FOCAL LENGTH


General

The focal length is the distance between the mirror surface and its focal point. For spherical mirrors this is half the radius of curvature. The focal length determines the FOV (Field Of View) for a given area at the primary focus. The magnification of a scope is determined by the focal length of the primary and the eyepiece. See the corresponding features.

Airy disk size

The angular size of the airy disk is determined by the size of the primary (assuming a perfect surface). The size of the airy disk is then determined by the focal length

Wavelength [nm]:

560

Aperture [mm]:

150

200

250

300

Angular Airy Disk [rad]:

0.00000455

0.00000342

0.00000273

0.00000228

Focal length [mm]

1000

0.004555

0.003416

0.002733

0.002277

1250

0.005693

0.004270

0.003416

0.002847

1500

0.006832

0.005124

0.004099

0.003416

1750

0.007971

0.005978

0.004782

0.003985

2000

0.009110

0.006832

0.005466

0.004555

2250

0.010248

0.007686

0.006149

0.005124

2500

0.011387

0.008540

0.006832

0.005693

The gray fields in the table above indicate the size of the Airy disk in [mm]. High sensitive film has a resolution of about 0.025 mm. Low sensitive film about 0.01 mm. The pixel size of an often used CCD is 0.009 mm.

The table clearly shows that for prime focus photography an 6" f/15 is no problem. The maximum magnification for eyepiece projection can be calculated by dividing 0.025 by the size of the airy disk.

 

Fast Versus Slow

A scope is called fast if the focal ratio is a small number (i.e. f/5), it is called slow if the focal ratio is a high number (i.e. f/8). When selecting a focal ratio for your scope to be you should be aware of the following optical considerations.

The amount of light received from a single object depends only on the aperture of the scope, i.e. the mirror diameter. (Minus the secondary)

The FOV in the primary focus of the scope depends only on the focal length of the main mirror. (In other words; the size of an object in the primary focus depends only on the focal length)

It is generally said that you need a 'fast' scope for imaging. This is of course only true if you need the bigger FOV that comes with the 'fastness'.

The size of the secondary is important for the contrast in the scope (see 'Obstruction' in "The Secondary Mirror"). Slower scopes can use a smaller secondary and thus can achieve a better contrast. This is the reason why they are often the preferred scopes for planetary observations.