Perspective

On 24 Jul, 21:53, "HEMI-Powered" wrote:
Andrey Tarasevich added these comments in the current discussion
du jour ...





N wrote:
If perspective has nothing to do with focal length and only
relates to the distance between the subject and camera, what
makes a 50mm lens normal?

If you expose a standard 35mm frame through a 50mm lens, print
a photograph and then view it from a "normal" viewing distance
(approximately the diagonal of the print or a bit more) the
angular sizes of the objects in the print will be about the
same as they were in the real life. That's what makes 50mm
lens normal.

That's the best explanation I have heard. Thanks Andrey. My
apologies for thanking you via a reply to HEMI but I only saw your
post as a reply to his.

In general, in order to achieve that effect with a photograph
taken with a lens of focal length L, a print magnified M times
has to be viewed from the distance of L*M. If you accept the
exact "diagonal" as the normal viewing distance and then apply
this law to the 24x36mm frame, you will easily arrive at about
45mm as the "normal" focal length for the lens. 50mm was
chosen for some technical/historical reasons.

I've never seen the analysis done quite this way, thank you. And,
I've never seen the math come out to show that "normal" is really
45mm. In my days of 35mm with a Nikon Photomic FTN, zoom lenses
weren't practical or any damn good, so I had the usual focal
length primes. Now, with a digital, I suppose I could try some
test shots and prints at 45 and 50mm equivalents, but I doubt I'd
like it.

I know portrait photographers like a mild tele, like 85mm,
because it reduces unflattering parts of the face like big ears
or a big nose. In my hobby of collecting car pictures, I find the
very same thing about cars. At car shows and museums, I can
seldom get to 85mm, but if I can back up, then I definitely will
shoot in that range because I think the proportions of the car
look more real, especially if I am shooting down low but do not
want that perspective distorted artistic look.

As to your supposition about historical or technical reasons for
the focal lengths we're all familiar with, I have no clue how
50mm was selected, but neither do I understand the 24mm and 35mm
wide angles I had for my Nikon or the 105mm telephoto. What
established those particular numbers as a standard? Who knows!
Ditto for exactly what we accept to this very day for f/stop
numbers. I understand that the peculiar looking number, to a
novice, are because each is 1/2X or 2X AREA of the aperture, but
how did the exact sequence of numbers become standard? Same
answer, I have no clue.


As an ex-mathematician and amateur photographer, the sequence of
numbers makes some sense.

As you probably know, (assuming simple lenses), the aperture is the
focal length of the lens divided by its width. The division makes
since a shorter focal length concentrates the light more and achieves
the same brightness on the film / sensor as a wider lens with a longer
focal length. Consider a scene viewed through a 50mm f/8 lens (6.25mm
wide). Now switch to a 100mm lens also 6.25mm wide, the image will be
twice as big. The portion that lands on the film or sensor will only
be 1/4 of that from the 50mm. 1/4 of the light spread over the same
area so dimmer. To correct this and get the same brightness, we need
to make the lens 4 times the area and hence twice as wide: 12.5mm.
Note that 100 / 12.5 = 8 so this wider but longer lens has the same f
number.

What has always puzzled me is why the division is focal length / width
so that lower is brighter rather than the reverse which would have
given higher is brighter. As a kid playing with cameras, some of the
other kids would assume that higher was best so that a lens with
apertures from f/4 to f/32 was better than one which had f/2.8 to f/
22.

That would still be odd in some ways since doubling this alternative
(inverse) aperture would increase the brightness by 4 not 2. (Since
it would mean doubling the width of the lens and hence quadrupling its
area). So, the square of the alternative division might have been a
good measure. Doubling the number would mean doubling the
brightness.

Back to apertures as they are. The standard stops are as sensible as
the definition allows. 1, 2, 4, 8, 16, 32 doubling each time but, as
explained above, these steps are decreasing the brightness 4 times per
step. So between 1 and 2, we need the square root of 2 which is (to 1
d.p.) 1.4. The other funny stops are simply 2, 4, 8, etc times this
number The standard sequence is powers of the square root of 2. The
lower number is often an exception since it is controlled by the
actual size of the lens and not an arbitrary width setting of the
iris. Every second f number is an integer and the others aren't
(would be irrational if ridiculous accuracy was used) Cameras that do
half stops will have a sequence of apertures going up by steps of the
4th root of 2 and those that do third stops will have a sequence going
up in steps of the 6th root of 2.

--
Seán Ó Leathlóbhair

Seán O'Leathlóbhair added these comments in the current
discussion du jour ...

[snip for brevity]
As to your supposition about historical or technical reasons
for the focal lengths we're all familiar with, I have no clue
how 50mm was selected, but neither do I understand the 24mm
and 35mm wide angles I had for my Nikon or the 105mm
telephoto. What established those particular numbers as a
standard? Who knows! Ditto for exactly what we accept to this
very day for f/stop numbers. I understand that the peculiar
looking number, to a novice, are because each is 1/2X or 2X
AREA of the aperture, but how did the exact sequence of
numbers become standard? Same answer, I have no clue.

As an ex-mathematician and amateur photographer, the sequence
of numbers makes some sense.

I was and still are an amateur photographer, but no longer pay
much attention to f/stop numbers other than to see that they are
either small enough or large enough for the DOF I want. I've
already said I haven't done any real math in a long time, but
even when I was a 35mm photographer prior to going to engineering
school, I didn't know where the exact sequence of f/stop numbers
came from, and still don't.

As you probably know, (assuming simple lenses), the aperture
is the focal length of the lens divided by its width. The
division makes since a shorter focal length concentrates the
light more and achieves the same brightness on the film /
sensor as a wider lens with a longer focal length. Consider a
scene viewed through a 50mm f/8 lens (6.25mm wide). Now
switch to a 100mm lens also 6.25mm wide, the image will be
twice as big. The portion that lands on the film or sensor
will only be 1/4 of that from the 50mm. 1/4 of the light
spread over the same area so dimmer. To correct this and get
the same brightness, we need to make the lens 4 times the area
and hence twice as wide: 12.5mm. Note that 100 / 12.5 = 8 so
this wider but longer lens has the same f number.

What has always puzzled me is why the division is focal length
/ width so that lower is brighter rather than the reverse
which would have given higher is brighter. As a kid playing
with cameras, some of the other kids would assume that higher
was best so that a lens with apertures from f/4 to f/32 was
better than one which had f/2.8 to f/ 22.

That would still be odd in some ways since doubling this
alternative (inverse) aperture would increase the brightness
by 4 not 2. (Since it would mean doubling the width of the
lens and hence quadrupling its area). So, the square of the
alternative division might have been a good measure. Doubling
the number would mean doubling the brightness.

Back to apertures as they are. The standard stops are as
sensible as the definition allows. 1, 2, 4, 8, 16, 32
doubling each time but, as explained above, these steps are
decreasing the brightness 4 times per step. So between 1 and
2, we need the square root of 2 which is (to 1 d.p.) 1.4. The
other funny stops are simply 2, 4, 8, etc times this number
The standard sequence is powers of the square root of 2. The
lower number is often an exception since it is controlled by
the actual size of the lens and not an arbitrary width setting
of the iris. Every second f number is an integer and the
others aren't (would be irrational if ridiculous accuracy was
used) Cameras that do half stops will have a sequence of
apertures going up by steps of the 4th root of 2 and those
that do third stops will have a sequence going up in steps of
the 6th root of 2.

Thanks for the excellent in-depth explanation, Sean. I reply
serially so I didn't see this last paragraph before writing the
"I still have no clue where the f/stops came from" comment. Now,
I do. I obviously have more than enough math background to
understand powers of 2, square roots, etc., so your explanation
makes excellent sense to me. Thank you.

--
HP, aka Jerry

Seán O'Leathlóbhair wrote:
snip

As you probably know, (assuming simple lenses), the aperture is the
focal length of the lens divided by its width. The division makes
since a shorter focal length concentrates the light more and achieves
the same brightness on the film / sensor as a wider lens with a longer
focal length. Consider a scene viewed through a 50mm f/8 lens (6.25mm
wide). Now switch to a 100mm lens also 6.25mm wide, the image will be
twice as big. The portion that lands on the film or sensor will only
be 1/4 of that from the 50mm. 1/4 of the light spread over the same
area so dimmer. To correct this and get the same brightness, we need
to make the lens 4 times the area and hence twice as wide: 12.5mm.
Note that 100 / 12.5 = 8 so this wider but longer lens has the same f
number.

What has always puzzled me is why the division is focal length / width
so that lower is brighter rather than the reverse which would have
given higher is brighter. As a kid playing with cameras, some of the
other kids would assume that higher was best so that a lens with
apertures from f/4 to f/32 was better than one which had f/2.8 to f/
22.

That would still be odd in some ways since doubling this alternative
(inverse) aperture would increase the brightness by 4 not 2. (Since
it would mean doubling the width of the lens and hence quadrupling its
area). So, the square of the alternative division might have been a
good measure. Doubling the number would mean doubling the
brightness.

Back to apertures as they are. The standard stops are as sensible as
the definition allows. 1, 2, 4, 8, 16, 32 doubling each time but, as
explained above, these steps are decreasing the brightness 4 times per
step. So between 1 and 2, we need the square root of 2 which is (to 1
d.p.) 1.4. The other funny stops are simply 2, 4, 8, etc times this
number The standard sequence is powers of the square root of 2. The
lower number is often an exception since it is controlled by the
actual size of the lens and not an arbitrary width setting of the
iris. Every second f number is an integer and the others aren't
(would be irrational if ridiculous accuracy was used) Cameras that do
half stops will have a sequence of apertures going up by steps of the
4th root of 2 and those that do third stops will have a sequence going
up in steps of the 6th root of 2.

--
Seán Ó Leathlóbhair


First, look at it not as 1, 2, 4, 8 etc, but as 1, 1/2, 1/4, 1/8 etc.
Second, when th f/stop notation was developed math education was not as
far advanced as it is today, regardless of what its critics say. (An
example: when I was a college student 60 years ago, calculus was a
college sophomore course; today, my son-in-law teaches Advance Placement
calculus in high school, and any student planning to major in any
science or engineering field is expected to have credit for it when
he/she enrolls in college--now, back to on-topic.) Back in those days,
over a hundred years ago, I doubt that the average person had a concept
of a square root. Another example: I have an old high school mathematics
text belonging to my grandfather from the 1880s that is nothing but
arithmetic--some of it thought-provoking, but still nothing but the
basic four math operations--not even any algebra.

Allen

"/\BratMan/\" wrote in message ...

what makes a 50mm lens normal?

You lot do overcomplicate things!
See for yourself... get your 35mm slr and 3 lenses, 1 around 28mm, 1 around
100mm and your "normal" 50mm... attach them in turn and look through the
viewfinder with right while keeping left eye open also.
When I do this I see:
28mm = right eye through viewfinder objects look smaller and further away
than left eye.
100mm = right eye through viewfinder objects look larger and closer than
left eye.
50mm = right eye through viewfinder objects look the same as left eye i.e.
"normal"
That is why it is referred to as a "normal" lens... things just look "normal"
in size and distance.

Sorry, this is not correct, but merely a byproduct of the particular
image magnification of your camera's viewfinder. Others will show
other results (remember that Leica rfdr cameras can be had with
three different VF magnification factors, for an extreme instance?).
--
David Ruether

http://www.donferrario.com/ruether

Allen added these comments in the current discussion du jour ...

First, look at it not as 1, 2, 4, 8 etc, but as 1, 1/2, 1/4,
1/8 etc. Second, when th f/stop notation was developed math
education was not as far advanced as it is today, regardless
of what its critics say. (An example: when I was a college
student 60 years ago, calculus was a college sophomore course;
today, my son-in-law teaches Advance Placement calculus in
high school, and any student planning to major in any science
or engineering field is expected to have credit for it when
he/she enrolls in college--now, back to on-topic.) Back in
those days, over a hundred years ago, I doubt that the average
person had a concept of a square root. Another example: I have
an old high school mathematics text belonging to my
grandfather from the 1880s that is nothing but
arithmetic--some of it thought-provoking, but still nothing
but the basic four math operations--not even any algebra.

I took Calculus as a freshman, but I agree, the college prep kids
intending to get a science and math degree start in H.S. But, the
rudimentary math for area calculations of lens apertures goes
back all the way to Galileo, even though his first telescopes had
only two lenses. I said I didn't know the origins of the exact
numbers commonly used, and I didn't until just this morning, but
I would say that it has been known that the sequence is related
to aperture area in a power of 2 sequence as far back as the
early photographers that at all had apertures. There is some
doubt in my mind that the very earliest ones that used exposures
in the multiple seconds range fully understood it, but it seems
historically plausible to me that this has been understood since
at least the late 19th Century.

You are obviously correct about the average person understanding
square roots. I'd say it was more like 150+ years ago, than 100,
but your point is well taken. In agrarian societies of the day,
illiterate or only partially literate people were common and few
children got more than simple arithmetic in the one room school
houses. But, the early photographers, especially any that are
considered at all "great" today, clearly understood all of this,
including DOF, what we now call camera shake, sharpness, film
contrast, and a full range of alternations to the film as it was
developed and the prints as they were being exposed. For those
who used cut sheet film, it was especially easy to customize the
type of film used according to lighting conditions and desired
results.

I have a set of 4 or 5 mathematics reference books that summarize
almost the entire spectrum of mathematics including finance that
dates back to the early 20th Century, nearly 100 years ago. It is
full of short-cuts to equations that were ill-understood in those
days and even more full of tables to be used in place of
complicated calculations that were difficult to do manually and
there were no calculators, not even the early Friden mechanical
ones used to produce artillery ballistics tables in the 1930s and
during WWII. Which brings us to digital computers. The real
motivation to develop the first one was to speed up the
production of those ballistic tables because even legions of
women clacking away on Friden's wasn't enough to keep up with the
rapidly changing field and naval artillery during the war.

Good discussion, I've learned a lot here. My thanks to everyone.

--
HP, aka Jerry

"David Ruether" wrote in message
...
"/\BratMan/\" wrote in message
...

what makes a 50mm lens normal?

You lot do overcomplicate things!
See for yourself... get your 35mm slr and 3 lenses, 1 around 28mm, 1
around
100mm and your "normal" 50mm... attach them in turn and look through the
viewfinder with right while keeping left eye open also.
When I do this I see:
28mm = right eye through viewfinder objects look smaller and further
away
than left eye.
100mm = right eye through viewfinder objects look larger and closer than
left eye.
50mm = right eye through viewfinder objects look the same as left eye
i.e.
"normal"
That is why it is referred to as a "normal" lens... things just look
"normal"
in size and distance.

Sorry, this is not correct, but merely a byproduct of the particular
image magnification of your camera's viewfinder. Others will show
other results (remember that Leica rfdr cameras can be had with
three different VF magnification factors, for an extreme instance?).
--
David Ruether

http://www.donferrario.com/ruether


But it is true of my D80 with 18-200VR lens, although I'm not sure what
setting I have for the viewfinder focus - it's just whatever works for me.

"N" wrote in message ...
"David Ruether" wrote in message ...
"/\BratMan/\" wrote in message ...

what makes a 50mm lens normal?

You lot do overcomplicate things!
See for yourself... get your 35mm slr and 3 lenses, 1 around 28mm, 1 around
100mm and your "normal" 50mm... attach them in turn and look through the
viewfinder with right while keeping left eye open also. When I do this I see:
28mm = right eye through viewfinder objects look smaller and further away than left eye.
100mm = right eye through viewfinder objects look larger and closer than
left eye.
50mm = right eye through viewfinder objects look the same as left eye i.e. "normal"
That is why it is referred to as a "normal" lens... things just look "normal" in size and distance.

Sorry, this is not correct, but merely a byproduct of the particular
image magnification of your camera's viewfinder. Others will show
other results (remember that Leica rfdr cameras can be had with
three different VF magnification factors, for an extreme instance?).
--
David Ruether

http://www.donferrario.com/ruether

But it is true of my D80 with 18-200VR lens, although I'm not sure what setting I have for the viewfinder focus - it's just
whatever works for me.

The viewfinder focus is only intended to accommodate your eye focus to
the viewing system for the sharpest view of the viewfinder screen. The
zoom FL settings are unlikely to be very accurate, and you will likely
find that at any given FL setting that changing the lens focus will change
its angle of view (with non-zooms, the angle generally narrows with
closer focus - but with many zooms, the angle widens with closer focus).
In other words, there is no set correspondence between FL and "normal"
using the VF as a guide other than as an approximation - and "normal"
FL has nothing to do with the way we see (for more on this, see my
comments in another post above, and in my article on this at
http://www.donferrario.com/ruether/a...l#perspective).
--
David Ruether

http://www.donferrario.com/ruether

"David Ruether" wrote in message
...


"N" wrote in message
...
"David Ruether" wrote in message
...
"/\BratMan/\" wrote in message
...

what makes a 50mm lens normal?

You lot do overcomplicate things!
See for yourself... get your 35mm slr and 3 lenses, 1 around 28mm, 1
around
100mm and your "normal" 50mm... attach them in turn and look through
the
viewfinder with right while keeping left eye open also. When I do this
I see:
28mm = right eye through viewfinder objects look smaller and further
away than left eye.
100mm = right eye through viewfinder objects look larger and closer
than
left eye.
50mm = right eye through viewfinder objects look the same as left eye
i.e. "normal"
That is why it is referred to as a "normal" lens... things just look
"normal" in size and distance.

Sorry, this is not correct, but merely a byproduct of the particular
image magnification of your camera's viewfinder. Others will show
other results (remember that Leica rfdr cameras can be had with
three different VF magnification factors, for an extreme instance?).
--
David Ruether

http://www.donferrario.com/ruether

But it is true of my D80 with 18-200VR lens, although I'm not sure what
setting I have for the viewfinder focus - it's just whatever works for
me.

The viewfinder focus is only intended to accommodate your eye focus to
the viewing system for the sharpest view of the viewfinder screen. The
zoom FL settings are unlikely to be very accurate, and you will likely
find that at any given FL setting that changing the lens focus will change
its angle of view (with non-zooms, the angle generally narrows with
closer focus - but with many zooms, the angle widens with closer focus).
In other words, there is no set correspondence between FL and "normal"
using the VF as a guide other than as an approximation - and "normal"
FL has nothing to do with the way we see (for more on this, see my
comments in another post above, and in my article on this at
http://www.donferrario.com/ruether/a...l#perspective).
--
David Ruether

http://www.donferrario.com/ruether


In doing that quick look through the viewfinder mentioned above, I was
focusing on an area about 15 feet away.

"Gino" wrote:
Me:
It's a hideous focal length: it's too short for isolating the subject and
it's too long to show the space and context the subject exists in.

Have to disagree David.

50mm on a 1.6 cropped body is spot on (as you know, close to 85mm on a
full frame body).

Hehe. Right you are. If you have a cropped body. (What a procrustecian world
we live in with so many of our bodies being cropped.)

David J. Littleboy
Tokyo, Japan

On Fri, 27 Jul 2007 19:30:46 +0900, "David J. Littleboy"
wrote:


"Gino" wrote:
Me:
It's a hideous focal length: it's too short for isolating the subject and
it's too long to show the space and context the subject exists in.

Have to disagree David.

50mm on a 1.6 cropped body is spot on (as you know, close to 85mm on a
full frame body).

Hehe. Right you are. If you have a cropped body. (What a procrustecian world
we live in with so many of our bodies being cropped.)

David J. Littleboy

Indeed! Where is theseus now that we really need her.

-----------------------------
Your yak is weak.