Sunday, 19 August 2012

Focal length of digiscopes compared to camera lenses

Does that mean you don’t have to fiddle about putting a camera on the telescope, then?

That was the question asked when I was showing off the capabilities of the Nikon P510 at the 35 mm camera equivalent of 1000mm. The question was also loaded in that it implied I would not need to buy a camera for digiscoping to replace the old Canon Ixus that fitted the scope awkwardly. The follow-up question — Surely that 1000 mm lens is as good as a scope isn’t it? — sent me in search of data. Evidence that useful as the 1000 mm is, it could not match the focal lengths of a telescope plus camera was needed. What is the focal length of a digiscope set-up in terms equivalent to a 35 mm full-frame camera?

I thought I could remember that the formula was the focal length of the camera lens multiplied by telescope magnification (with the focal length of the camera lens expressed in 35 mm full-frame camera equivalents). Sure enough, that is the formula given on the Swarovski website:

To determine the equivalent focal length for a digital camera compared to a 35 mm camera, you need to carry out a few calculations. Each digital camera has a 35 mm equivalent figure. For the Nikon P-6000, for example, the 35 mm equivalent figure is 28–112 mm. Since the Nikon P-6000 has a digital focal length of 6–24 mm, this results in a factor of 4.66 (28 mm divided by 6 mm). This factor or the 35mm equivalent focal length is usually stated in the camera’s user manual.
In this case, the equivalent focal length is the adjusted focal length of the digital camera multiplied by the factor 4.66. Example: The Nikon P-6000 is set to a focal length of 14 mm. 14 mm x 4.66 = 65.2 mm focal length equivalent for a 35 mm camera.
To obtain the entire 35 mm equivalent focal length from your digiscoping equipment, you need to multiply that focal length by the magnification of your scope.
Example: Your telescope is set at 20x magnification. 65.2 mm x 20 = 1,304 mm total 35 mm equivalent focal length
To determine the total digital focal length of your digiscoping equipment, you simply need to multiply the focal length of your digital camera by the magnification settings of your telescope.
Example: Your digital camera is set to 14 mm focal length; the telescope is at 20x magnification: 14 mm x 20 = 280 mm total digital focal length

So I thought I would try it out in practice, because as, we shall see below, this is not the only formula doing the rounds on the internet. The old Ixus is ‘on loan’ and I had to use the only camera in the house that was vaguely suitable — my wife’s underwater Panasonic Lumix DMC-FT3 with its square lens housing. I managed to hold this to the eyepiece and zoom in until there was a full frame without vignetting. I then looked at the metadata. The camera focal length was 7 mm. The factor needed to convert to 35 mm equivalent was calculated from the actual zoom range of 4.9-22.8 mm and the stated 35 mm equivalent of 28-128 mm. 28/4.9 is 5.71 and 128/22.8 is 5.61 so I took the mean of 5.66. The telescope magnification was 40. Therefore, the 35 mm equivalent focal length of the whole set-up was 5.66 x 7 x 40 = 1584 mm.

The story does not end there because the Google search showed other sites which showed calculations for focal length. In the first (, I could not see how the writer had derived the formula or the constants used. Putting the same values into his formula I came up with a focal length of 2263 mm! Another website ( provides an Excel spreadsheet which came up with 1720 mm. In the latter case, the difference is in the way the 35 mm equivalent focal length of the camera lens is calculated but since I do not know how a constant used for the calculation was derived I cannot comment further.  These cases demonstrate how dangerous the internet is for spreading and retaining incorrect information. I have shown the web addresses but not shown them as links for this reason.

Just in case you are wondering whether Swarovski got it wrong and the other guy is right (even though I could find no basis for the formula he came up with), I did stand in the same place with my Nikon P510 and take a picture at 1000 mm equivalent of the same object at the bottom of the garden. I then measured the size of the object in relation to the width of the frame on the screen. In my crude Lumix digiscoped shot, the object occupied 0.58 of the total width; in the Nikon it occupied 0.36 of the width. Dividing one by the other, 0.58/0.36 = 1.61. Thus, the focal length of the digiscope was 1.61 times that of the Nikon or 1610 mm, remarkably close to the calculated 1584 mm given the crudity of the size measurements. Clearly, the formula given by Swarovski is the one to use when calculating the focal length of a digiscope set-up when using a digital compact camera. I just hope that people find that one first in any Google search.

The focal length of any digiscope set-up can be calculated from the camera focal length (found in the metadata after taking), the manufacturer’s stated zoom range in 35 mm equivalents and the magnification of the telescope eyepiece.

And, just in case you were wondering, great as the 1000 mm equivalent lens of the Nikon P510 is for birds, it does not replace the digiscope entirely. Much longer focal lengths can be achieved with the latter but whether there is enough light or time to set up the scope is another matter.