Calculating Efficiency of LED Without Plastic Dome

[Septim]

Greetings everyone,

I need to calculate the efficiency of an LED without a plastic dome, thus total internal reflection is a limiting factor in this case. The book asks me to show that TIR at the interface with air reduces the emission efficiency by the factor 1-cosθ where θ is the critic angle. In addition to that how can I calculate the solid angle of a cone with half angle say β. Any help is appreciated.

Thanks

 

[CWatters]

Try here..

http://en.wikipedia.org/wiki/Solid_angle

Presumably the efficiency = Solid area of the bit not subject to TIR/Solid area of 180 degrees

 

[Septim]

Thanks for your help, I was able to figure it out.