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Name: Barry F.
Status: Educator
Age: 40s
Location: N/A
Country: N/A
Date: January 22, 2004

I am helping a high school student with a science project involving characterization of minerals. She has remarked upon refractive index (RI) being a very common physical property that is listed for minerals. As we have investigated on the web, we have learned much about optics and the determination of RI values.

We are puzzled by one thing, however. How is the RI of opaque minerals, metals, etc. determined? The Becke line method would not work for opaque materials and the other methods seem only suitable for man-made thin films. Can this property be calculated from other measured values?

Hello Barry-

The index of refraction tells more than how much light will bend when crossing a boundary between substances. It also tells how much will reflect off the boundary, like a weak mirror. And it tells what angle will be the Brewster Angle, the slant angle at which one polarization is totally absorbed.

Consider black glass, like obsidian. It is really just glass: light wave goes in and swims through the solid just as it does for clear glass, but the light dies slowly as it goes forwards, and little or no light makes it out the far side. But everything about the reflection is still fair game.

A laser beam pointed at the polished front face will go in and die out. But about 5% will bounce back into a photocell. The amount which bounces back is proportional to the square of the index change at the face:

R = [(n1-n2)/(n1+n2)]^2 (in air, n1=1.000)
For plain glass, n2=1.55 -> R=0.046 = 4.6%
For water-clear sapphire, n2=1.77 -> R=0.077 = 7.7%
For dark gray glass, n2=(1.55+j*0.001); R=4.6%, and also the forward-transmitted light dies by a factor of 2.7 every millimeter.
If that glass was a ball 100mm across, no light would get to the other side, and it would look very black. I guess you would call it opaque.

You can measure this adequately with a 1cm2 photo-diode or small, good solar cell and a cheap digital voltmeter on microamps range, and a laser pointer. Oh, and a dark room. You must polish one "front" face to measure index of refraction, but it does not need to be a thin slice, or be polished on the back. Do not point the laser exactly perpendicular to the flat shiny face, but put it 10 degrees off to one side. Put your solar cell at 10 degrees off to the other side of the imaginary perpendicular line, so it will catch the reflected laser beam. Before you place the solar cell, you can see the reflected beam on the wall or a white paper. Measure how many micro-amps your solar cell drives through the current meter due to the reflected beam, Then move your solar cell in front of the stone and measure a larger number of microamps, maybe milliamps. The ratio can tell you the index.

Usually it is hard to catch exactly all the light in the laser beam, so it is hard to measure reflectance to better than about 1% error. Index-matching fluids can be more precise. You immerse the glass or rock in a series of liquids of varying index until one of them makes the very minimum reflectance.

If for glass n2=1.55, and for the liquid n1=1.54, then the reflectance is 1.05 x 10^-5 or 1/100,000. From your 2mW laser pointer that will reflect 0.02 microwatts in a beam, and you can still see that on a white paper in a dark room. So you change the liquid's index till you cannot see any. Sometimes a mix of two known liquids works fine, and the index is proportionally interpolated.

A white polyester thread in the right index-matching liquid in a clear glass will be surprisingly invisible, but only for a surprisingly narrow range of fluid indexes. Powders, too. I guess this is useful for whitish rocks that are not bi-refringent. Grind it to dust and drop it in. It will look darkest and least defined when matched.

Water is useless for most rocks because its index is only 1.33. Glycerin is a start because it is 1.47. I am having trouble finding anything water-soluble that is higher than that. Maybe saturated KI. High-index chemicals tend to be exotic and toxic. Toluene is an OK start at1.50. The right di-cloro-benzene can get you to 1.55. Unfortunately, moth-ball para-dichlorobenzene is the wrong one. Carbon di-sulfide is 1.63. It is flamable and CA-Prop65 reproductive toxic.. It dissolves sulfur, which is a joker at 1.96. and toxic, spontaneously flammable, white phosphorus at 2.14. Hexabromo-ethane is 1.6x, and I have seen a bottle of di-iodo-methane for this. Biphenyls are good, 1.6 or so, but do you know their toxicity? Di-phenyl ether is 1.58. Maybe they are OK. I guess that means Santovac 4 or 5 diffusion-pump oil is good, and safe. Only $500/pt.

You can buy little bottles of purpose-made index-matching fluid, but they might be pricey for disposable, high-school use.

What is "opaque"? it is either:

- forward light fading before it gets out the other side, which we call black, or
- total mirror-like reflectance, which we often call silvery, or
- an overwhelming amount of messy scattering by partial reflection or by refraction, which we call white.

or any combination of the above. Opaque red is a combination of white powder plus clear red dyes. Red light goes in, bounces around in the scattering-maze of white powder, and eventually most of it escapes back out through the front face. But greens and blues slowly fade before they escape.

Black is a slow absorption and a nearly normal index. Metal has such fast absorption, that it adds to the reflection as much as, or more than, the index . White stuff has a normal index and makes specular (mirror-like) reflection off the polished front surface, but then the transmitted light bounces back out, not mirror-like but spread over all angles. This is called diffuse reflection. Milky white glass does some diffuse plus some small specular reflection. You can measure the specular reflection separately from the diffuse reflection, by standing well back and blocking out all light except the beam, or by looking for the mirror image or bright glint in the mirror-like surface, while trying to ignore the white or glowing background.

Jim Swenson

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