Resolving Power Of Optical Instruments

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An astronomer wants a telescope to distinguish two closely spaced stars more clearly, and a student proposes ways to improve its resolving power.

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NCERT relates the resolving power of a telescope to its ability to separate two nearby point sources, governed by the diffraction limit $	heta_{min}=\frac{1.22\lambda}{D}$, where $D$ is the objective diameter and $\lambda$ the wavelength. A smaller $	heta_{min}$ means finer resolution, so increasing the aperture diameter $D$ directly reduces the minimum resolvable angle and lets the telescope separate closer stars. This is precisely why research telescopes are built with enormous mirrors. The option about increasing eyepiece focal length is wrong because that changes magnification, not the fundamental diffraction-limited resolving power set by the objective. The option about using longer wavelengths is wrong because a larger $\lambda$ increases $	heta_{min}$, worsening resolution. The option about reducing the aperture is wrong because a smaller $D$ enlarges the diffraction limit, blurring the stars together. As stated in NCERT Class 12, Chapter 10, resolving power improves with a larger aperture and shorter wavelength. A consistency check confirms that the two stars separate only when $	heta_{min}$ falls below their angular separation, achieved best by widening the objective.

Resolving Power Of Optical Instruments

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