Quote of the Day
There may be honor among thieves, but there’s none in politicians.
— TE Lawrence, Lawrence of Arabia. Our 2016 presidential election seems doomed to support Lawrence's assertion.
Introduction
Figure 1: Great Photo of the Moon and a Ship (Source).
I often see photographs that appear to show objects with different size relationships than we usually see. In Figure 1, for example, we see the Moon as nearly the same size as the sailboat. This happened because the sailboat is some distance from the camera, and its angular extent is comparable to that of the Moon.
These types of photographs are easy to setup and can be useful when you want to control the angular relationships in a photograph. The technique is called forced perspective and has been used in movie making since the beginning. Even today, I often see movies that use force perspective to create the illusion of huge monsters or people. The Lord of the Rings movies made extensive use of forced perspective. The following Youtube video does a good job showing how they setup these scenes.
Background
General Information
There is an abundance of material on how a camera captures angular relationships, so I only provide a few reference links for those who want more details. The following links are very good.
One fact that I will use is that the Moon subtends an angle of ~0.5 °. We can easily determine this value as shown in Figure 2.
Figure 2: Computation of the Angular Extent of the Moon.
Objective
My plan here is to:
- Provide a qualitative explanation for the seeming distortion of angular sizes in photographs.
- Show how we can extract some information about the sailboat in the photograph.
Analysis
Angular Relationships
Figure 3 illustrates the basic angular relationships involved. The reason that the ship and the Moon appear to be about the same angular size is because they are roughly the same angular size, which is determined by the object size divided by its distance from the observer.
Figure 3: Illustration of the Angular Dimensions.
Sailboat Characteristics
I can use Figure 4 to estimate:
- The distance from the waterline to the top of the mast.
- length of the sailboat.
Only the relative values of the numbers in Figure 4 are important – the specific numbers represent the particular units used by the graphics program I was have. In the photo, I see that there is a person leaning against the cabin. I will assume that the actual distance from head-to-foot of this leaning person is 5 feet – this is close enough for this kind of exercise.
Figure 4: Measurements.
Knowing the person's height, I can now estimate the size and distance of the sailboat from the camera (Figure 5).
Figure 5: Determination of Sailboat Characteristics.
Conclusion
I can state the following facts about the sailboat and its position:
- It is ~1.1 miles from the camera.
- It is ~45 feet long.
- It is ~67 feet from the waterline to the top of the mast.
These are all reasonable numbers that would provide a you a beautiful picture of a silhouetted sailboat at sunset.
Postscript
I was just watching the commentary track for the movie Shane, and the movie's assistant producer Ivan Moffat commented that they shot many scenes of the movie using a telephoto lens to make the Grand Teton mountains appear extra large. Here is a scene that is a good example (Figure 6).
Figure 6: Cemetery Hill Funeral Scene from Shane.