13 Jul 2026

Resolving Power of an Astronomical Telescope

practical pg-i telescope resolving-power optics

Aim

To determine the resolving power of a telescope using two closely separated illuminated objects.

Apparatus

Astronomical telescope, two illuminated pinholes or double-star simulator, micrometer arrangement, and measuring scale.

Experimental arrangement

The telescope is focused on two close object points and the separation is reduced until the Rayleigh limit is reached.

Theory

Light from a point object reaches the objective as an approximately plane wave. Because the objective has a finite circular aperture, the wave is diffracted and forms an Airy pattern rather than a geometrical point image. Two close stars can be distinguished only when their diffraction patterns are sufficiently separated. Using the Rayleigh criterion for a circular aperture of diameter $D$, the minimum angular separation for just resolution is

\[\theta_{min}=1.22\frac{\lambda}{D}.\]

The resolving power is the ability to distinguish small angular separations. Thus, when the angle is expressed in radians,

\[R=\frac{1}{\theta_{min}}=\frac{D}{1.22\lambda}.\]

The objective diameter improves resolution, whereas a longer wavelength makes the diffraction disc wider and reduces it.

Observations

Aperture $D$ (cm)	Wavelength (nm)	Minimum angular separation (arcsec)
5.0	589	2.97
7.5	589	1.98
10.0	589	1.49

Result

The resolving power increases with telescope aperture and follows the diffraction relation.

Viva Questions

1. What limits telescope resolution? Diffraction at the objective aperture.
2. What is the Rayleigh criterion? The central maximum of one image coincides with the first minimum of the other.
3. Why is a larger objective useful? It reduces the diffraction angular width.