Question
Define the term ‘resolving power’ of an astronomical telescope. How does it get affected on:
  1. Increasing the aperture of the objective lens?
  2. Increasing the wavelength of light used?
  3. Increasing the focal length of the objective lens?
Justify your answer in each case.

Answer

Resolving Power of an Astronomical Telescope:The resolving power of an astronomical telescope is its ability to form separate images of two neighbouring astronomical objects (e.g. stars).
The least distance between two neighbouring objects for which astronomical telescope can form separate images is called the resolving limit. The angular limit of resolution is given by:
$\theta_\min=\frac{1.22\lambda}{\text{d}}$
Where $\lambda $ is wavelength and d is diameter of aperture objective lens. Smaller the resolving limit, greater is the resolving power.
$\therefore$ Resolving power $=\frac{\text{d}}{1.22\lambda}$
  1. RP $\alpha$ d, so by increasing aperture of objective lens, the resolving power of telescope increases.
  2. RP $\alpha\frac{1}{\text{y}},$ so by increasing the wavelength of light, the resolving power of telescope decreases.
  3. Resolving power of telescope is independent of its focal length, so there is no effect on resolving power if focal length of objective lens is increased.

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