Final answer:
The statement is false as a larger angle associated with a higher numerical aperture (NA) actually results in a smaller, more intense focal spot due to the wave nature of light and diffraction effects.
Step-by-step explanation:
The statement 'a larger angle results in a larger effective focal spot and a smaller angle results in a smaller effective focal spot' is false. When referring to optical systems such as microscopes and telescopes, the term 'angle' often relates to the numerical aperture (NA), which acts as a measure of the lens's ability to gather light and resolve fine specimen detail at a fixed object distance.
A high NA indicates a larger ability to gather light and hence a smaller focal spot because of the increased angle at which light is collected. This is in contrast to geometric optics, where we consider the focal point to be infinitely small, an unphysical oversimplification.
Wave optics, which takes into account the diffraction of light, shows us that a focal point is not a single point but rather spreads out to form a focal spot. The size of this focal spot decreases, and the intensity increases, as the NA of the objective lens increases. This is due to the wave nature of light where diffraction plays a significant role in determining the size of the focal spot.