Calculating Focal Length Range for Projector with Varying Distances

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SUMMARY

The discussion focuses on calculating the focal length range for a projector with a diagonal pixel size of 5 mm and a screen distance varying from 1 to 2 meters. The relevant formula for this calculation is the lens formula, 1/f = 1/u + 1/v, where 'f' is the focal length, 'u' is the object distance, and 'v' is the image distance. The calculation involves determining the focal lengths at both 1 m and 2 m distances and then deriving the range from these values. The use of similar triangles is also mentioned as a method to visualize the relationship between the dimensions involved.

PREREQUISITES
  • Understanding of basic optics principles, specifically lens equations.
  • Familiarity with the concept of similar triangles in geometry.
  • Knowledge of projector specifications, including pixel size and screen distance.
  • Ability to perform calculations involving distances and focal lengths.
NEXT STEPS
  • Study the lens formula in detail, focusing on its application in optical systems.
  • Learn about similar triangles and their application in optics calculations.
  • Research projector specifications and how they affect image quality and focal length.
  • Explore practical examples of focal length calculations in various optical devices.
USEFUL FOR

Optics students, projector designers, and engineers involved in optical system design will benefit from this discussion, as it provides foundational knowledge for calculating focal lengths in projector applications.

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Hi. There's a question that has given some variables which am not sure how to compute to some previous lens/optics equations. These are not the actual variable values by the way.

If a projector (square pixel SXGA) has a diagonal size of 5 mm which uses a screen of 1 m in which the distances vary from 1 to 2 m, how would the focal length range be calculated?

Would you just calculate the focal length at 2 m, then 1 m then take these values away giving the range?

And would the 1/f = 1 / u + 1 / v equation be used? It is the diagonal size and horizontal size that am not sure about.

Thanks.
 
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Just draw a diagram
The ray goes from one corner of the screen pixel through the lens centre to one corner of the focal plane pixel.
The distance from the centre of the lens to the focal plane is the focal length
Then it's just similair triangles if you know all the other dimensions.
 
Thank you for your reply. Is the distance not from the lens to the screen? And would it not be 1/f = 1 / u + 1 / v? Am also not sure where triangles would come into calculating the focal length.

Thanks.
 

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