# Zoom lenses and fstops

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Posted 05 March 2007 - 05:54 PM

By my understanding the fstop equals the focal length of the lense divided by the width of the aperature i.e. a focal length of 50mm and an aperture diameter of 25mm = f2.

This makes sense on a prime lense but I dont understand how zoom lenses work. At 50mm with an aperture value of f2 their is very little difference in light transmittence when zoomed to 200mm.

Could some one please clarify fstops for me, every book and article I read tends to add more confusion to the subject.

Best

David
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Posted 05 March 2007 - 06:29 PM

As In understand it, they introduce stops into the design. A stop is basically an iris that can't open or close. In effect blocking off light at the wide end so as to match the longer ends aperture which always will be the design aperture. In stills photography, where this isn't important, you'll often find a zoom that has one stop for the long end and one wider stop for the short end.
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### #3 Troy Warr

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Posted 05 March 2007 - 06:51 PM

I'm reading a book on optics, and although it's insanely complex, I think I got the gist of the explanation on this.

The f-number is the diameter of the entrance pupil in terms of the effective focal length of the lens. The entrance pupil is not necessarily (and often is not) the same size as the lens aperture. In order for the f-number to remain constant at different focal lengths (i.e. in a zoom lens), the entrance pupil has to change in proportion to the focal length so that the ratio (f-number) stays the same.

In lenses where this ratio does not change in proportion as you zoom, you get a variable aperture. It just depends on the design of the particular lens.

There's a pretty good explanation of f-stops on Wikipedia - that's the least confusing explanation that I've found to date.
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Posted 05 March 2007 - 08:30 PM

thanks Adam, Troy, that pretty much clarifies it for me. I was just unsure if the aperture in a zoom lense was variable.

So if a zoom lense at 30mm in focal length at f2 has a physical aperture diameter of 15mm then when zoomed to 70mm the aperture will compensate and become 35mm in diameter in order to maintain a ratio of 1:2(f2).

So in theory an fstop is a constant and is merely an expression of a ratio relative to focal length.

Assuming thats correct then I may have finally made sense of all the mess I've been reading.

'Hecht, Eugene (1987). Optics, 2nd ed., Addison Wesley' - looks to be a good read regarding optics. Apparently there is a 4th edition dated 2002 on the shelf so if anyone else is interested maybe this would be a good place to start.

Edited by David Bradley, 05 March 2007 - 08:32 PM.

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### #5 Leo Anthony Vale

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Posted 06 March 2007 - 03:02 PM

By my understanding the fstop equals the focal length of the lense divided by the width of the aperature i.e. a focal length of 50mm and an aperture diameter of 25mm = f2.

This makes sense on a prime lense but I dont understand how zoom lenses work. At 50mm with an aperture value of f2 their is very little difference in light transmittence when zoomed to 200mm.

Could some one please clarify fstops for me, every book and article I read tends to add more confusion to the subject.

On a simple level, a zoom can be divided into two sections: a backing lens, where the aperture is located & the zoom section, where the image size changes.

When you add an afocal attachment to a prime, the effective focal length of the system changes but the physical size of the aperture doesn't. The backing lens is viewing a different size image.

This is the same with the backing lens in the zoom. It's still a prime lens only it's looking at an image whose size is changing.

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### #6 Michael Collier

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Posted 06 March 2007 - 03:53 PM

Your confusion lies in your calculation. Fstop is not a relationship of FOCAL LENGTH to iris appeture, rather its a measurement of the FRONT ELEMENT to the IRIS appeture (what troy called entrance pupil) Since the zoom lens does not change its front element, the F-stop remains contsant.

Now to explain the entrance pupil and how what I just said is not quite right. As you zoom in the angle of view changes yes? As that angle changes you will see that on the wide side of the lens, light is being collected from the entire surface of the glass (more or less) but when you zoom in, as the angle grows more accute, suddenly the entire surface of the glass is not transmitting light to the sensor or film. as that angle cuts off part of the glass, your calculation needs to reflect a smaller effective diameter, and so as you zoom, the fstop will rise.

As was mentioned before, zooms for film cameras compensate to give you a solid T-stop and F-stop reading, video lenses do not compensate (you can see your exposure and typically open up if you zoom in) and for still lenses they are marked with two readings and you pick which to go by based on your focal lenght.

so again, fstop is a relation of the effective front element (or entrance pupil...new one to me troy. probably more accurate from an opticle engeneer standpoint) and the iris. if it were based on the focal lenght, then the speed of the lens would loose a stop every time you double the focal lenght (even with compensation, soon you'd be wide open) At most you loose a stop or two in the entire range on a zoom. a 7.5mm-120mm lens would not loose 4 stops over its range.
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### #7 Stephen Williams

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Posted 06 March 2007 - 04:10 PM

Your confusion lies in your calculation. Fstop is not a relationship of FOCAL LENGTH to iris appeture, rather its a measurement of the FRONT ELEMENT to the IRIS appeture (what troy called entrance pupil) Since the zoom lens does not change its front element, the F-stop remains contsant.

Hi Michael,

The entrance pupil on a lens is the point that DOF is calculated from! On a zoom lens it probably is not the front element & will move as you zoom!

To make the FOV the same on a prime & zoom lens the entrance pupil's must be in the same place, so the camera will have to be moved. This is also the reason that seperate DOF charts are supplied for zooms. (We measure from the film plane to make our lives easy)

Stephen
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Posted 06 March 2007 - 07:11 PM

so, a zoom lense consists of a back element containing the aperature and a front element containing the zoom. This is essentially like having a prime lense with an afocal attatchement only it can vary in focal length.

The back element views an image that has increased in size and decreased in field of view as one zooms in.

That makes sense, but how does the lense compensate for the loss of light as the field of view and the amount of light hitting the film plane decreases?

Just yesterday I was dead certain that the 'f' in fstop represents Focal length and the stop number is a fraction i.e. 50mm lense at f2 = 25mm aperture diameter. Is this not correct and can someone just clarify, does an aperture compensate for a loss in light transmittence as a lense zooms in and less light hits the film plane?
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### #9 Troy Warr

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Posted 06 March 2007 - 09:49 PM

Just yesterday I was dead certain that the 'f' in fstop represents Focal length and the stop number is a fraction i.e. 50mm lense at f2 = 25mm aperture diameter. Is this not correct and can someone just clarify, does an aperture compensate for a loss in light transmittence as a lense zooms in and less light hits the film plane?

This article should explain that more clearly. The "f" is actually just a variable, and is used quite often within equations in this optics book that I'm reading.

A brief quote from the aforementioned link:

"The slash indicates division. For example, f/16 means that the pupil diameter is equal to the focal length divided by sixteen; that is, if the camera has an 80 mm lens, all the light that reaches the film passes through a virtual disk known as the entrance pupil that is 5 mm (80 mm/16) in diameter. The location of this virtual disk inside the lens depends on the optical design. It may simply be the opening of the aperture stop, or may be a magnified image of the aperture stop, formed by elements within the lens."

Regarding your question about aperture compensation, if you're asking whether the aperture changes its size as you zoom, it does not. Zoom lenses with a constant aperture are designed differently than lenses with variable aperture; the lens elements move in such a way as to preserve the focal ratio as the lens zooms, but this is not done by any manipulation of the aperture size.
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### #10 Chris Keth

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Posted 06 March 2007 - 10:05 PM

Your confusion lies in your calculation. Fstop is not a relationship of FOCAL LENGTH to iris appeture, rather its a measurement of the FRONT ELEMENT to the IRIS appeture (what troy called entrance pupil) Since the zoom lens does not change its front element, the F-stop remains contsant.

This is simply not correct. The definition of an f/stop does not change when it is applied to a zoom. Your way gets you to the same place as the correct calculation, however. The entrance pupil (or as you say the effective front element size) does change and it changes with focal length. In fact, it changes exactly proportional to the focal length with good cine zooms. This relationship is how you end up with a constant stop.
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### #11 Mike Rizos

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Posted 06 March 2007 - 11:31 PM

There are two methods for the movements of the elements within the lens. Optical and mechanical.

To maintain constant f-stop: The mechanical method is to use a cam that adjusts the size of the diaphram opening as the focal length is changed. The optical method is to use a positive element in front of an afocal component in the front group of elements, that allows the moving element group(s) to focus, AND the diaphram to be a constant distance from the film plane.

To zoom: The optical method moves a group of elements the same distance. The mechanical method involves moving different elements by different amounts.
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