Part of JOP-01 — Ray Optics: Mirrors, Lenses & Instruments

Telescopes and Resolving Power

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An astronomical telescope uses a large-aperture, long-focal-length objective and a small-focal-length eyepiece. In normal adjustment (image at infinity): M = fofe\frac{f_o}{f_e}, tube length = fof_o + fef_e. For image at near point: M = fofe\frac{f_o}{f_e}(1 + fef_e/D). The Galilean telescope uses a concave eyepiece, producing erect images with a shorter tube (fof_o - |fef_e|). The resolving power of a telescope = D1.22λ\frac{D}{1.22λ} depends only on the objective aperture D — larger apertures resolve finer angular details. Light-gathering power scales as D2D^{2}, making large telescopes essential for observing faint objects. A terrestrial telescope adds an erecting lens (increasing tube length by 4f) to produce erect images. Reflecting telescopes (using mirrors instead of lenses) eliminate chromatic aberration entirely. JEE commonly tests the relationship between magnification, focal lengths, and tube length, often as a system of two equations with two unknowns.

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