristics of spherical mirrors.
Step-by-step explanation:
The statement is true: the smaller the target angle, the smaller the effective focal spot and the better the resolution. In optics, particularly when dealing with wave optics, the focal point due to diffraction effects is not a single point but spreads out to form a focal spot. The size of this spot decreases with an increasing numerical aperture (NA), which in turn increases the intensity within that spot. A larger NA equates to a larger cone of light entering the lens, collecting more of the diffraction patterns, which results in higher resolution of the microscope and better image clarity.
Regarding a telescope, the objective lens and the eyepiece focal planes are closely aligned, and for greater angular magnification, it is advantageous to have a longer focal length for the objective and a shorter one for the eyepiece. As the angular magnification increases, objects appear larger and more details become visible provided the lens quality is adequate and atmospheric disturbance is minimal.
In the context of a spherical mirror, the smaller the radius of curvature, the smaller the focal length, and thus the more powerful the mirror becomes. This is relevant because a more powerful mirror focuses light more tightly, improving resolution.