Question

Resolving power of telescope increases when:
A. Wavelength of light decrease
B. Wavelength of light increases
C. Focal length of eye-piece increases
D. Focal length of eye-piece decreases

Answer 1

Hint: Resolving power of a telescope is defined as the reciprocal of distance or angular separation between two objects which can be just resolved when viewed through the telescope. Wavelength and focal length both affect the resolving power of the telescope.

Formula used: $\mathrm{\Delta }\theta =1.22\times {\displaystyle \frac{\lambda }{d}}$
Resolving power=${\displaystyle \frac{1}{\mathrm{\Delta }\theta }}={\displaystyle \frac{d}{1.22\times \lambda }}$

Complete step-by-step answer:
Resolving power of a telescope is defined as the reciprocal of distance or angular separation between two objects which can be just resolved when viewed through the telescope.

A telescope can resolve distant objects like stars of galaxies which subtend very small angles on the telescopes ie) separate far away objects that are close together, into individual images. To resolve such angles, large apertures are needed. Thus using Rayleigh’s criterion, the angle of separation between two objects is given by

$\mathrm{\Delta }\theta =1.22\times {\displaystyle \frac{\lambda }{d}}$
Resolving power=${\displaystyle \frac{1}{\mathrm{\Delta }\theta }}={\displaystyle \frac{d}{1.22\times \lambda }}$

Thus, less the wavelength $\lambda$ more the resolving power.
Also, increasing the diameter of objective lens of telescope, more the resolving power of telescope
Hence the answer is A.

Note:
Resolving power is the ability of an instrument to resolve two points which are close together. According to Rayleigh criterion, two point sources are regarded as just resolved when the principal diffraction maximum of one image coincides with the first minimum of the other, the resolution depends on the ratio of wavelength to the width of the aperture. The angular resolution is used to resolve small images to distinct, this is the principle behind the human eye, telescope, microscope, and cameras. However the criterion has minor changes with respect to different optical tools used.