[pure-silver] Re: Formula needed
- From: "Richard Knoppow" <dickburk@xxxxxxxxxxxxx>
- To: <pure-silver@xxxxxxxxxxxxx>
- Date: Sun, 26 Sep 2004 18:26:29 -0700
----- Original Message -----
From: "Stein" <rstein@xxxxxxxxxxxxxx>
To: <pure-silver@xxxxxxxxxxxxx>
Sent: Sunday, September 26, 2004 3:51 PM
Subject: [pure-silver] Formula needed
> Dear Friends,
> I am currently constructing a camera and need to know
> a formula for calculating the in-focus point for the main
> subjects. The camera has a fixed extension of 466 mm from
> the film plane to the lens mount. If I mount a 300 mm len
> with the nodal point just about at that 466 mm point, what
> will be the distance between the lens and the in-focus
> subject plane?
>
> I know I have the formula somewhere but cannot find it.
>
> Thanks in advance.
>
> Uncle Dick
>
Fundamental relations are:
1/F = 1/u = 1/v
Where:
F = Focal length
u = Object distance
v = Image distance
Lens to Image distance v= Fu/u-F
Lens to Object distance u= Fv/v-F
Another useful relation is the focus displacement:
x= F^2/u-F
Where x is the distance from the infinity focus point to
the focus point for the distance u. This is useful for
making focusing scales and for predicting the extension
required for focusing at a given distance.
Note that the distances are to be measured from the
principal points of the lens.
If you know the true focal length the principal points
are, by definition, one focal length from the image to the
lens when the lens is focused at infinity.
The rear or second principal point is found when the lens
is in its "normal" position, the front or first principal
point when the lens is turned around.
The exact infinity focus can be found by autocollimating.
From that you can also find the focal length.
To autocollimation is easily done with the lens mounted
in a view camera, which then becomes a simple optical bench.
Prepare a white card with a small hold in the center. A
light is placed behind this hole, a small flashlight will
do. The card is placed behind the lens. Place a flat mirror
over the lens. Ideally this should be a first surface mirror
but a shaving mirror will do. Make sure its not a magnifying
mirror but a plane one.
Place the card so that the light from the hole is focused
back onto the card near the hole. Adjust the lens for
sharpest focus. It is now exactly at infinity focus with
reference to the plane of the card.
Once the infinity focus position is known the focal
length can be found by setting the lens up for exactly unity
magnification. The displacement of the lens from the
infinity focus position will be exactly one focal length.
This can be checked by the relation that the object to image
distance at unity magnification is exatly four focal length.
Finding the position of the principal points is a matter
of simple measurement from the focal plane at infinity focus
back toward the lens.
Note that nodal points are not by definition the same as
principal points but when the entire lens is in the same
medium they are coincident.
A rough way of autocollimating is to place a pencil flash
light against the ground glass near the center and adjust
focus until the beam of light reflected back is sharp. A
pencil mark on the ground glass will make this more
accurate. Make sure everything is parallel on the camera
when you do this.
---
Richard Knoppow
Los Angeles, CA, USA
dickburk@xxxxxxxxxxxxx
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