Is there an equation to calculate efficiency of an optical fiber to transmit sunlight for length of 4 m I want to transmit sunlight over a distance of approx 4 m via optical fiber. Ideally I want to light up the whole house with sunlight.
I was reading that the largest diameter for an optical fiber may not be the right way to solve this issue. I was wondering if there some sort of equation where I can insert the length that I would like to carry light over (length is a variable) and maybe the number of cores of optical fiber (also a variable) with the output of this equation being the efficiency or loss in transmission.
This way I can integrate all variables in one equation and optimize against the cost to procure.
 A: NOT A PHYSICIST, BUT:
I was just passing through and saw your question.  I've been interested in "light transfer through rapped fiber" for many years.  
A consistent original source would be open to computation, but the Sun is actually not consistent.  There would be high's and low's of the Sun's spectrum, thus you couldn't regularly optimize the direct light to a specific result.
In about 1962, GM used light transfer through rapped fiber to transfer the dashboard illumination (12vdc) to and outside front fender 'indicator' light.  What's interesting is that the term indicator "light", does not imply that there was, in fact an actual electric bulb associated the light seen through the windshield, on the front fenders.
This explains my theory of a consistent source, i.e. the 12vdc bulb.  The miniature bulb was less than 1/2in dia, while the fiber strands numbered 8-12, were not fused, but wrapped in a black 'friction' type tape.  The strand traveled approximately 15' without any loss of illumination.  I think, because of the consistent source, the illumination could have been carried infinite distances.
That, of course, led me to the believe that such fiber transfers of light could be achieved in the same manner over great, great distances.  But like data encoding, each fiber strand, unto itself, holds it's own individual light or data, therefore by wrapping the strands the light itself seems to be more unobstructed and 'dedicated' to it's journey and/or 'termination'.
Remember, incandescent bulbs generate Heat because of the Energy used to generate the light.  The transfer of light from the 12vdc will NOT transfer any heat through fiber (such as in a fluorescent bulb),  But in the 1962 Cadillac light transfer that I've described, the strand was output terminated at a clear or colored lense.  In today's world, the wrapped fiber strands would be terminated into a 'magnified' lense, which by the nature of magnification would project some heat, but many time the original light, of course depending on the lense itself. 
