I am working on the eyes of aquatic beetle larvae, and would like to
perform behavioral tests by altering the refractive index of the
medium in which they swim.  I am looking for a non toxic, transparent
chemical that could be added to water or replace the water resulting
in a refractive index of about 1.36.  Ideally the medium is clear, has
low viscosity and only marginally increases the buoyancy of the
animals.  I have tried a solution of Sodium Silicate, which fulfills
all the requirements except for the buoyancy issue.  Unfortunately in
it my animals float to the surface and are unable to behave naturally.
 Is it even possible to have such a medium or does anything that
increases the refractive index also increase the density and hence
results in increased buoyancy? What would be the most promising
substance to try?

I think you have quite a difficult problem. Ethyl Alcohol is about the
optical density you want. The refractive index is not necessarily
related to physical density of a material. Read the excerpt below
which comes from

http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l1d.html

In general you are interested in relative speed of light in various
mediums not the physcial density. However, often physically dense
materials are also optically dense materials e.g. Glass. However there
is some relationship for gases and refraction and physical density.
Given the difficulty of your problem wouldnt it be better to consider
an alternative approach by thinking outside the box. Instead of
changing the medium change the beetle eyes. You can probably superglue
some plastic lenses in place over their eyes relatively easily. You
just need the correct material. Infact you may be able to use some
straight neat adhesive like an acrylate based adhesive to make a lense
in situ.

"Like any wave, the speed of a light wave is dependent upon the
properties of the medium. In the case of an electromagnetic wave, the
speed of the wave depends upon the optical density of that material.
The optical density of a medium is not the same as its physical
density. The physical density of a material refers to the mass/volume
ratio. The optical density of a material relates to the sluggish
tendency of the atoms of a material to maintain the absorbed energy of
an electromagnetic wave in the form of vibrating electrons before
reemitting it as a new electromagnetic disturbance. The more optically
dense which a material is, the slower that a wave will move through
the material.

One indicator of the optical density of a material is the index of
refraction value of the material. Index of refraction values
(represented by the symbol n) are numerical index values which are
expressed relative to the speed of light in a vacuum. The index of
refraction value of a material is a number which indicates the number
of times slower that a light wave would be in that material than it is
in a vacuum. A vacuum is given an n value of 1.0000. The n values of
other materials are found from the following equation:


The table below lists index of refraction values for a variety of
medium. The materials listed at the top of the table are those through
which light travels fastest; these are the least optically dense
materials. The materials listed at the bottom of the table are those
through which light travels slowest; these are the most optically
dense materials. So as the index of refraction value increases, the
optical density increases, and the speed of light in that material
decreases."

Thanks knickers-ga for your helpful comments.  Making lenses for the
beetles is something that I have indeed considered.  However, the
larvae that that I want to study have four eyes, the lens of each of
which is only about 100microns wide.  To make convincible prediction
on how the behavior should change I need to correct all 4 lenses the
same way.  This is why I was hoping to just find a medium that does it
for me.