0

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
  • 11
  • Please make the subject line of you post more specific. – garyp Feb 08 '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 08 '17 at 14:24
  • 1
    @jaromrax - I think just "seeing things in focus without a mask" is the goal here. – Floris Feb 08 '17 at 14:55
  • @Floris - yes, this your question is much better than the original – jaromrax Feb 08 '17 at 14:58
  • Yes. The question is how to see as clear as possible using a lens as a sight correction. – xbuster Feb 08 '17 at 16:43

1 Answers1

0

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...

Community
  • 1
Floris
  • 118,905
  • 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 08 '17 at 13:48
  • @xbuster - OK, answer updated. – Floris Feb 08 '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 08 '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 08 '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 08 '17 at 14:39
  • Coating is unlikely to help much. The focal length of the lens you need is "roughly" (back of the envelope) $\rm{2(1.2(distance~to~eye + 24 mm))}$. The $2*$ is for the effect of seawater (lowering the focal length about 2x), the $1.2$ accounts for the lens inside the eye. – Floris Feb 08 '17 at 14:52
  • So if I understand it right for 20 mm distance to the eye it will be 2(1.2(20+24))=106 focal length in water then you divide by 2, so the lens focal length outside of the water should be 53 mm. Is this what you've meant? – xbuster Feb 08 '17 at 16:49
  • Sorry - I wrote that backwards. The $2\times$ should be $0.5\times$ - the focal length of the lens "in air" needs to be shorter so it will be correct in the water. – Floris Feb 08 '17 at 17:22
  • If the person has prescription eye glasses, how that can be taken into account when choosing the optimal lens? – xbuster Feb 09 '17 at 08:16
  • Can you please answer this it's important for people with sight disabilities: If the person has prescription eye glasses, how that can be taken into account when choosing the optimal lens? – xbuster Dec 31 '17 at 14:17
  • @xbuster I am not sure what more I can say. Even people with perfect vision can’t see well under water because of the high refractive index of water (close to the index of the eye itself). It is really impractical to try to wear glasses under water to correct your vision - much better to wear a mask and the problem goes away. – Floris Dec 31 '17 at 17:50
  • Thank you for your answer. I just wanted to know theoretically speaking how the formula changes to target specific diopter in case a person has Myopia or Hyperopia? Can the lens stay the same - PCX or it has to be changed? – xbuster Dec 31 '17 at 21:31