How Is Angular Width Calculated in Lens Optics?

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SUMMARY

The angular width of a scene projected onto a flat screen using a converging lens with a focal length of 50.0 mm and a screen width of 37.0 mm is calculated using the tangent function. The correct approach involves determining the actual distance from the lens to the image, rather than assuming it is equal to the focal length. The proper calculation involves using the formula tan(θ) = opposite/adjacent, where the opposite side is the screen width and the adjacent side is the distance from the lens to the image.

PREREQUISITES
  • Understanding of lens optics, specifically converging lenses
  • Familiarity with trigonometric functions, particularly tangent
  • Knowledge of the lens formula and image distance calculations
  • Basic algebra for solving equations
NEXT STEPS
  • Study the lens formula to understand the relationship between object distance, image distance, and focal length
  • Learn how to calculate image height as a function of distance from the lens
  • Explore the concept of angular width in optics and its applications
  • Practice problems involving different lens configurations and distances
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding lens behavior and image projection techniques.

SamTsui86
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Homework Statement



A converging lens with a 50.0 mm focal length is used to focus an image of a very distant scene onto a flat screen 37.0 mm wide. What is the angular width of the scene included in the image on the screen?

Homework Equations





The Attempt at a Solution



Basically I just did tan-1(37/50) = 36.5

What are I doing wrong?
 
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Do you know how to calculate the height of the image as a function of it's distance form the lens? Use that to find get the distance and then use the distance and width to get the angle. Your problem is that you assumed that the distance was the focal length which isn't true.
 

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