At What Focal Length? (85mm f/1.8 vs 70-200mm f/4L)

Let me label the diagram you posted with the terminology I am using. We call the distance from the point "Camera" to the point "Subject" the subject distance, which we might label S. The distance from "Subject" to "Lights" is the subject-to-background distance, or B. We will use the traditional F for for focal length and N for f-number. Finally, not directly shown in your diagram is the subject magnification M, which is the ratio of the size of the subject on the image plane, to the size of the subject in the object plane. In other words, M is simply the size of the subject in focus on the sensor divided by the size of the same subject in real life.


When you say that you want to maintain the same "frame of view," what you are actually meaning is that you wish for M to remain the same. For a pair of different focal lengths as you have drawn in your diagram, what this requires is a change in S, which you have also drawn. You have also shown that because F relates to angle of view, changing S also changes the relative size of the blur circle at S+B.


But as you have correctly surmised, by stopping down in the lower diagram, you are able to decrease the size of the blur circle to match those in the upper diagram. Alternatively, you have also correctly inferred that, if the f-numbers of the upper and lower diagrams are fixed at, say, f/1.8 and f/4, then there is a relationship between the focal lengths that would result in the same degree of background blur.


However, what my previous posts have explained is that this relationship would only hold true for a SPECIFIC subject distance S and a SPECIFIC subject-to-background distance B. If you changed either of these, then the focal length required in the lower diagram to match the degree of blur in the upper diagram will also change. Even worse, there are certain combinations of S and B for which NO focal length in the lower diagram will give you the same degree of blur.

Fortunately, I have created this nifty tool to illustrate the relationship between focal length, f-number, magnification, subject-to-background distance, and blur circle diameter. Below, we assume a fixed magnification M = 1/30. For the focal lengths being compared, the subject distance is automatically calculated so as to achieve this value of M. Then the value of B is logarithmically plotted on the horizontal axis, and the blur circle diameter in the image plane is plotted on the vertical. We have two hypothetical lenses, an 85/1.8 and a 189/4. This chart demonstrates the principle we previously discussed, in that for a background at infinity, the blur circles for both lenses are the same size (about 1.56mm). But as you can also clearly see, when a background object is not infinitely far away, the blur circle it projects on the image plane will not be the same in both cases--the longer lens' blur circle is smaller at each value of B. it should also be noted that, for any lens at f/4, 188.88mm is the shortest focal length that will yield this behavior; any shorter, and the blur circle will ALWAYS be smaller than 85/1.8, even at infinity, no matter the magnification chosen.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/5381.coc06.gif[/img]


Next, we show another comparison, the same 85/1.8 against a 300/4, for the same subject magnification (M = 1/30). Note the red curve is unchanged (only the vertical scale has changed), but now the 300mm lens shows that at a subject-to-background separation of about 8.5 meters, the two lenses will have the same blur circle diameter. Beyond that, the 300/4 renders objects much more blurry.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/5700.coc07.gif[/img]


Finally, we see how changing the subject magnification also affects the degree of blur. Here, we have chosen a relatively large value of M = 1/5, again between the 85/1.8 and 300/4. Notice that the shape of the curves appears to have shifted to the left, but also the vertical scale has increased greatly, so that the blur circles are MUCH larger than in the M = 1/30 case. In this scenario, the crossover occurs around 1.6 meters.


[img]/resized-image.ashx/__size/716x0/__key/CommunityServer-Discussions-Components-Files/12/3007.coc08.gif[/img]


I hope these diagrams help. It is my intent to make this interactive tool freely available for use by the general public in the near future.

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Originally Posted by wickerprints

Fortunately, I have created this nifty tool to illustrate the relationship between focal length, f-number, magnification, subject-to-background distance, and blur circle diameter.

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Now I have to ask this, and this questions is for the OP as well: Why? What would a scenario be that aperson would need to know the blur circle of two diffrent lens and try and match them to the same size?

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Originally Posted by wickerprints

It is my intent to make this interactive tool freely available for use by the general public in the near future.

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Great work! I'd love a copy, when it's ready for sharing. Looks like it'll run on my Mac. [H]

Wow! Thanks for the amazing explanation to go along with your extremely clever tool!!


So would a high-level generalization be that if your subject is close to the background then the most blur will come from aperture butif the subject is far from the background then most blur will come from iris size?

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Originally Posted by HDNitehawk

Now I have to ask this, and this questions is for the OP as well: Why? What would a scenario be that aperson would need to know the blur circle of two diffrent lens and try and match them to the same size?
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To be clear, I did not create this tool in specific response to the OP's question. It has existed for some time now, because I was initially interested in exploring the question of which lenses will give me the greatest amount of background blur for a given set of conditions; and as you can see, the answer is not as straightforward as you may be initially led to believe. In fact, there are certain cases where, say, a 50/1.2 will give more background blur than an 85/1.8 but only up to a certain subject-background separation. I was not specifically interested in the point at which two lenses will yield the same blur circle diameter--but this tool happens to be easily adapted to show this.


Developing this tool has helped me to weigh my future lens purchases. It took about an hour of programming and debugging in Mathematica 7, then a few more hours of tweaking to make it look pretty. I plan to put it in a standardized notebook format with appropriate annotations, to prepare it for publication via the Wolfram Demonstrations Project.

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Originally Posted by wickerprints

To be clear, I did not create this tool in specific response to the OP's question.

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Darn! I would have been so honored! [;)]


Thank you so much for the elaborate explanation! I think I understand what your are trying to say but I'll be re-reading this multiple times for sure.


For those who were wondering. I was not trying to get the exact same OOF as the 85mm f/1.8, but just seeing if the lens itself was capable of creating OOF that was equivalent to or better than the 85mm f/1.8. As explained by wickerprints, the answer wasn't as simple as I had hoped for, but I now know that if used correctly I could basically substitute (to a degree) the 85mm f/1.8 (which I don't have) with the 70-200mm f/4L (which I do have)


Just trying to save myself ~$350 by utilizing my current gear to it's fullest [:D]

Thanks for the great diagrams, wickerprints, very informative.