Large Diameter Telescopes

Physics: AQA A Level, topic 9.1.4

Resolving power

Telescopes are good for looking at distant stars but when two stars are close together there is a limit at which we can no longer tell them apart.

When light passes through a lens it diffracts (bends) slightly and is slightly distorted.
This diffraction means that if two objects are too close together we will not be able to tell them apart as the diffraction patterns will merge the images into one.

The Rayleigh criterion states that two images are just resolvable when the centre of the diffraction pattern of one object is directly over the first minimum of the diffraction pattern of the other.
For a circular lens the equation for the angular location (in radians) of the first minimum of a diffraction pattern is:
Angle = (1.22 x the wavelength of light) ÷ (the diameter of the lens)
${\theta}=1.22{\times}\frac{{\lambda}}{D}$

Larger telescopes gather more radiation.

Collecting power is directly proportional to the square of the diameter of the aperture or primary mirror.
The total power of detected light is equal to the intensity from the source × the gathering area.

Because the gathering area is equal to π × r² for a circular telescope mirror, the total power is directly proportional to the radius squared and so the diameter squared.

A CCD (charge-coupled device) converts electrical signals to digital. The eye and the CCD unit both detect light. In many ways, they are similar.

A lens is required to focus light on to a detector.
The eye has rod cells and cone cells in the retina designed to give an electrical response to a light stimulus. The CCD chip performs a similar function, but with tiny slivers of silicon.
Neither the CCD nor the eye needs any development, as it would with camera film.

The eye’s ‘shutter’ speed is fixed and the eye cannot perform long exposure imagery.
The CCD device can take exposures as long as several hours. This lets much fainter objects be detected.

Why does diffraction limit the resolution of a telescope?
The Rayleigh criterion is true for what type of lens?
Why is the collecting power of a telescope proportional to the square of the radius of the aperture?
If the radius of a telescope aperture increases by a factor of 2, what factor does the collecting power of that telescope increase by?
If the radius of a telescope aperture increases by a factor of 6, what factor does the collecting power of that telescope increase by?