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From: Andreas.Nicklass@usa.net (Andreas Nicklass)
Newsgroups: rec.photo.equipment.35mm
Subject: Re: 500mm zoom
Date: Thu, 24 Sep 1998
Vortex bfe2709@mail.telepac.pt wrote:
Does anyone knows how far a 500mm zoom can magnify?
Compared to a 50mm normal lens the magnification of a 500mm lens
is 10x.
If you are asking for the maximum ratio between image and object,
then the answer depends on the closest focusing distance of the
lens:
focusing distance 2m 3m 4m 5m 6m 8m 10m magnification 1.00 0.27 0.17 0.13 0.10 0.07 0.056
Andreas
Date: Thu, 24 Sep 1998
From: Andreas Nicklass Andreas.Nicklass@usa.net
To: Robert Monaghan rmonagha@post.cis.smu.edu
Subject: Re: formula? Re: 500mm zoom
Hi Bob!
can you supply the formula for doing the image height
calculation?
I used two fundamental equations. The general lens equation
1/f = 1/g + 1/b (1)
and the definition of magnification
M = B / G = b / g (2)
with:
By combining (1) and (2) you can either eliminate g or b:
The focusing distance (which is measured between film plane
and object) is simply b+g, as long as we neglect the distance
between the two principal points:
This is a quadratic equation in M which can be solved analytically:
The other root describes magnifications M > 1 and is of no
relevance in most cases.
Notice that there are no solutions for d < 4f. Thus no lens can
focus closer than 4f. The magnification at d = 4f is exactly 1
and the focusing distance increases again with magnifications
beyond 1. For 'real life' lenses the actual numbers may vary be-
cause there is a non-negligible distance between the principal
points and more important, internally focusing lenses loose
focal length when you focus closer.
Andreas
f : focal length
g : distance object - front principal point of the lens
b : distance film - rear principal point
B : image height
G : object height
M : magnification
b = f ( 1 + M ) (3)
g = f ( 1 + 1/M ) (4)
d = b + g = f ( 2 + M + 1/M ) (5)
M = ( d - 2f - sqrt( d^2 - 4df ) ) / ( 2f ) (6)