Calculating Torch Brightness Using Angle & Distance

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In summary, the person is seeking help with understanding the relationship between the angle of a light source, the distance from a wall, and the brightness on the wall when shining a torch. They provide a formula they have found and ask for confirmation on whether it is correct or not. They also reference a website with formulas that may be helpful for solving the problem.
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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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You might find the formulas near the bottom of the page at

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

useful.
 

FAQ: Calculating Torch Brightness Using Angle & Distance

How do you calculate the brightness of a torch using angle and distance?

To calculate the brightness of a torch, you will need to know the luminous intensity (in candelas) and the distance (in meters) at which the measurement was taken. The formula for calculating luminous intensity is: I = L ÷ A, where I is the luminous intensity, L is the luminous flux (measured in lumens), and A is the area of the light source. Once you have the luminous intensity, you can use the inverse square law to calculate the brightness at a certain distance, which is given by B = I ÷ D², where B is the brightness and D is the distance.

What is the inverse square law and how does it apply to calculating torch brightness?

The inverse square law states that the intensity of light decreases as the distance from the source increases. In other words, the further away an object is from a light source, the dimmer it will appear. This law applies to calculating torch brightness because as the distance from the torch increases, the brightness will decrease according to the inverse square of the distance.

Can the angle of the torch affect its brightness?

Yes, the angle of the torch can affect its brightness. The wider the angle of the torch, the more spread out the light will be and the less concentrated the brightness will be. This means that at the same distance, a torch with a wider angle will appear less bright than a torch with a narrower angle, even if they have the same luminous intensity.

How can I measure the angle of a torch?

The angle of a torch can be measured using a protractor or angle measuring tool. Place the base of the protractor on the center of the light source and align the zero degree mark with the direction of the light beam. Then, read the angle measurement where the light beam intersects with the protractor's scale.

Is there a way to increase the brightness of a torch without changing its angle or distance?

Yes, there are a few ways to increase the brightness of a torch without changing its angle or distance. One way is to use a more powerful bulb or LED in the torch. Another way is to use reflective material around the light source to direct the light in a more focused direction. Additionally, keeping the torch clean and free of any obstructions can also help improve its brightness.

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