The aperture of a telescope objective is increased to produce (a) larger image (b) smaller spher

step 1 In this question we have a telescope and we know that resolving power of telescope r p is equal

The aperture of a telescope objective is increased to...

Key Concepts

Optical Aberrations

Optical aberrations are imperfections that cause light from different parts of an optical system to focus at different points. Spherical aberration arises because rays passing through the edge of a lens or mirror may focus at a different point than those passing near the center, while chromatic aberration occurs because lenses disperse light into its component colors due to differing refractive indices. Understanding these aberrations is essential for designing optical instruments, although increasing the aperture alone does not directly reduce these aberrations without additional corrective optical elements.

Aperture

In optics, the aperture of an instrument refers to the diameter of the primary light-collecting element, such as a lens or mirror. A larger aperture allows more light to be gathered, which is critical for observing faint objects and for achieving better image clarity. It also influences the system’s resolving power by reducing the diffraction limit, thus playing a central role in telescope performance.

Resolving Power

Resolving power is the ability of an optical instrument to distinguish between two closely spaced objects. It is fundamentally limited by the diffraction of light, where a larger aperture results in a smaller diffraction limit and therefore improved resolution. This concept is key in applications where fine details must be observed, as in astronomical imaging.

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