Becke Lines and Index of Refraction in a Uniaxial Crystal
Goal: To find the indices of refraction, ω and ε, of an unknown uniaxial mineral using oils with known indices of refraction by using the Becke Line method.
Materials:
- Microscope with power source
- Mineral samples
- Oils with different indices of refraction
- Acetone
- Detergent
- Kim Wipes
- Paper towels
- Marker
- Scoop
- Slide
- Cover slips
Procedure:
- Set up the microscope.
- Take the microscope out of the case by holding the base and the arm. Plug in the microscope and turn the light on.
- Rotate the condensing lens out of the way.
- Rotate the Bertrand lens out of the way
- Make sure the polarizers are not crossed by moving the analyzer into the same direction as the lower polarizer (make sure light is visible).
- Make sure the microscope is on its lowest magnification.
- Set up the slide.
- Clean the slide.
- Put a couple of squirts of detergent on the slide and gently rub with fingers, then rinse.
- Be sure to only touch the slide on the edges from now on.
- Dry the slide with a paper towel.
- Spray a small amount of acetone on the slide and wipe it dry with a kim wipe. Place the kim wipe in the toxic waste bucket.
- Clean three cover slips the same way that you clean the slide.
- Choose three oils between n=1.4 and 1.64 that have n values sufficiently far apart to make it easier to narrow down your mineral's index of refraction.
- Use a marker to write on the slide the three n values as far apart from each other as possible.
- Next to the written n values, use the eye dropper in each oil bottle to put a very small amount of oil on the slide. First, rub the dropper along the inner edge of the bottle to remove excess oil, then put the drop on the slide without touching the slide. Do not touch the slide with the dropper because it could contaminate the oil when you put the dropper back in the bottle.
- Take the scoop and clean it with the acetone and kim wipe. Put it in the mineral grain sample bottle and pick up a few grains. Tap your hand that is holding the scoop over an oil drop so that a few grains fall into the oil. Repeat for each oil sample and then put the cover slips on the oil samples. Then close the mineral grain sample bottle.
- Clean the slide.
- Find ω.
- Put the slide on the microscope. Look for the grain in plain light under low power.
- Change the objective to medium power and make sure the analyzer is off.
- Swing the condensing lens into place and if you see a bright line bordering part of the grain, called the Becke line, then you are in the oil.
- Focus on the Becke line, you may need to close the iris to get a better view of it.
- While continuing to look at the Becke line, lower the stage by focusing
out using the coarse adjustment. Note the movement of the Becke line:
- If the Becke line moves inwards, toward the grain, then the oil's refractive index is lower than the grain's refractive index and an oil with a higher index of refraction should be tried.
- If the Becke line moves outwards, toward the oil, then the oil's refractive index is higher than the grain's refractive index and an oil with a lower index of refraction should be tried.
- If the Becke line is not visible, then the oil has the same refractive index as the oil and you can stop.
- Determine the Optic Sign.
- Use the same oil that you used to find ω. Cross the polarizers and look for a different grain that goes extinct four times when the stage is rotated 360°.
- Once you find a grain, orient it so that it is at one of the extinction positions.
- Uncross the polarizers and look at the grain:
- If the Becke line and relief are present, then look at what the Becke line is doing when you lower the stage. If the Becke line moves into the oil, than ε is lower than ω and the mineral is optically negative. If the Becke line moves into the grain, than ε is higher than ω and the mineral is optically positive.
- If the relief of the grain is very low and there are no Becke lines, then you are looking in the ω direction. You will need to rotate the grain another 90° to the next extinction position and repeat the previous step.
- Find ε.
- To find ε, you need to try oils that have an index of refraction higher than ω if the mineral is optically positive or oils that have an index of refraction lower than ω if the mineral is optically negative.
- Follow the steps in III that are used to find ω in order to
find ε:
- If the mineral is optically positive and the Becke line goes into the oil, then that means that you are looking in the ω direction or that the oil's index of refraction is too high. Rotate the stage 90° and examine the Becke line again. If it goes into the grain, then you need to try an oil with a higher index of refraction. If the Becke line goes into the oil, then the index of refraction is higher than both ε and ω and an oil with a lower index of refraction should be used.
- If the relief of the grain, the Becke line, and color are not visible, then you have a match for ε.
- Put everything away.
- Clean the slide and the cover slips again and place them back in their original spots. Put the microscope back under low power magnification, turn the light off, and unplug it. While holding the base and arm, place the microscope back in the case.
Results: I had mineral grain sample UA. Five oils were tried. The first one, with an index of refraction equal to 1.502, had Becke line movement into the grain, so I tried a few more oils with higher indices of refraction. The oils with indices of refraction equal to 1.504, 1.550, and 1.578 all resulted in the Becke line going into the grain. The next oil had an index of refraction equal to 1.580 and I did not see a Becke line, so 1.580 is the value of ω.
| no | Becke line |
|---|---|
| 1.502 | Into grain |
| 1.504 | Into grain |
| 1.550 | Into grain |
| 1.578 | Into grain |
| 1.580 | No Becke line |
Then, while still in the oil with an index of refraction equal to 1.580, I found a grain that went extinct four times with a 360° stage rotation and made sure it was not oriented along the ω axis. The Becke line moved into the oil meaning that the mineral grain is optically negative and that the value of ε must be less than the value of ω.
I used six oils in order to find the value of ε. They all resulted in the Becke line going into the oil, so I kept trying oils with lower indices of refraction. I finally tried the oil with an index of refraction equal to 1.540 and no Becke line appeared, so that is my value for ε.
| no | Becke line |
|---|---|
| 1.578 | Into oil |
| 1.576 | Into oil |
| 1.570 | Into oil |
| 1.566 | Into oil |
| 1.560 | Into oil |
| 1.540 | No Becke line |
Conclusion: Becke lines appear because of refraction at the lens-like edge of a grain. If the grain has an index of refraction lower than the oil, the grain will act like a diverging lens and the Becke line will go into the oil. If the grain has an index of refraction higher than the oil, the grain will act like a converging lens and the Becke line will move into the grain. If the grain and the oil have the same index of refraction, then the light will not be refracted and a Becke line will not appear. If the mineral is anisotropic, there will be more than one index of refraction depending on the vibration direction of light in the crystal.
The UA mineral grain sample and the oil with an index of refraction equal to 1.580 did not create a Becke line along the ω axis, so ω is equal to 1.580. I observed that grains in the ω oil that were oriented along the ε axis had their Becke lines move into the oil, so the mineral is optically negative. The oil which produced no Becke line along the ε axis had an index of refraction equal to 1.540. Using these values for ω and ε, I determined that the sample is Mizzonite.
