How Is the Solid Angle for a Circular Detector Calculated?

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SUMMARY

The solid angle subtended by a 100 cm² circular detector at a distance of 1 meter is calculated using the formula Ω = A/r², where A is the area of the circle. The area is determined by A = πr², leading to the conclusion that the radius r is approximately 5.6 cm when solving for the area of the detector. The discussion highlights the importance of correctly applying the formulas and understanding the variables involved, ultimately reinforcing that the solid angle can be simplified to 4π steradians for a full sphere.

PREREQUISITES
  • Understanding of solid angles in steradians
  • Familiarity with the area formula for circles (A = πr²)
  • Basic algebra for solving equations
  • Knowledge of geometric relationships in three-dimensional space
NEXT STEPS
  • Study the derivation of solid angles in spherical coordinates
  • Learn about the applications of solid angles in physics and engineering
  • Explore the relationship between solid angles and detector efficiency
  • Investigate the impact of distance on solid angle calculations
USEFUL FOR

Physicists, engineers, and students studying optics or radiation detection who need to understand the calculation of solid angles for circular detectors.

MickieDBaca
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1. The solid angle subtended by a 100 cm^2 circular detector at a distance of 1 m is ______steradians.

2. Ω = A/r^2 and A =∏r^2 (area of a circle)

3. I originally tried to find r by solving 100 = ∏r^2 and I got r = 5.6. I then tried to plug into the first equation for Ω only to realize that really, I had just gone in a circle and ended up with 4∏, which is the measure of sphere in steradians. Then I tried the tangent (5.6/100) to find the angle in degrees... The answer is .01 but I am unsure why...
 
Last edited:
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You need to keep in mind what the various quantities appearing in the formulas mean. Try again paying a bit more attention to which values go where.
 

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