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Are lenses inside liquid water invisible?

peterh
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Cynthia
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  • If it is dirty, if it is opaque, or if it has a different optical density as water, then it is visible. But washing glasses, also you can see that sometimes they are somehow... surprisingly hard to find under water. – peterh Dec 13 '16 at 09:06
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    Your Title states that they are not, and the body asks whether that is true. Maybe you need to clarify. – JDługosz Dec 13 '16 at 09:37
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    As the answers below point out, only if they have an index of refraction close to that of the water. One interesting lens is the cornea. Water refractive index is around 1.33 (at 20C) and cornea's refractive index is 1.376. Because of that, we don't see very well in water. – user3653831 Dec 13 '16 at 10:05
  • Somewhat related: http://physics.stackexchange.com/a/30379/10712 – The Vee Dec 13 '16 at 11:20
  • FWIW, carbon disulfide ($CS_2$) is a colorless liquid with a refractive index of 1.627. It's not easy to see normal glass submerged in $CS_2$, and it'd be quite possible to make a flint glass with the same refractive index as $CS_2$ (although it'd be tricky matching the dispersion as well). – PM 2Ring Dec 13 '16 at 11:49
  • Please [edit] this to make the title and body match. – curiousdannii Dec 14 '16 at 05:04

4 Answers4

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A lens suspended in a refractive medium would not be visible if it has the same, or at least very similar, optical properties. This means that the refractive index, opacity, and absorption spectra of both the lens and the liquid should have values very close to each other. Additionally, the lens in question should transmit much more light than it reflects, as reflected light would make the lens visible in the liquid.

GenericHumanoid
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    Reflection (at least the one you mean) and refraction both happen due to the transition from one refr. index to another. So, if both indexes are the same, there is no refraction nor reflection. – sweber Dec 13 '16 at 10:02
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This is simply because the Refractive index of the material of the lens is equal or nearly equal to the Refractive index of the liquid medium. The geometrical bending of light rays do not take place as the velocity of light in both the medium is same, which is clear from the idea of equal Refractive index.So the lens is not visible.

So lenses inside liquid water may not be invisible.It depends on the difference of refractive indices of the material of the media.

Safikul
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The refraction index of water is about 1.33, of air is 1. How about the lens material? Probably about 1.5. So it’s somewhat less of a difference, and in the other direction.

Also, did you try it? Seems easy enough to answer that way.

JDługosz
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For a full analysis have a look at Fresnel Equations

For normal incidence the amount of light reflected at an interface depends on the refractive index of the medium through which the light is travelling $n_1$ and the refractive index of the medium it is trying to enter $n_2$.
The fraction of the light which is reflected is

$$\left | \dfrac {n_1-n_2}{n_1+n_2}\right |^2$$

So there is going to be more reflected light between an air, $n=1.00$, and glass $n=1.50$ interface than a water, $n=1.33$, and glass $n=1.50$ interface.

Farcher
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