Calculating mountant RI by measuring real and apparent depth

Beatsy · Post by **Beatsy** » Sat Mar 21, 2015 3:37 pm

I've been using a focus depth technique to (supposedly) measure the refractive index of mountant between coverslip and slide. It's not giving quite the results I expected though. I'm obviously miscalculating something but I'm not sure what.

Conditions: Scope focus knobs are accurately graduated in microns. Slides are held perfectly flat and orthogonal to the focus travel. Coverslips are equal thickness throughout and usually (but not always) of known RI. Coverslips may not be parallel to the slide surface (i.e. mountant thickness may vary across a coverslip).

Method: I focus on the slide surface next to the edge of a coverslip (in air, not under the coverslip) and note the focus knob reading (SS). I focus on the underside of the coverslip (again in air, on the outside edge of the slip) and note the focus reading (CU). I focus on the top (out)side edge of the coverslip and note the focus reading (CO).

Assuming RI of air as 1.0
SS-CU = actual mountant thickness at edge (MT)
CU-CO = actual coverslip thickness all over (CT)

I move to just inside the edge of the coverslip and repeat two of the measurements through coverslip and mountant. Surface of slide "apparent" depth (SSa), underside of coverslip apparent depth (CUa).

SSa-CUa = apparent mountant thickness (MTa)
CUa-CO = apparent coverslip thickness (CTa)

Note: Actual mountant thickness (MT) can now be recalculated for any other position under the coverslip by focussing on the top (out)side to measure a new CO value, then MT (at that point) = SS-CO-CT (because SS and CT are constant).

Coverslip RI = CT/CTa and this matches well when the RI of the coverslip is known. At first, I didn't think I really needed this measurement and just used it as an accuracy check. But...

I assumed mountant RI = MT/MTa, but now think coverslip thickness and/or coverslip RI should be included in this calculation too, but I don't know how.

Chances are this is simple stuff, but the solution eludes me. Help appreciated.

TheLostVertex · Post by **TheLostVertex** » Sun Mar 22, 2015 12:18 pm

I would assume that MT/MTa is equal to the relative refractive index of the two medium if this works for calculating the coverslip RI. So RIr = RI2 / RI1

If your technique works, then I think it would be

Cover Slip RI(CT/CTa ) * Relative RI(MT/MTa) = Mountant RI

Maybe you could give some actual numbers you help us understand fully what you are doing?

rjlittlefield · Post by **rjlittlefield** » Sun Mar 22, 2015 12:38 pm

I disagree with Steven about the analysis. It seems to me that the simple formula RI = MT/MTa should be correct.

My rationale is that the cover slip can be viewed as just part of the optics -- a very thin planar "corrective lens element" if you like. Since you're then viewing through the same optics when you measure the apparent position of the top and bottom of the mountant, any effects of the cover slip get canceled out when you difference those two positions to get the apparent thickness of the mountant.

I agree with Steven that it would help to have some numbers.

--Rik

TheLostVertex · Post by **TheLostVertex** » Sun Mar 22, 2015 1:43 pm

rjlittlefield wrote: My rationale is that the cover slip can be viewed as just part of the optics -- a very thin planar "corrective lens element" if you like.

Perhaps my logic is flawed somewhere. The way I see it is that while the coverslip is "part" of the optical system in the sense that you want to use the cover slip for viewing an object, in his test scenario it is not. He is using the objective and eye piece as his optical system, and that system is then used for measuring the subjects (coverslip and mountant). If the cover slip was part of the optical system he was using to make measurements, then he couldn't measure the coverslip's RI. Instead the coverslip and mountant are a pair(they share a junction) and the apparent mountant thickness is both the coverslip and mountant RI.

g4lab · Post by **g4lab** » Sun Mar 22, 2015 2:30 pm

I think the Rik's analysis is correct. This method is used to determine the RI of gemstones at a macro level. Because there is no(convenient) contact liquid for critical angle refractometers above 1.83 or so for Over The Limit stones this method is used.

The stone is measured for actual thickness with a micrometer or caliper.
The apparent thickness is measured by having a dial indicator affixed to the stereoscope or macroscope. The table plane can be delineated with a fingerprint or some chalk dust.

The method is due to the duc de Chaulnes

http://catalogue.museogalileo.it/biogra ... ulnes.html

http://catalogue.museogalileo.it/object ... Gauge.html

http://catalogue.museogalileo.it/object ... scope.html

http://www.opticsinfobase.org/josa/view ... -428&seq=0

http://www.opticsinfobase.org/josa/abst ... a-58-3-428

http://ieeexplore.ieee.org/xpl/login.js ... r%3D262562

http://www.opticsinfobase.org/josa/abst ... 54-10-1225

rjlittlefield · Post by **rjlittlefield** » Sun Mar 22, 2015 2:52 pm

TheLostVertex wrote:If the cover slip was part of the optical system he was using to make measurements, then he couldn't measure the coverslip's RI

In my thinking, that's a different situation. When he's measuring the coverslip's RI, he's only looking through the coverslip for one measurement -- the coverslip's bottom surface. The constant optics in that case are just the objective and everything in back of it, excluding the coverslip. But when he's looking at the mountant, he's looking through the coverslip for both measurements, so the constant optics include the coverslip.

As for sharing a junction, imagine for a moment that the mountant and the coverslip were separated by an infinitesimally thin layer of any other medium. Assuming the angles are not so extreme as to provoke total internal reflection, the infinitesimally thin layer would not affect the ray paths. It's unclear to me how your formula would extend to handle this case, but however it does, I think it should end up producing the same result with and without the extra layer. Does it?

An interesting physical experiment might be performed by using two coverslips. Put one on a slide and measure it. Then put another one on top of it, and measure the bottom one again. Repeat, with a bit of oil between the pair, then compare all the measurements to see what happened.

--Rik

TheLostVertex · Post by **TheLostVertex** » Sun Mar 22, 2015 3:27 pm

I was thinking as a control scenario Beatsy could preform his test with a coverslip of known thickness and RI, and with a mountant of known RI (maybe water or oil, with spacers between the slide and coverslip to simulate the desired thickness). Then we might have some numbers which to check ourselves against.

The two coverslip experiment might also be interesting to see in action.

Beatsy · Post by **Beatsy** » Mon Mar 23, 2015 2:39 am

Thanks for the responses all. I don't have any tabulated numbers I can supply just now, only a jumble of scribblings from previous measurements. The idea using oil is a good one, I'll try that and report back.

I am leaning toward the simpler calculation being correct again. I've found many references that say the coverslip can be ignored, I just couldn't see why. But now I do (the RI difference between coverslip and mountant is smaller than that between mountant and air, so the coverslip's contribution to reducing apparent depth is cancelled out. I think.

Anyway, I suspect my problem was simply inaccurate measurements so I'll do some tests with marks deliberately placed on the relevant surfaces. Couple of other priorities to deal with first, but I'll post results within a couple of days.