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Water Lenses, Quite A Good Idea

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Water has a refractory index (n) of 1.333. Light penetrates it and part of it gets absorbed, but not to much to prevent usefull energy to be available in the focal point, if you care to design the lens right. Using the below formula to calculate the focal length of a lens 

Where R1 and R2 are radii n is the refractory index (1 for air) d is the thickness of the lens we can calculate the focal length. As a waterlens with open top has a flat side one of the radii (r2) will be infinite (it’s a so called plano convex lens), the term will be zero. Radius R1 is set by deciding that the maximum thickness of the water can not be more than 2,5 cm. 

The formula for a plano convex lens is actually a lot simpler : f= R/(n-1)

But what will R be, if the water is kept thin then R will have to be large. Using an online calculator and a Chord (Koorde) AB and Segment height ED at 2 meters and 10 cm we arrive at a radius of 505 cm. This in turn leads to a focal length of 1516 cm. Quit far. One could use a reflector on the ground or opt for other dimension.

 Cord  Depth Radius Focal length
 200 cm  10 cm  505 cm  1516 cm
 100 cm  10 cm  130 cm

 390 cm

 100 cm  5 cm  252.5 cm  758 cm
 500 cm  50 cm  650 cm   1951 cm

Efficiency

Efficiency is always a funny term when energy would have been wasted otherwise. If people are so stressed about efficiency, then why burn coal which is a lot of work if you compare it to sitting back and letting a solar panel generate your energy! But how much energy can be concentrated using above examples? It is not answered simply because water does absorb heat radiation. It has a specific sensitivity in the low frequencies, which is why it looks bleuish. According to a list about seawater absorption it’s still about 40% after 100 cm without qualification of what type of light is left. In all these lense should be kept thin.

Concentration

The amount of concentration in a circular bowl of water can be enormous because all the light will end up in one point. So if the surface area is 1 meter squared and the insolation is 800 Watt, the loss is 30% you still got 490 Watt hitting 1 square millimeter, and that’s a lot of power. Of course wind and vibrations will deteriorate the lens quality (if you let it). Still, this method is nearly costless and it can increase the yield of f.i. pv cells working at 5 times concentration considerably (while actually keeping them a bit cooler than ususal).  

Best design 

The best design is yet unseen online, it’s the solar/parabolic trough. Usinng water to build a parabolic trough should be easy, and it prevents the problem of the short lived focal point as the sun moves along the sky. It does require one to move the spot where one collects the concentrated sunlight. This is unavoidable. But water troughts positioned North-South should work fine. This calls for a real life experiment! 

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