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Multiplication of Fractions

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The Reciprocal Rule

Credit: Russell James Smith
Source: http://www.flickr.com/photos/russelljsmith/64452466/
License: CC BY-NC 3.0

Imagine that you want to take a picture of your friend. Right before the flash, your friend moves suddenly. What kind of photograph did you produce? If you said blurry, you are correct. Photographers and filmmakers know how to manipulate this effect by changing camera settings in order to create or eliminate blurs.

The Math Connection

The shutter speed of a camera refers to how long the shutter stays open when you take a picture. It influences whether a picture is clear or blurry. The speed is calculated in fractions of a second. For instance, some cameras allow you to select a shutter speed of 1/8000th of a second! Photos taken with the shortest shutter speeds seem to be able to freeze objects, such as falling rain droplets, in motion. Photographers manipulate shutter speed and other variables to create photographs like the one below.

Credit: jetsandzeppelins
Source: http://www.flickr.com/photos/jz909/2841325679
License: CC BY-NC 3.0

The focal length of a camera is the distance in millimeters between the lens and the image sensor. The focal length determines the camera’s field of view, or how much of the scene will be captured, and the magnification, or how “zoomed-in” the scene will be. Cameras with longer focal lengths capture smaller amounts of the scene and give you a more zoomed-in picture. The reciprocal rule in photography states that for any given focal length, you should use a shutter speed that is equal to or greater than the reciprocal of the focal length. Even if your hands are a little shaky, if you follow this rule, you will not accidentally blur photographs of stationary objects.

See for yourself: http://www.youtube.com/watch?v=Bnt6hb3Tyks

Explore More

Let’s say you are taking another picture of your friend. This time, the shutter speed of your camera is 1/20th of a second, and the focal length is 70mm. Determine whether the photo will turn out to be clear or blurry.

Image Attributions

  1. [1]^ Credit: Russell James Smith; Source: http://www.flickr.com/photos/russelljsmith/64452466/; License: CC BY-NC 3.0
  2. [2]^ Credit: jetsandzeppelins; Source: http://www.flickr.com/photos/jz909/2841325679; License: CC BY-NC 3.0

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