Depth of field and focal length

Hi all: I'm reading "The Camera" and have been studying the lenses

section and I need help understanding the last part of the following

quote:

 

(from the "Focus and Depth of Field" section, para 4)

 

"The factors affecting depth of field are governed by the following

principles:

 

1) The depth of field doubles if the f-number is doubled (e.g.,

from f/8 to f/16).

 

2) If you double the subject distance, the depth of field

increases by four times; triple the distance, the depth of field

increases by nine times (depth of field is proportional to the square

of the distance).

 

3) If you reduce the focal length by one half, the depth of

field increases by four times (depth of field is inversely

proportional to the square of the focal length). "

 

Can someone explain #3 to me? I?ve studied this section for hours and

I am just not getting it.

 

Many thanks,

Gloria

I didn't really know where to put this post. If the moderators know of a more appropriate place, please move it! Thanks.

I am a beginner so here is my take on #3......

 

Say you have a 300mm lens, you get a depth of field that is good for potraits and blurry backgrounds etc. ie a shallow depth of field.

 

Now say you have a wide angle lens, the depth of filed is better suited to other subjects like lanscapes, more depth of field.

 

Unless you love math or need to calculate the depth of field very precisely, I reckon that it is easier just to use certain lenses for certain jobs etc. Like, this is my portrait lens, or this is my landscape lens.

 

 

I may be totally wrong of course!

 

Cheers.

Also, it depends what format you wish to use.

 

I use a big rangefinder, I have to know what the depth of field will be for each separate lens. I also use an slr with depth of field preview, I can see the depth of field through the lens.

 

Cheers.

If you understood #2, note that #3 is saying almost exactly the

same thing.

<p>

Suppose you had a 200mm lens at f/8, focused on a

certain target with a certain depth of field. Now, let's apply

rule two backwards. Move closer, so that now you're half the

original distance to the subject. According to rule 2, your depth

of field got cut down to 1/4 what it was in the original scenario.

<p>

Note that a side effect of halving your subject distance is

that your original subject no longer fits in the viewfinder like

it did at the start. If you want the original subject to fit

in the viewfinder with something like the original composition

from your closer vantage point, you'll have to halve the

focal length, or go to a 100mm lens at f/8.

<p>

Rule 3 just says that when you halve the focal length, you quadruple

the depth of field, in other words, restoring the depth of field

to what it was in the original scenario with the 200mm lens at f/8

from the original vantage point farther away.

<p>

Someone will probably point out that these rules aren't entirely

accurate if you're measuring to great precision, but they are

very good first order approximations, especially for close-ups.

Lets denote d = depth of field and f = focal length. The book says d is inversely proportional to f^2, that is, (f X f). This is equivalent to d = k/fXf where k is an unknown constant. If f = 25, d = k/25X25 = k/625. If f = 50, then d = k/50X50 = k/2500. So when x changes by 1/2 (from 50 to 25) d changes by (k/625) divided by (k/2500) = 2500/625 = 4. So d becomes four time when x changes by 1/2. Hope this helps.

But who's on first?

 

OOOOO!

Inversely proportional means that something increases or decreases in the opposite direction to something else. Kind of like the height of you and a friend on a teeter totter. As one goes up, the other goes down, and vice versa.

 

So all #3 is saying is that if your focal length increases (or your focal length squared), then dof decreases. Conversely, if you reduce the focal length by half (eg. 100mm to 50mm), then your depth of field increases by 4 times.

 

That seemed to easy. I don't think that answered your question.

 

Looking at it some more, it also seems to say that a simple doubling or halving of the focal length won't double or halve the dof. It's not DIRECTLY inverse. That's why they say the SQUARE of the focal length. So if you double the focal length (from 50mm to 100mm for example), you only have 1/4 the dof. If you quadruple the focal length (from 50mm to 200mm for example), you'll only have 1/16th the dof.

 

The opposite will also be true then, so that if you halve the focal length (from 200mm to 100mm for example) then you'll have four times the dof.

Gloria:

 

There are really only three factors governing the subject of depth of field for 35mm cameras specifically and other film formats generally.

 

Hopefully, the following discussion will boil them down for you, but before we get into that topic, there are a few basics you will need to know.

 

1. First of all the eye doesn't see so well - especially under available or poor lighting conditions. The general consensus is that the human eye can see a circle as a dot, if that circle has a diameter of l/100 of an inch or less on an 8 X 12 (or sometimes 7 X 10) enlargement held approximate ten inches away.

 

That means that in order for the circle of confusion (it's correct name) to be see as a dot on the above standards, that circle of confusion has to be 1/800 of an inch in diameter on the negative.

 

Thus - the need for critical focusing = especially when shooting at wide aperatures under available light conditions. The problem of critical focusing under such conditions has been solved in various ways - i.e. the use of rangefinder cameras or using high aperature lenses on SLR cameras, i.e. a 50mm F/1.4 lens versus a 50mm F/2.0 lens.

 

Obviously, if you're slightly out of focus with a 35mm F/2.0 lens on a 35mm SLR camera - which can easily happen especially under low light conditions - you may start off with a large "circle of confusion" on the negative or slide. The more you enlarge an unsharp image (negative or slide), the greater the unsharpness will be noted in the final enlargement or projected image.

 

For that reason, discussions of depth of field cannot be separated from the issue(s) of critical focusing - again and especially under available light conditions.

 

If you wish to check this out, you can simply put on a wide angle lens on your SLR, turn off the lights in a room to make it semi-dark - like in the late evening and then walk about 12 - 15 away from the subject or point of focus. With an SLR camera, you may find it very difficult to be certain of accurate focus under these conditions. For example, you may find that you're actually focused at infinity when in reality the subject is only 12 feet away.

 

Why? For one thing, our eyes don't see to well; for another, a wide angle lens on a 35mm SLR camera will make the image appear smaller and/or further away, thus making the "details" more difficult to see. Under such conditions a split image focusing screen can be very helpful. Depending upon the type of rangefinder camera, a rangefinder camera will be able to focus both accurately and rapidly under nearly all available light conditions using lenses from 21mm or lower to up to either a 90mm focal length or a 135mm focal length. An old Leica M-3 would be a good example.

 

To give you another example, my 90mm Summicron F/2.0 focused at the closest distance (about 3.5 feet) and using the lens wide open (F/2.0) has exactly 3/4 of an inch of depth of field - which is less than the distance from the tip of most people's noses to their eyes. So what's the point of focus to be and how accurate is it going to be? are useful questions to ponder and/or resolve.

 

Now that you have, hopefully, understood this discussion - let's go onward to the two important factors regarding depth of field and then we'll tackle the third and most important factor.

 

2. From a technical stand point, depth of field is dependent upon only two factors (1) the aperture of the lens and (2) the ratio of reproduction. Or to put it in another way, all lenses will exhibit exactly the same depth of field if they are used at the same aperture and at the same ratio of reproduction.

 

Verification of this basic factor can be found in some of the older and better books on photography - namely - most editions of The Pentax Way or The Leica Way, etc. In the back of these books, you find a series of depth of field tables, especially for macro work or photomacragraphy.

 

In short, a 50mm macro lens and a 100mm macro lens set at F/4.0 and at a reproduction ratio of 1:2 will have exactly the same depth of field.

 

Obviously, this may bring up - in your mind - the topic of what is meant by the "ratio of reproduction".

 

The ratio of reproduction represented by the 1:2 - above - indicates - first - your film size, or 24mm X 36mm or approximately 1 X 1.5 inches. The second number (2) indicates that the area that your lens is covering - in this case it is twice as large as your negative or 2 X 3 (1 x 1.5) X 2. Therefore, a reproduction ratio of 1:10 would indicate that your lens is covering an area of 10 x 15 inches. And so on and so forth.

 

Therefore, you should now realize that the only reason that wide angle lenses "appear" to have a greater depth of field to most people is that they are simply standing in the same place, but changing their normal lens (50mm - for example) and putting a 28mm lens on the camera. Obviously, you have automatically changed the ratio of reproduction by simply including a far wider area with the 28mm lens.

 

However, if you would change back to the 50mm lens and then walk backwards to include the same area of coverage as your 28mm lens, you would end up with exactly the same depth of field.

 

Obviously, you should now understand the statement made in the third sentence.

 

One of the most unfortunate aspects of photography is that you (and many others) will encounter a host of explanations for various kinds of photographic techniques, procedures, etc. and equally unfortunate much of it will amount to little more than "verbage" or outright "BS".

 

One good example that I well remember came from reading Ansel Adams explanation of his famous photograph of the moon rise taken somewhere in the southwest - New Mexico, I believe. Sorry, I can't remember the exact title given to this wonderful photograph.

 

In reading his discussion of how this photograph was taken, Adams goes through all sorts of language contortions about the exposure value of moonlight, how he calculated the "exposure" of this moonlight, etc., etc., etc. And then his finishes the discussion by stating that he made one or several "calculated safety shot(s)."

 

When I originally read his discussion, I laughed out loud at his "calculated safety shot(s). What a "BS'er" I thought and still do. Why can't this man use the same term that everyone else does?

 

A rather highbrow term for the simple matter of "bracketing."

 

Obviously, Ansel Adams was a good photographer, but he was also, IMHO, rather pretentious and verbose. Somewhere there is another example of Ansel's verbosity, you'll find it in a discussion between Ansel Adams and Peter Stockpole who wanted to join the F/64 group and who was fired for using a "miniature camera" on the job. The "miniature" camera in question was an early screw mount Leica. Sorry, I can't remember the title of the book, but I think it was in a book written by Peter Stockpole about his photographic experiences and/or working on photographing the building of the Golden Gate brige.

 

At the beginning of this discussion, I indicated that there were three factors concerning depth of field and that the third factor was the most important.

 

Well, what is the third factor?

 

Aesthetics - pure and simple.

 

At this point, you must learn to merely keep in mind the basic principles that I've discussed (clearly, I hope) above and concentrate more on what you wish to convey artistically.

 

Years ago, when I was at New Salem State Park - near Springfield, IL - the park had an interesting event going on - during the early winter.

 

One of the events being "exhibited" were a small group of women quilting in one of the log cabins. I approach one of the women and began discussing whether or not she had read the book or seen the play of nearly the same name: The Quilters: Women and Domestic Art. (I highly recommend both reading the book and/or seeing the play.) Mostly, because I wanted to convey the information to her and secondly it was a means of breaking the "ice" when photographing people.

 

While I was discussing the book and the play, I took an incident light meter reading and set my shutter speed and lens opening accordingly. I can't remember the shutter speed, but the aperture was set at F/2.0 since I was using Kodachrome 64 slide film, my Leica M-4 and the 50mm Summicron.

 

I deliberately focused on the women's eyeglass frame, composed and tripped the shutter. Turn out superb!! Again IMHO!! ;>)

 

Generally, most people might have focused on her eyelashes or her eyeball, but I chose the eyeglass frames instead because I wanted them to be in sharp focus. And more importantly, because I deliberately wanted to soften the lines in her somewhat aged skin, i.e. soften the wrinkles in other words. In my head, I already knew that the depth of field was going to be rather, if not very, shallow.

 

In short, I simply made quick use of my technical knowledge and previous experiences and use them to determined what kind of aesthetic results I wanted.

 

Obviously, now that you know something more about depth of field, you are going to have to do some experimenting with different focal lengths and/or apertures to see what kind of results you will obtain and then use the results to narrow them down to what you wish to obtain. It may take some time and practice, but that's the fun and sometimes fustrating part of photography.

 

My best wishes in your endeavors and I do hope this not so brief discussion clears things up.

 

Bill

 

 

There are a lot of misconceptions about Depth-of-Field. The statements you have listed are correct for images taken from a fixed position. As to #3, think of the size of the aperture as seen from the front of the lens. Let's say that you are shooting with a 4"x5" field camera, and had a 10" (254mm FL) lens on it to get that alligator on its nest. At f/8 the entrance pupil diameter, as seen by you, is 1.25". Now you want to get a wider view of its habitat so you switch to a 5" (127mm FL) to get twice the view. Looking at the front of the lens set at f/8, the aperture is only 0.63" and you haven't moved the camera. (Or so you hoped.) This restricted aperture now "sees" 50% less around any detailed subject like a branch, bird or flower. Well that accounts for a doubling of the depth of field right there. But what about the final image? Well it is 50% smaller so the blurring of the out-of-focus edges are also 50% less. Combined, that gives you a reduction of the Out of Focus portions to only 25% of what the 10" lens gave you. You now have a four-fold increase in DofF!

 

I would want to point out that this does not apply when you are moving your camera around to gain what you may have lost in changing lens focal length:

 

For any given image size, depth of field depends only on relative aperture!

 

This may not seem self-evident, but the analogy is similar to the previous logic with a fixed location, and changing FL. It even holds for changing format sizes when the final image (print) is identical.

Different focal lengths will now change the size, and degree, of the out-of-focus backgrounds (and foregrounds) for control of composition and distracting elements.

 

DoF is not an easy subject to understand. I heard a lecture on it last year where the speaker espoused several errors that I didn't have the heart to address.

 

Nikon has an interesting brochure that shows a series of photos on the effect of keeping the subject size constant while varying the focal length, and then keeping the distance constant. If you are interested, I'll see if they are still avaliable.

 

Hope this is of help to you.

Gloria:

 

A shorter and second round of discussion.

 

If you link to the site listed below, you'll find a good example of what I was previously discussing. Once you arrive on the scene - so to speak - scroll down until you find the photograph - on the right side - titled "Premiere at La Scala, Milan," 1933 read the notes about the photograph or the whole article and then scroll all the way down and read the last paragraph and take note!!!

 

If you wish to explore this photographer a little further - Eisenstaedt was one of the original photographers for Life magazine - there is an excellent book entitled: "The Eye of Eisenstaedt". Unforuntately, it is out of print, but may be found at or through the inter-library loan system at your local public library.

 

This book is an excellent "arm chair read" - where you can curl up on a comfortable place, sip on some coffee, tea, wine or some other beverage and read and learn in an enjoyable manner. The book combines a little autobiography, good basic, but small, discussions on (his) photography, etc., but most important is is a book on how to see photographically.

 

http://artscenecal.com/ArticlesFile/Archive/Articles1997/Articles0397/AEisenstaedt.html

 

Again, I hope that this added tidbit is useful in your endeavors.

 

Best regards,

 

Bill

Gloria:

<p>

Here is a parallel application of the same rule.

<p>

If you are taking a photo on 35mm film with a 50mm lens set at f/8, the hyperfocal distance is 45 feet.

<p>

You you switch to a 24mm lens (cutting the focal length to a hair less than half of the 50mm lens), the hyperfocal distance at f/8 will now be 11 feet, very close to 1/4 of the 50mm hyperfocal distance).

<p>

A look at <a href="http://jimdoty.com/Tips/Depth_of_Field/Hyperfocal_Distance/hyperfocal_distance.html"> this chart might help</a>.

<p>

If you are working in a different format, the numbers will change but the principle is the same.

<p>

Happy Shooting!

<p>

Jim

Holy smokes. Ask and you shall receive... Thanks a bunch, folks! It's a litle early right now so I'm going to print this thread and read it in a couple of hours when I'm more awake.

 

THANK YOU!

Jim, you wrote these backwards... the 24mm has the larger range in focus...

Like they said, a 24mm lens has 4X the DOF of a 50mm lens at the same f/stop.

 

OTOH, I hear you're shooting 4x5 now, Gloria. Keep in mind, that once you've tilted the lens relative to the film, depth of field becomes very complicated, to the point where "normal" DOF calculations can safely be thrown out the window. Also, LF lenses usually offer you the ability to stop down to where diffraction becomes more important than defocus. With LF cameras, the f/number you get from standard DOF tables and formulas is often not the optimal one.

Thanks Alan. I am just beginning to explore the differences between 35mm and LF lenses, and that little tidbit is going to help. I have to give you technical folks your due for knowing your stuff.

 

Actually, I spent the day painting yesterday, two days in a row of studying lenses was just not going to happen for me. I'm back on the case today and hopefully lights will go on and bells and bells will ring very soon. Thanks again everyone, what a wonderful resource.

Dear Gloria:

 

You're more than welcomed with all of the information regarding depth of field; I am glad to be of assistance.

 

Now - here's some more information, which I also hope you will find very useful.

 

Decades ago, I taught "Architectural Photography" for a number of years at Illinois Central College in East Peoria, IL.. Since the course was taught under the auspices of the Architectural Department, it was basically a course in good, 35mm photography with an architectural emphasis, especially as none of the students had or could afford a 4 X 5 view camera with one or several lenses.

 

Somewhat surprising to me at the time was the fact that many of my students also had difficulty in understanding depth of field. From that point onward, I thought and still believe that the best way to understand and work with depth of field is to approach photography with a sense of aesthetics first and then make use of various techniques to (hopefully) achieve the results you wish to put on film. A point which will lead us back to a further discussion of Alfred Eisenstaedt's photograph of the young society lady at the La Scale Opera house decades ago.

 

Using the SWAG method ("scientific" wild ass guess), I suspect that Eisenstaedt took this photograph with a 35mm lens on his screw mount Leica camera. One of the reasons why I choose this photograph was to - obviously - introduce you to this original Life photographer and, of course, to show you this particular photograph as an example of using a sense of aesthetics and then using

various techniques to achieve the results you want.

 

As Eisenstaedt correctly states, the young society lady makes this photograph 'come alive'!! Without her and, especially, her expression, the photograph would have been dead in the water. The viewer's eye is first directed to her presence and expression and then wanders around to the rest of the photograph. It is a good example of how aesthetics play the defining role in determining depth of field - as it well should be.

 

Equally obvious is the fact that had Eisenstaedt attempted to create a greater depth of field, this photograph would have been dead in the water as well. Why? Well, any time that you make use of a smaller aperture you have to have a corresponding increase in exposure time in order to obtain a correct exposure. Had he attempted to have everything in focus from foreground to background, he would have had to make use of a rather small lens opening and his exposure - under these available light conditions - would have been incredibly long. Since the point of the photograph was to rapidly record the young's expression in the foreground, the point of focus had to be on her face. So now we are back to the starting point of my first response, i.e. accurate focus!

 

Another example to share.

 

Several decades ago, I traveled to Alameda, California to visit my cousin and his bride to be. Since Ken was still teaching at the local community college during the week, I took off to downtown San Francisco and begin to wander around one of the more famous downtown squares to see what I could photograph.

 

While visiting one of the more famous downtown gathering places, I immediately spied two older ladies who were dressed in their Sunday best; who were also sitting close together; and chatting away in a rather delightful and animated manner. I knewthat if I pointed my camera at them that they might immediately recognize that I was about to take their photograph to which they might object and/or which might have made them both self-conscious. I also noted the fact that these women - like most - didn't mind being physically close to one another, but for some reason most of us men seem to need to have some "space" between ourselves and another man.

 

Since I had the 90mm Summicron F/2.0 on my Leica M-4 camera, I knew that it had a limited depth of field in comparison to my 50mm Summicron. From my previous experiences, I knew that using a lens opening of F/8.0 that I would have slightly more than enough depth of field to cover a little more from foreground to a little more in the background of the two ladies sitting on the park bench. I also suspected that at this aperture I had enough depth of field to cover any possible error in focusing.

 

I quickly focused on an area that was a similar distance from the two ladies; took a meter reading to determine the shutter speed for an aperture of F/8.0; set the lens opening and shutter speed accordingly, swung around; rapidly composed the photograph; and tripped the shutter.

 

Even though the Leica's shutter is extremely quiet and soft and I made no 'noise' - ;>) - to bring attention to myself; the two elderly ladies must have suspected that they were being photographed and immediately asked me to desist and not take anymore photographs. Obviously, I responded by simply smiling and acknowledged their wishes. Why? Because I had simply achieved the results I wanted.

 

By the way, I was using Plus-X B & W 35mm film and developed the negatives in Microdol-X at a 1:3 ratio to give me a long tonal range and enlarged it - easily - up to a 16 x 20 print using a used Leitz Valoy II enlarger that I had purchased used.

 

Here again, we are simply making use of a sense of aesthetics and then subjecting our technical knowledge and experiences to achieve the results that we want.

 

You now know - or should know - that wider apertures, such as F/2.0 or F/4.0 will provide you with a relatively shallow depth of field; that moderate apertures, such as F/5.6 or F/8.0 will provide you with a moderate depth of field; and that smaller apertures, such as F/11 or F/22 will provide you with a greater depth of field.

 

You now know - or should know - that if you change from a normal, i.e. 50mm lens to a wider angle lens, i.e. a 35mm or a 28mm lens, you will cover a wider area or angle of view, which will make everything seem to be smaller and further away, and that because of the greater ratio of reproduction, i.e. greater angle of view, you will correspondingly increase your depth of field using the same vantage point.

 

You also now know - or should know - that if you change from a normal, i.e. 50mms lens to a narrow angle lens, i.e. a 90mm, a 135mm or a 200mm lens, etc., you will cover a narrower area or angle of view and thus make everything appear to be closer and larger and that because of the smaller ratio of reproduction or lesser angle of view, you will correspondingly decrease your depth of field using the same vantage point.

 

You also now know - or should know - that each of your lenses will provide you with a different angle of view, if you stand in the same position and that if you change positions your lenses, will give you a different perspective in achieving your photographic projects

 

You also now know - or should know - that in the area of photomicrography - your lenses will provide you with exactly the same depth of field - provided you are (1) covering the same ratio of reproduction and (2) are using the same lens opening.

 

You also now know - or should know - that if you change your lenses and your position from the subject so that each of the lenses will cover the same area, you will not only achieve a different perspective, but that you will have exactly the depth of field, if you make use of the same aperture.

 

Except in the field of photomicrography, you will or may not need to critically address the matter of depth of field. You will or should, however, keep all of the above "technical" factors in mind when you photograph and then, as I will state - once again-* let your sense of aesthetics determine the various photographic techniques and/or lenses, etc., etc. to be used to produce the results intended.

 

Since you paint, you realize that you would not use a broad brush and/or a broad brush stroke to achieve fine detail in your painting. The same artistic principles hold forth in photography as well.

 

So for all of the above reasons, I would again urge you to read "The Eye of Eisenstaedt" by Alfred Eisenstaedt. It will provide you with an interesting biography of an excellent photographer, further encourage you to "see" better photographically and add to your wealth of knowledge and experiences.

 

I would also encourage to you to read "Better Colour" by Walther Benser, an old Leica photographer. Again and unfortunately, this excellent book is out of print, but it still has much to offer, especially in further introducing you to seeing better photographically and showing you how lenses provide you with a varied range of perspectives. Again, you should be able to obtain a copy at or through your local public library (interlibrary loan).

 

It is a little out of date with regard to film and cameras - Benser used a Leica M-3 and the then current range of Leica lenses and used Agfa film, since he was a German photographer, who gave illustrated slide lectures throughout the United States decades ago. Although Leica now makes an M-7 and a range of other types of cameras along with a current range of lenses, his book will also provide good background should you consider adding an older Leica and lenses to your photographic palette.

 

A final recommended book contains wonderful photographs, but has little or nothing to do with photography. It does contain photographs of various women who made quilts and many of the quilts that they made. The book also contains an excellent discussion of how the quilts these women made reflected various aspects of their lives.

 

Fortunately, it is still in print and should available at or through both your public library or better bookstores. Its title is "The Quilters: Women and Domestic Art" by Patricia Cooper, et al. If by chance, you come across a play of the same name, i.e. "The Quilters" please take the time to enjoy the experience, as it is based upon this book.

 

In the introduction in this book, the two authors - sorry I can't remember the name of the second woman author - recall their experience when interviewing one couple in gathering up materials for this book.

 

They were surprised to find out that this woman's husband quilted right along with her; even more surprising, they couldn't tell the difference between her stitches and his. Even more significantly, was the comment made when the two authors were leaving their home. He wanted to make certain that "he only did the quilting. She's was the one who made the light shine."

 

What a wonderful acknowledgment of the artistry of one person by another!!!!

 

Again, I hope all of this extensive discussion greatly assists you in your photographic endeavors. By the way, I am posting this response on photo.net for others to enjoy or use.

 

Again, my best wishes!

 

Bill