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Aspect Ratio and Hotspot/Beam relation to Horizontal FoV in Free Spot Light?

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Anonymous
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Aspect Ratio and Hotspot/Beam relation to Horizontal FoV in Free Spot Light?

I have a rectangular Free Spot light and I need to precisely know the effective Horizontal and Vertical "Field of View" of the light (HFOV and VFOV) based on the Hotspot/Beam angle and the aspect ratio.

 

This is pretty easy when the aspect ratio is 1, since HFOV=VFOV=Hotspot/Beam. However if the aspect ratio is different then obviously HFOV does not equal VFOV. 

 

Does anyone know the equation to relate HFOV and VFOV to aspect ratio and Hotspot/Beam?

 

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