9.1.4

# Large Diameter Telescopes

Test yourself

## 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.

### Distinguishing stars

• 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

• 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)
• ${\theta}=1.22{\times}\frac{{\lambda}}{D}$

## Collecting Power and Size of Large Diameter Telescopes

### Collecting power

• 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.

### Collecting power cont.

• 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.

## Charge-Coupled Devices and the Eye

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.

### Similarities

• 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.

### Resolving power

• The retina has significantly greater resolving power than a CCD chip.

### Exposure

• 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.