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How to Measure Focal Length of Converging Lens

Whether they realize it or not, most people have experienced the effects of focal length. This property of a lens is what makes eyeglasses improve people's vision or a camera take a picture that is in focus. Focal length describes the distance between the lens and the focal plane when the lens is focused at infinity. However, measuring this distance is awkward at best and often impossible. An easier way to determine focal length is to examine the image plane, or the place at which the lens projects a focused image.

Things You'll Need

Measuring tape

Instructions

Gaussian Lens Formula
- 1
  Measure the distance in millimeters between the object and the center of the lens when the lens is focusing an image of the object on the focal plane. Record the reciprocal of this number. For example, if the distance is 50 mm, record it as 1/50.
- 2
  Measure the distance between the center of the lens and the image plane. If the distance is 75 mm, record it as 1/75.
- 3
  Add the two measurements together and reduce the fraction to its simplest form. This is the inverse focal length: 1/50 + 1/75 = 125/3750, or 1/30.
- 4
  Turn the fraction upside down. This is the focal length of the lens. The focal length is 30 mm.
Photographic Measurement
- 5
  Focus the lens on an object.
- 6
  Measure the distance in millimeters between the object and the front of the lens. For example, 10,000 mm
- 7
  Measure the height and width of the imaging surface in millimeters or find the CCD dimensions in the documentation that came with the camera For instance, a 1/3 inch CCD chip is 4.8 mm by 3.6 mm.
- 8
  Measure the height and width of the object in millimeters. For example, a human who is six foot tall and two and a half feet wide at the shoulders is 1,828.8 mm tall and 762 mm wide.
- 9
  Substitute the measurements into the height and width focal length equations:
  
  Focal Length of the Height = Object distance * CCD Height / Object height + CCD height
  
  Focal Length of the Width = Object distance * CCD Width / Object Width + CCD Width.
  
  For example, the focal length of height would be 10,000 * 3.6 / 1,828.8 + 3.6, or 19.6. The focal length of width would be 10,000 * 4.8 / 1,828.8 + 4.8, or 26.2.
- 10
  Examine the answers to both equations. The smaller number is the approximate focal length of the lens. The lens has a focal length of 19.6 mm.

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