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I'm trying to determine what is th best lens to use in the seawater.

Lets say I'd like to open my eye in the seawater (no mask or any air between the eye and water), see thru lens located about 20 mm from my eye and get the sharpest, realistic scale of the objects and the best FOV possible (closest to the FOV of human eye outside of the water). Only one lens has to be used!

I understand that a the higher refractive index is better. Can a formula be constructed to play with possible variables to get the best outcome?

The variables are (from what I understand):

  1. Diameter of the lens
  2. Effective Focal Length
  3. Coating
  4. Refractive index
  5. Lens type (I think PCX in this case)

Thank you!

xbuster
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1 Answers1

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The easiest "lens" in this case is no lens at all... it is a curved mask with the curvature centered on the optical center of your eye. This will ensure that all rays continue in a straight line towards your eye.

I explained this in more detail in this answer

If you actually want to immerse a lens in seawater to achieve the same effect, then you need to somehow overcome the fact that the interface between your cornea and the sea is less effective. In a sense, underwater you are focused "beyond infinity" and need a lens that has a focal length of about 5 cm while immersed in water. This would require a convex lens. The highest index you can "reasonably" buy is 1.74 for high-index plastic lenses (higher index materials exist but are not usually used for commercial grade lenses, and I assume you want this to be costeffective).

Now the index of refraction of sea water is about 1.34; the index of refraction of the cornea is 1.376 - very close to that of seawater. So we can assume it does not provide any focusing. The lens in the eye provides about 20% of the total refraction of the incident light (according to this), so we need about 80% of the focusing power of the eye.

Now the total length of the eyeball (according to the same link) from cornea to retina is about 24 mm. Add to this a distance of 2 cm from cornea to the lens we want to use, we need this lens to provide focusing about 44 mm - with about 20% of that provided by the lens in the eye, we need a focal length (in sea water) of about 55 mm.

With a refractive index of 1.74 in a medium of 1.34, we are at "roughly" half the refracting power that you would normally need. So a high index lens with a focal length of 55 mm in sea water would need a focal length of about 28 mm in air. That's roughly 35 diopters - more than you would "normally" get for lenses in ordinary eyeglasses.

Obviously, if you put the lens further from the eye, the required focal length is less demanding - but in order to get the same FOV you would need a correspondingly bigger lens.

Just some thoughts to get you going...

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Floris
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