# How to determine best lens to use to clearly see in the seawater?

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!

• Please make the subject line of you post more specific. – garyp Feb 8 '17 at 13:41
• The question is wider than just on a refractive index, however, it is not clear what is your purpose. Do you want to change the apparent size of the objects back to normality? What is their size if you dont have any air between eye and a glass? – jaromrax Feb 8 '17 at 14:24
• @jaromrax - I think just "seeing things in focus without a mask" is the goal here. – Floris Feb 8 '17 at 14:55
• @Floris - yes, this your question is much better than the original – jaromrax Feb 8 '17 at 14:58
• Yes. The question is how to see as clear as possible using a lens as a sight correction. – xbuster Feb 8 '17 at 16:43

## 1 Answer

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...

• I'm not talking about a mask. There is no air between the eye an the water. Just 3 objects in play - water, eye and lens. – xbuster Feb 8 '17 at 13:48
• @xbuster - OK, answer updated. – Floris Feb 8 '17 at 13:57
• Thank you. What will be the optimal lens diameter? If the distance between lens and eye changes how this will affect the lens choice? – xbuster Feb 8 '17 at 14:15
• "optimal" diameter is "as big as possible". Your field of view will be limited by the angle that the lens subtends at the (center of rotation of the) eye. The further the lens is from the eye, the bigger it needs to be for a given FOV. – Floris Feb 8 '17 at 14:17
• In the second question I meant to ask if I decide to put lens closer to the eye - lest say 10 mm from the eye, what focal length lens will I need? Is there a formula to calculate it? What lens coating (if any) will further improve the vision? – xbuster Feb 8 '17 at 14:39