Truth in Perspective
an exercise based fact deduction activity
from the Materials and Processes of Photography course notes at SPAS/RIT
The photographer who made the original photograph claimed that they were made with two different focal length lenses and that he changed his position with respect to the church building in the foreground by some unknown factor. His statement is included below. Was he telling the TRUTH about his change in lens focal length and by what factor did he change his distance to the foreground church building?
So, how did you do? Just to review the "concept" in this little exercise associated with one of about 25 different topics included in the Materials and Processes of Photography course that every photography student in the School of Photographic Arts and Sciences at RIT is required to complete ... the underlying optical parameters or relationships are that:
OK ... no cheating now ... work out the problem first and then go on to the next few paragraphs to find the answer to this exercise in photo-logic.
1. Given distant objects (such as the two mountain tops) changes in focal length of the camera lens result in corresponding changes in image size. Another way of saying this is that the image size of a distant object is directly related to lens focal length.
In this example, if you measure the distance between mountain-tops in the left image and then in the right image you will find that the image size has changed by a factor of 1.8X and thus the photographer must have used a 270mm lens (approximately) given that the photograph on the left was made with a 150mm lens.
2. On the other hand, image sizes (to any subject but perceived mostly to nearby subjects) change inversely with object distance. That is, the smaller the object distance the larger the image. Obviously small changes in camera position, even of a few hundred feet, when it comes to subjects several miles away (such as implied by these photograph that include mountaintops) have little effect in the size of the reproduction of those landscape features. One would have to move significantly closer or farther away to detect a perceptible change in distance between mountaintops.
* note: this assumes that the camera lens does not need to be refocused as this effectively changes the lens to film distance - this is of particular "concern" in close-up photography but the effects tend to be minimal under most normal conditions.
In this example, the change in focal length should have increased the size of the image of the church in the foreground by the same factor as the focal length was increased by (based on the increase in distance between mountaintops). If in the left image the church is 2 inches then in the right one it should have been 3.6 inches or about 1.8x bigger in the second photo than in the first. But it is not.
This must have been the result of the camera position having been altered. So, once we know how much bigger the church dimensions _should_ be (due to change in focal length) we compare that to the what what it really _is_ and we find that the church is about 2.4x smaller than what it should be.
In other words, this diminution is image size over what was expected is accounted for by the fact that the camera position was changed so that the new position is 2.4x farther from the church than where the camera was for the first photo.
You can follow along by substituting YOUR measurements into the following text.
Since your monitor may display the images at a different size than mine I will assume that the distance between mountaintops in left photo is: 2 inches and in the right photo it is: 3.6 inches. 3.6 divided by 2.4 = 1.8
150 mm original focal length multiplied by 1.8 is 270 mm which is the determined new focal length.
Measuring the distance between edges of the church I find that the church in the left photo measures 2 inches while in the right photo the distance between the same edges is 1.5 inches. Yet it _should have been_ (as a result of the focal length change) 2 inches times 1.8 or about 3.6 inches. So, how much farther than the original camera position would the camera have to be moved to to cause a _decrease_ in image size of 3.6 inches to 1.5 inches? You guessed it, 3.6 / 1.5 or 2.4 times farther than its original position.
Church edges in left photo are 2 inches apart. This should have made the church be 2 inches times 1.8 or 3.6 inches in photo on left.
But church measures 1.5 inches. Why? Camera distance to church was changed! By what factor? Well, 3.6 inches divided by 1.5 inches or a factor of 2.4x.
So, there you have it! This is but ONE of several perspective related questions M&P students used to be exposed to in the Perspective Workshop in M&P. I hope you found this little exercise informative.
Give yourself a pat on the back if you completed this project successfully! :)
If you are a School of Photographic Arts and Sciences faculty member or, in fact, a pro or amateur or faculty member elsewhere, want to answer a few questions? If you are a SPAS faculty member send the answers to Andy Davidhazy if you want to. My email address is: firstname.lastname@example.org Otherwise maybe raise this topic as one of interest on photo mail lists or whatever other photo venue you wish. Here are the questions:
1. Do you think that SPAS photography students (or other photo students in fact) should be exposed to material such as this?
2. Do you think that material like this is too difficult for SPAS students (or photo students elsewhere) to tackle if they don't have an advanced mathematical background?
3. Would you like to see additional future "hints" as to what M&P in SPAS is all about?
4. Was an error made in this workshop? If so we would be delighted if you would point it out so we might do better in the future.
5. Would you like a copy of the Workshop book that M&P students have to purchase from the bookstore? (This "deal" only for faculty members in the School of Photographic Arts and Sciences at RIT!)
hmmmm ... I can't think of any other questions. Have a nice week!
- who is obviously impressed by the simplicity of this project and its educational value