# Snell's law and the concept of critical angle

Mentor

## Main Question or Discussion Point

This is first of questions, I may have more, hence the very general title of the thread. I know the basic optics involved, two most important things here are Snell's law and the concept of critical angle - no problems here, even if I am just skimming on the surface.

Problems start when I am trying to find how the refractometers are built and work. While there is plenty of information available, it is often either contradicting itself or unclear. For example - I am trying to find how Pulfriсh refr. is made. Some sources claim it is a critical angle device (see for example here, definition is taken from McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.), and show this (or equivalent) picture:

(this particular one is from wikipedia). OK, θ is a critical angle, we measure φ as it appears as the bright-dark boundary, some simple math and we have n of sample.

But other sources - like this lab manual from University of Lepizig and Optical sensors and microsystems: new concepts, materials, technologies book - show pictures similar to this one:

While it is obvious how it works, it is very different and it is not a critical angle device.

So, which one it is?

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Andy Resnick

There are different types of refractometers. The first image you posted looks like a "Abbe refractometer", while the second appears to be a "Pulfrich refractometer".

I see you found the same lab manual document I pulled up... I also found this:

http://www.humboldt.edu/scimus/RefracExhibit/ChemRefrac.htm

Which claims the Pulfrich refractometer has higher precision. Both work using the principle of total internal reflection (or critical angle measurements).

Mentor

So you suggest wikipedia image is wrong? That won't be surprising, however, if my second picture is right, I fail to see a critical angle in Pulfrich. The way I see it bright/dark boundary observed is just a bottom edge of the V-shaped prism filled with the solution. Similar effect, but completely different principle.

dlgoff
Gold Member

So you suggest wikipedia image is wrong? That won't be surprising, however, if my second picture is right, I fail to see a critical angle in Pulfrich. The way I see it bright/dark boundary observed is just a bottom edge of the V-shaped prism filled with the solution. Similar effect, but completely different principle.
You got me curious and doing a little searching. Yea, I don't think the Pulfrich uses critical angle to determine in index. Here's a little PDF from a lab class that shows the "Derivation of the equation to calculate the index of refraction using the Pulfrich refractometer".
http://www.uni-leipzig.de/~prakphys/aprak/english/optics/O-05e-AUF.pdf"

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Mentor

You got me curious and doing a little searching. Yea, I don't think the Pulfrich uses critical angle to determine in index. Here's a little PDF from a lab class that shows the "Derivation of the equation to calculate the index of refraction using the Pulfrich refractometer".
I linked to this document in my first post, so I am not surprised by the content :tongue2:

Trick is, different sources tell different things. See for example The light fantastic: a modern introduction to classical and quantum optics By I. R. Kenyon - it obviously shows the same picture wikipedia does, and it calls it a Pulfrich. This is book published by Oxford University Press, so not some random source.

This discrepancy between sources is the source of my confusion.

There is more to it - some publications show pictures aimed at explaining work principles, pictures which IMHO don't make sense, but that'll be the next stage...

dlgoff
Gold Member

oops. Sorry. Missed that.

Andy Resnick

So you suggest wikipedia image is wrong? That won't be surprising, however, if my second picture is right, I fail to see a critical angle in Pulfrich. The way I see it bright/dark boundary observed is just a bottom edge of the V-shaped prism filled with the solution. Similar effect, but completely different principle.
Here's a brief description of the instrument:

http://www.humboldt.edu/scimus/RefracExhibit/SpecCatDesc/Hilg_Pulf_AT21.jpg

There's also a couple of pages in Johnson's "Optics and Optical Instruments" (pp 168-169) that discuss the operating principle.

Both those sources use the same image- and neither shows the v-shaped prism. You are correct, the v-block does not appear to use total internal reflection, and instead an accurate measurement of the amount of refraction that occurs.

Mentor

I know the page. I really did my HW

Both those sources use the same image- and neither shows the v-shaped prism.
So we are back at square one. What is a Pulfrich refractometer, and what is a V-shaped one?

You are correct, the v-block does not appear to use total internal reflection, and instead an accurate measurement of the amount of refraction that occurs.
Thanks, at least my thinking didn't fail.

Andy Resnick

It *is* somewhat odd. Personally, I have only used the Abbe 3L refractometer.

Aha! I found the magic reference:

Methods in High Precision Refractometry of Optical Glasses
Alan J. Werner May 1968 / Vol. 7, No. 5 / APPLIED OPTICS 837

The V-block method is given it's own subsection, and has nothing to do with Pulfrich! Here's the original source:

J. V. Hughes, "A new precision refractometer", J. Sci. Instrum. 18, 234 (1941).

Mentor

Methods in High Precision Refractometry of Optical Glasses
Alan J. Werner May 1968 / Vol. 7, No. 5 / APPLIED OPTICS 837
This is about solids, I am more interested in liquids. But I am adding it to my list of possibly interesting things. I have to check if someone in Warsaw has it (I have no access to literature - unless I pay from my own pocket).

The V-block method is given it's own subsection, and has nothing to do with Pulfrich! Here's the original source:

J. V. Hughes, "A new precision refractometer", J. Sci. Instrum. 18, 234 (1941).
So it is relatively new; strange that it is present in so many places. My guess is someone mistaken these two designs when writing a book that became popular; after that everyone just copied the error.

Does the v-shaped have a specific name?

Hm, I did some googling. Hughes paper (I have seen just abstract) is about measuring refractive index of glass (not surprising if it was discussed in the Werner's paper). How come his design often discussed as a device to measure refractive index of liquids?

Andy Resnick

You have to realize that (for a while, at least) refractometry was mostly concerned with glass- since lenses etc. are made of glass, and there are lots of different optical glasses. Besides quality control, there was the development of glasses with particular dispersion properties for use in chromatic aberration correction.

I suspect the v-block refractometer (that's the only name I've seen associated with it) found a use for refractometry of liquids simply because that geometry lends itself to holding a volume of fluid without a cuvette.

There's a lot of refractometers on the market that measure the refractive index of liquids:

http://www.atago.net/USA/products.html

I have no idea how the small hand-held ones work.

Mentor

You have to realize that (for a while, at least) refractometry was mostly concerned with glass
I guess that comes with a background. From my point of view refractometry is mostly an analytical method. As far as I can tell Abbe refractometer was designed for liquids.

I suspect the v-block refractometer (that's the only name I've seen associated with it) found a use for refractometry of liquids simply because that geometry lends itself to holding a volume of fluid without a cuvette.
External cuvette is popular also in a critical angle devices.

There's a lot of refractometers on the market that measure the refractive index of liquids:
Yep. On the page you linked to there are basically two types of hand helds. The digital ones from the first picture are those critical angle/external cuvette types; I more or less know how they are built, but I am missing something, so I don't understand how they work. That will be next part of the thread . Some of others (http://www.misco.com/traditional.php) are basically Abbe refractometers, just without a movable telescope, but with a scale to read critical angle. They are usually already scaled in concentration units (or Brix units) and made for analysis of a single substance (sugar, alcohol, sulfuric acid, glycol and so on). Some models have a bimetallic element moving scale or optical wedge, so that they do automatic temperature compensation.

Mentor

Additional thing - does anyone know about some simple optics program, that will let me build simple devices (combinations of prisms, wedges, blocks, mirrors - I don't need lenses) and do some simple ray tracing (I guess that's not the correct term - I want to be able to see what happens when I change direction of the incident ray, and I want effect similar to the white picture I posted earlier) for them? It doesn't have to be 3d, more like I prefer something working only in two dimensions.

I know of Sinopt, but that's an overkill, I am looking for something much simpler.

Andy Resnick

I don't know of anything out there that is more simple than OSLO (Sinopt) or Zemax. Since you don't need much, you may be best off writing your own routine in something like Excel or Mathematica- ray tracing is simple matrix multiplication.

I was surprised that PhET doesn't have something similar to their circuit construction kit:

maybe if you contact them, they would develop one- a simple 'spectroscopic' app is what you need.

POV-ray is a free, open source rendering program. I've never used it, it's aimed at computer graphics folks, but you may be able to do something with it:

http://www.povray.org/

Mentor

I suspect the v-block refractometer (that's the only name I've seen associated with it)
And when you think you finally know something, you look into Walt Boyes Instrumentation Reference Book to find this:

So here it is Hilger-Chance. What a mess.

Andy Resnick

And when you think you finally know something, you look into Walt Boyes Instrumentation Reference Book to find this:

So here it is Hilger-Chance. What a mess.
Sheesh!

"The Hilger-Chance refractometer, developed initially in the laboratories of Messrs. Chance Brothers Ltd.,[HUGHES J,. V. J. Sci. Instrum., 18, p. 234 (1941).]" and Hughes' paper is called "A new precision refractometer".

Here's something:

"The refractive index at the surface of a material may differ to an important extent from that of the body of the material. This surface phenomenon plays an important part in critical angle refractometry but the Hilger-Chance refractometer measures the refraction of the mass of the specimen."

So that's a significant difference in approach.