Calculating Torch Brightness Using Angle & Distance

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SUMMARY

The discussion focuses on calculating the brightness (B) of a torch's light on a wall based on the angle (X) of the light and the distance (D) from the wall. The user proposes the formula B=1/(π*(D*TanX)²), which relates brightness to the distance and angle of the light. The relationship indicates that as the distance increases or the angle widens, the brightness diminishes. The user seeks validation of this formula and references additional resources for further exploration.

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  • Understanding of basic trigonometry, specifically tangent functions.
  • Familiarity with the concept of light intensity and its distribution.
  • Knowledge of mathematical plotting tools, such as Wolfram Alpha.
  • Basic principles of physics related to light propagation.
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  • Research the physics of light intensity and its inverse square law.
  • Explore advanced trigonometric functions and their applications in light calculations.
  • Learn how to use Wolfram Alpha for 3D plotting of mathematical functions.
  • Study the effects of different angles on light spread and intensity in practical scenarios.
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Students and enthusiasts in physics and mathematics, particularly those interested in optics and light behavior, as well as educators seeking to explain the relationship between angle, distance, and brightness.

jackbrookes
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Hi I'm new here and I'd like some help with something that's been niggling me for the past few days. I've yet to study Maths or Physics at A Level (UK), so this should be easy for some of you.

If I were to shine a torch that shone a circular, even spreading of light, what would be the relationship between the angle of the light coming from the torch, the distance from a wall, and the brightness on the wall?

Here's what I've got: (this is assuming there isn't a property of light that I don't know about)

B=Brightness
D=Distance from wall
X=Angle, As in Shining at 90 degrees would actually shine 90 up and 90 down

B=1/(pi*(D*TanX)^2)

D*TanX=Radius, so pi*r*r=a

http://www.wolframalpha.com/input/?i=Plot3D[Cot[X

However it just doesn't seem right. Is this right or wrong?
 
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Mathematics news on Phys.org
You might find the formulas near the bottom of the page at

http://www.dcmsistemes.com/medidasi.html

useful.
 

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