Quote from someone above: �By definition a "normal" lens is of a focal length approximately equal to the diagonal of the frame.�
That�s total nonsense. How could it be �by definition�? There has to be a scientific reason behind it (which I�m going to give you).
It will once and for all dispel these �myths� about normal lenses and what they mean. Also the �normal� lens on a 35mm camera is not even that close to the length of the diagonal. The diagonal of the frame is 43mm the �normal� lens is 50mm. That�s a 16% difference! Hardly a good match.
If you take a 35mm photo with any focal length lens (this applies equally to any other format camera too), there has to be a unique position somewhere in front of you where you could hold up the print and it would fit EXACTLY and perfectly over the scene just shot.
The distance might be 6� in front of you or it might be 60� in front of you but it will be somewhere. It�s probably best to imagine a print printed on to a plastic sheet so that you can view the real scene through it.
Well �normal� lenses are all to do with viewing the print (or the plastic sheet in my example) at the NORMAL READING DISTANCE of the eye; usually taken to be around 10� (250mm). Of course we need more information to do a calculation, like what size print are we talking about and what angle of view is the camera seeing.
This angle has NOTHING to do with the angle the naked eye sees views at. As someone above pointed out the area of clear focus is very small (it�s actually only about 7 degrees) while the angle of peripheral vision is huge (> 120 degrees).
(As an aside the reason the eye sees like this is that the brain would require far too much processing power if it had to cope with perfectly focussed vision at all times over a large angle of view. So instead the eye scans a scene to make the best use of brain �bandwidth� and concentrates only on a small central region - the "fovea").
Right, we have our distance (250mm) but how large is the print? This will make a difference obviously to where we can hold the print in front of us and cover the scene. So an arbitrary �normal� size print is chosen by the industry of approx 7� x 5� (whose diagonal is therefore 8.6� or 218mm). It can be shown mathematically, by trigonometry, that the angle subtended by the diagonal of a 7" x 5" print at a distance of 10" is 47 degrees. For those interested it is
tan(x/2) = (print diagonal)/(2 x distance)
where x = the angle we are trying to find
therefore x = 2arctan[(print diagonal)/(2 x distance]= 47 degrees in this case
So the calculation becomes, what focal length lens on a 35mm camera will produce a 7� x 5� print that exactly covers the real scene at a distance of 10� with a 47 degree angle of view?
From trigonometry it can be shown that:
tan(x/2) = 218/(2x250) for the print
and also, tan(x/2) = 43/(2 x F) for the camera
where x = 47 degrees and F = the focal length of the lens
Therefore by equating these two and rearranging:
F = (43 x 250)/218 = 49mm and the industry happens to round it to 50mm. QED.
Generically therefore, F = (diagonal of frame) x (reading distance) / (diagonal of print)
Of course, if you decide that an 8� x 5� print is a more realistic �normal� size (and you are perfectly entitled to choose this or any other size) then a �normal� lens would be:
F = (43 x 250)/240 = 45mm (much closer to the frame diagonal dimension by the way).
So there is a scientific basis to �normal� lenses but I see and read so many fairy tales being perpetuated on the subject I thought I would give the mathematical basis for it.
Incidentally it is interesting to do the calculation for other focal length lenses (eg: 100mm and 200mm etc) to ascertain what distance the resulting print needs to be held from the eye to exactly cover the scene and for it to look "normal".
For a 100mm lens on a 35mm camera, substituting back into my equation (and using a 7" x 5" print), the distance is about 20 inches.
What is a "normal" lens?
in Medium Format
Posted
Quote from someone above: �By definition a "normal" lens is of a focal length approximately equal to the diagonal of the frame.�
That�s total nonsense. How could it be �by definition�? There has to be a scientific reason behind it (which I�m going to give you).
It will once and for all dispel these �myths� about normal lenses and what they mean. Also the �normal� lens on a 35mm camera is not even that close to the length of the diagonal. The diagonal of the frame is 43mm the �normal� lens is 50mm. That�s a 16% difference! Hardly a good match.
If you take a 35mm photo with any focal length lens (this applies equally to any other format camera too), there has to be a unique position somewhere in front of you where you could hold up the print and it would fit EXACTLY and perfectly over the scene just shot.
The distance might be 6� in front of you or it might be 60� in front of you but it will be somewhere. It�s probably best to imagine a print printed on to a plastic sheet so that you can view the real scene through it.
Well �normal� lenses are all to do with viewing the print (or the plastic sheet in my example) at the NORMAL READING DISTANCE of the eye; usually taken to be around 10� (250mm). Of course we need more information to do a calculation, like what size print are we talking about and what angle of view is the camera seeing.
This angle has NOTHING to do with the angle the naked eye sees views at. As someone above pointed out the area of clear focus is very small (it�s actually only about 7 degrees) while the angle of peripheral vision is huge (> 120 degrees).
(As an aside the reason the eye sees like this is that the brain would require far too much processing power if it had to cope with perfectly focussed vision at all times over a large angle of view. So instead the eye scans a scene to make the best use of brain �bandwidth� and concentrates only on a small central region - the "fovea").
Right, we have our distance (250mm) but how large is the print? This will make a difference obviously to where we can hold the print in front of us and cover the scene. So an arbitrary �normal� size print is chosen by the industry of approx 7� x 5� (whose diagonal is therefore 8.6� or 218mm). It can be shown mathematically, by trigonometry, that the angle subtended by the diagonal of a 7" x 5" print at a distance of 10" is 47 degrees. For those interested it is
tan(x/2) = (print diagonal)/(2 x distance)
where x = the angle we are trying to find
therefore x = 2arctan[(print diagonal)/(2 x distance]= 47 degrees in this case
So the calculation becomes, what focal length lens on a 35mm camera will produce a 7� x 5� print that exactly covers the real scene at a distance of 10� with a 47 degree angle of view?
From trigonometry it can be shown that:
tan(x/2) = 218/(2x250) for the print
and also, tan(x/2) = 43/(2 x F) for the camera
where x = 47 degrees and F = the focal length of the lens
Therefore by equating these two and rearranging:
F = (43 x 250)/218 = 49mm and the industry happens to round it to 50mm. QED.
Generically therefore, F = (diagonal of frame) x (reading distance) / (diagonal of print)
Of course, if you decide that an 8� x 5� print is a more realistic �normal� size (and you are perfectly entitled to choose this or any other size) then a �normal� lens would be:
F = (43 x 250)/240 = 45mm (much closer to the frame diagonal dimension by the way).
So there is a scientific basis to �normal� lenses but I see and read so many fairy tales being perpetuated on the subject I thought I would give the mathematical basis for it.
Incidentally it is interesting to do the calculation for other focal length lenses (eg: 100mm and 200mm etc) to ascertain what distance the resulting print needs to be held from the eye to exactly cover the scene and for it to look "normal".
For a 100mm lens on a 35mm camera, substituting back into my equation (and using a 7" x 5" print), the distance is about 20 inches.
Cheers
Chris UK