Physics 111 Fall 2011: Pinhole Camera Scenario #4

(Caution: Numbers have been made up; they may not be realistic.)

In Pinhole Photography: Rediscovering a Historic Technique, Eric Renner (2004) traces knowledge of pinhole phenomena from the 5th century B.C in writings, for example, by a Chinese philosopher, Mo Ti (400 B.C.), a Greek philosopher, Aristotle (330 B.C.), a Greek architect, Anthemius of Tralles (555 A.D.) who drew a ray diagram, and the Italian Leonardo da Vinci, who used a pinhole camera to study perspective (1485 A.D.). Renner, E. (2004). Pinhole Photography: Rediscovering a Historic Technique. (3rd Ed.) Burlington, MA: Elsevier Focal Press.

4. Pinhole cameras have been used in many imaginative ways: In 1961, East Germany had built a wall to keep its citizens from leaving the country. Many had crossed from East Berlin to freedom in West Berlin in West Germany. The Berlin Wall became a symbol of the oppression of the East German communist regime. Political changes resulted in the pulling down of the wall in 1989 amid great celebration of the German peoples. A book published in 2009 commemorated the fall of the Berlin Wall two decades earlier. The book consisted of photos taken with a pinhole camera. The process was described as follows:

“Marcus Kaiser used holes in the wall to make pinhole images looking both toward East Berlin and toward West Berlin. To accomplish this, he taped a pinhole onto one side of a broken hole in the Berlin Wall, then taped a film holder to the other side of the hole and made an image. Kaiser then reversed the process to produce a series of metaphoric pinhole images celebrating light finally being able to travel both east and west, no longer blocked by the Berlin Wall.” You can see the image here: Click on this URL and the click on “view full size image”

Sketch a ray diagram to represent how the pinhole photo was made. State the relevant powerful ideas and use these to explain how the photo was made.

Now state in words a mathematical relationship that would allow the height of one of the street lamps to be estimated. Justify this mathematical relationship.

Set up an algebraic expression for the height of the street lamp. Use the following symbols: H = height of the street lamp h = height of the image of the street lamp D = distance from pinhole to the street lamp d = distance of image from the pinhole

Use the following estimates to calculate an estimate of the street lamp’s height. First draw a ray diagram for this scenario roughly to scale.

D = distance from pinhole to the street lamp = 50 meters. h = height of image of the street lamp = 1 centimeter d = distance from pinhole to image = 5 centimeter

State the algebraic equation that expresses the relationship among these quantities. Restate it algebraically in the form that facilitates solving for the height of the street lamp Substitute numerical values. Calculate the height of the street lamp.

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