Trying to measure the focal length of my refractor (100mm f/5 Skywatcher). Is the focal length measured from the front surface to the focal point or from the back surface to the focal point?

Started by
Steve Dodds
, Jan 23 2021 03:31 PM

11 replies to this topic

Posted 23 January 2021 - 03:31 PM

Trying to measure the focal length of my refractor (100mm f/5 Skywatcher). Is the focal length measured from the front surface to the focal point or from the back surface to the focal point?

Posted 23 January 2021 - 03:43 PM

Search effective focal length vs back focal length. The webs can splain it better than I.

Posted 23 January 2021 - 03:45 PM

The **effective focal length** is the distance between the on axis focal point and where the light cone diameter is the same as the clear aperture of the lens. That is usually somewhere between the first and last surface of the lens.

Ray tracing can give you an idea where that would be relative to the last surface of the lens.

Posted 23 January 2021 - 03:46 PM

I did search and I am getting answers for both of them. Which is correct.

Posted 23 January 2021 - 03:54 PM

The focal length of a lens is the distance between the focal point and the nodal point, typically somewhere between the two elements of a doublet lens. https://www.youtube....h?v=Hm3ZWI6I6pI

**Edited by Richard O'Neill, 23 January 2021 - 04:12 PM.**

Posted 23 January 2021 - 04:13 PM

A little complicated but I think I get it. It's somewhere inside.

Posted 23 January 2021 - 04:41 PM

In second order optics (sidel equations) there are 2 principle planes in an objective; and it is the plane closest to the back from which the focal length is measured.

The 2 planes correspond to where the light ray appears to have been bent; the first plane is where the light ray appears to have been bent looking in fron the front, and the second is lookiing in fron the back.

In any event, the clear aperture and the angle of convergence of the marginal ray can be used to calculate the focal length (assuming you can measure the angle of convergence to sufficient accuracy).

FL = aperture/2 Ã— ATAN( pi/4 - ( angle-of-convergence/2 ) ) // in radians

FL = aperture/2 Ã— ATAN( 90 - ( angle-of-convergence/2 ) ) // in degrees

Posted 23 January 2021 - 04:53 PM

"It's somewhere inside."

Yep, you got it, plenty close enough for Government work!

Posted 23 January 2021 - 08:16 PM

Very accurate way: using a camera with known pixel pitch, take short exposures of star fields like Orion's sword, the Pleiades, etc. The positions of these stars are fixed (over our lifetimes, anyway) and known to hundredths of an arc-second or better. Calculate each angle A between them using:

cos A = cos Î´1 cos Î´2 cos (Î±2 âˆ’ Î±1) + sin Î´1 sin Î´2

where Î±1 and Î±2 are the right ascensions and Î´1 and Î´2 are the declinations of the objects. Then measure the distance "d" between their images in number of pixels. The effective focal length is then

d

EFL = ------------

2tan(A/2)

Measure several angles and distances, then average the results. The exposures need to be just long enough to see the stars without overexposing them, which reduces determination of their pixel positions.

You can also pick stars within about Â±2Âº declination and let them drift across the unguided camera for a precise period of time, measure the trail length and use the fact that stars move 15 arc-seconds per time second. I've done it both ways and like using short exposures of star fields better.

Posted 23 January 2021 - 09:51 PM

Mikes method, or timing a star drifting across a field stop of known width (use callipers to measure the field stop precisely), are the valid ways. Simple geometry with a tape measure is unlikely to give an accurate answer.

Posted 23 January 2021 - 10:09 PM

How accurate does it need to be? I have always found removing the EP and focusing

the image of the moon on a screen and measuring that distance to the rear element

perfectly sufficient for anything I've needed.. That would be the BFL.

Posted 24 January 2021 - 12:23 AM

It just depends on the accuracy you want or need. The distance from the last glass surface to focus is the back focal length (BFL). The BFL is only loosely related to the effective focal length (EFL), which is what determines image scale, focal ratio and magnification. For most astronomical objectives the EFL will be longer than the BFL. As said already, you have to have the actual lens prescription to calculate the EFL, whereas the BFL can be directly measured. The EFL can also be measured, indirectly by imaging but very accurately.

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