# Optical Forums > Ophthalmic Optics >  Measuring refractive index of a lens

## haya

Hey everybody,

A simple question but I am having great difficulty in expressing myself in my answer...

'How can i measure the refractive index of a lens?'

thanks, :D  haya

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## Steve Machol

To do this with any degree of precision, you'd need to use an abbe refractometer and the test specimen needs to be a flat surface.  

Here's a Google search on 'abbe refractometer':

http://www.google.com/search?sourcei...+refractometer

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## Jeff Trail

Haya,

   Steve is right (if you can afford to do it right)..BUT there are some less expensive way to go about it if you have a surface program and some digital sag gauges..might not be as precise as Steve's but can get fairly close

    You have some "given" numbers to work with.. you have the base curve (front of the lens), you have the ocular curves or curve depending on if you have a sphere or compound power (cross/base) and the refractive power.. now if you have a precise sag gauge you can take those two (or three) measurements and plug them into a surface program and than at the top you can change the "index of material", you just tinker with the index till you get the numbers to match up. :-)

     Remembering that the material has a distinct effect on the amount of ocular curve needed to get the same refractive power..

   Here is an example: I have a 6 base lens (3.74 sag)TC 6.20.. a refractive power of +1.50 wanted... now in CR39 the amount of curve needed on the ocular side would be -4.62/-4.62... NOW take those same numbers but change the index ONLY to a 1.60 than to get the SAME refractive power of +1.50, I would only have to cut a -5.00/-5.00 ocular curve :-)

    So technically once you have all the correct numbers you can plug in the index to make all the numbers match to you sags on the lens and get a fairly decent idea of what the index of the material is at least with in a point or so... you could determine the index and than knowing something about the manufactures you can even narrow it down further or indexes...The least amount of information you could gain is if it were a CR39/mid-index/high-index material ... 

    Maybe not as "fancy" as Steve's way of doing it, but a lot less expensive :-)

Jeff "sometimes a little leg work saves some money" Trail

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## haya

That is great info that you have provided...

I was thinking along the lines of using a focimeter and a lens clock/measure which has been calibrated for crown glass (with the helium 'd' wavelength used to give a refractive index of 1.523, commonly used in the UK).

Then i would use the lens clock to determine surface powers and the focimeter for vertex powers.

Finally using appropriate calculations to measure a simple lens form such as a minus plano concave lens where all the refraction occurs at the back surface, i came up with:

refractive index (n) = [ (BVP/BSP) 0.523 ] + 1

(where BVP is the back vertex power, and BSP is the back surface power).

Any opinions? Would appreciate any comments to help my lack of knowledge.

Cheers,

haya

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## JRS

Due to the complexity of the calculations, this formula is broken down into useable fragments for a handheld calculator. The Power piece equals lensometer (digital readout preferred) power achieved.

 	Frd = ABS (530 / True Base Curve)
 	Rrd = ABS (530 / True Rear Curve)
 	A1 = Frd - Rrd - Center Thickness
 	B1 = 1000 * (Frd - Rrd) + (Rrd * Power) * (Frd - Center Thickness)
 	C1 = 1000 * Rrd * Frd * Power
 		If Power < 00.00 then............	Index = (-B1 + SQRT (B12 - 4 * (A1 * C1))) / (A1 * 2)
 		otherwise...............................	Index = (-B1 - SQRT (B12 - 4 * (A1 * C1))) / (A1 * 2)



Cloned this out of an old set of notes. Forgotten now where I even got it. Seemed to work when last I used it.

Jeff's post will work too, but I wouldn't use rounded tooling (back curves). Measure the actual rear curve with a good sag gauge.

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## Jeff Trail

Haya,


 Now before we jump into this to heavily remember I'm just a lowly lab rat:)  and you'll see the other "math bugs" coming out of the woodwork when we get started..(Jim,Darris,Darryl,Pete,John  and the rest)

   OK, some problems you may run into in doing that way (using back and front vertex power) is when a lens is thick the nominal power is not accurate.. 
That said we can go to the basic formula's of vertex power..for the back  Db=D1/1-(t/n)D1+D2

D1=front surface power
D2=back surface power
t=thickness between front and back (meters)
n=index of refraction of the material

    the front vertex power (neutralizing power) FVP to most of you guys heavy into the "contact" side of this ..
DF=d2/1-(t/n)D2+d2

   All that to the side you could (theoretically) have all the numbers to the equations BUT the index already and than do sort of a reverse formula to find the index of refraction...

    My original was a lot easier to figure out (using a surface program to do the math for you) The biggest problems being using the formula to try to get the base numbers you run into accuracy problems when dealing in "thick" lens..
      I made a chart a few years back with a scale that gave the front curve, the ocular and the power and it gave a pretty close indication of the index of material, made a bunch and gave to my wholesale accounts..I'll see if I can find it and post it and it sure saves a lot of "mathematical" head scratching time..
      Any others want to jump in here and go "math" crazy? One thing about this board I know I'm not the only one who enjoys tinkering with formula's :Cool:  

Jeff "just a little ole lab rat" Trail

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## Jeff Trail

JR...

   Come on brother what kind of of an answer you expect from someone geared to the "lab" side :Cool:  I do have both digital lens clocks and digital sag gauges.. and using the surface program you'll have to understand and convert the curves to something the computer understands (surfacing program) one thing that may throw a wrnch into the process as the index of the tools used..mine are glass but some people run  lap tools based on CR39....BTW that calculater you have do windows too? 
    All in all I think as long as you get "real" close and are familar with the materials you can narrow it down to be able to fairly well match.. if that was the whole reason you trying to determine index of refraction and needed to replace only one lens...

    Don't you just love this math? Wish I had listened closer to the instructors in Trig and Geo in school..;) 

     One thing a lot of the lurkers may want to check into is one of the classes offered at Hillsbourough C. C. in the opticians degree,
Geometric Optics.. that class was kind of fun... HEY and it can be taken Via the web!!!!!!!!

Jeff "changing my name to Geo man" Trail :cheers:

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## JRS

Goes to show how old those notes are - traced back to where I got them, and it sorta pre-computer days. Use to use a HP112 or 115 (I think) handheld. Reverse polish notation too. I ought to write it up in an Excel sheet and save myself time. But like I said, hadn't used it in years. 
I too wish I'd paid more attention in school. Of course then my plan was to get as far away from school as possible. Now I go any chance I get. Had to get my math skills back up when I was writing Design documents and troubleshooting for the software company (optical). Had to learn some programming too, which was a bummer. Fortran, MS Basic, Apple Basic, and some C. Somehow managed to avoid Cobol.

Did I read your post right - your laps are GLASS (1.523) indexed? Not "tool index" (1.530) as most. And yes, some people have laps cut in CR index, but many of the new ones are now being cut in 1.6 index (and 1/10's).

PS - the handheld didn't do windows, but neither do I. So it was in good company. Good optical formula book on the market, answers many of the unusual calcs. You should pick one up.


X-lab rat too Jeff. Can remember back in '65 when I was cutting laps (Oldfield template cutter) and kept seeing these funny numbers on the setting plates - took me awhile to figure out they were Radius values. My how time has flown.

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## Jeff Trail

JR,

  Not to go off on a tangent from the thread but, yea I made a boo-boo on the lap, I just got in this bad habit of saying "glass" I know, but it just made it easier in the lab when we talked about it and I am having a hard time breaking our in-house quirky habits from the "real world" posts at times.... :p 

   Now onto the other part that book you mentioned wouldn't happen to be Optical Formulas Tutorial by Stoner & Perkins? So far it's one of the better I have found and chock full of stuff that comes in useful.

   I just wish I could find my old copy of the B&L coachmans manual!! It was my very first book I ever got when I got sucked into optics :D  I still got a kick out of people I loaned it to when it started talking about blocking lens with "pitch"!!;) But as far as starting out with the basic principles in our field and explaining things I have not found a better book for lab guys to cut their teeth on.
    If you ever run across a copy of one let me know...

    Oh to go even further off the beaten path... have you been in any labs using microtints? I was thinking about checking them out and seeing how they might work.. the color selection is a lot wider.. and if I can make my life easier I'm all for something new to try...

Jeff  Trail

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## haya

You guys have completely lost me i am afraid....way over my head.....off on a tangent....BUT,  managed to get some use from what you were writing about.

BTW JRS, here in good ole England we are still in the pre-computer era. Me is still in uni doing my 2nd year of optometry... 
:(

haya  :hammer:  head

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## JRS

Sorry Haya,

Didn't mean to lose track of the initial request. Have a tendancy to ramble on sometimes. My fault.

Back to your original thread now..... basically, if you take the regular thick lens formula (where you solve for the rear curve) just change the unknown from curve to index. Then re-arrange the formula. Essentially, that is what my post was doing. If my breakdown (previous post) wasn't clear enough, let me know and I'll post again with an example - or perhaps clearer thoughts (difficult task, but I'll try).





Jeff - I picked up 2 B&L Job coach manuals at a used book store in Portland. POWELLS BOOKS - largest used bookstore in US (takes up 2 city blocks). They even give you a map to help you find your way around. Anyhow, go to www.powellsbooks.com and search. They have a huge assortment of optics in their technical section.

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## haya

JRS,

WEEEEELLLLLL, as you have offered very kindly, JRS, an example would not go amiss!!!

Thanks a bunch!!!

 :bbg: 

haya

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## JRS

As requested Haya, I worked up an example for you. One note though... in looking over the last lines (INDEX=), I discovered that the returned value was expressed as just the value to the right of the decimal. So I modified that line to convert to a index that comes out the way you expect it to look like. Works either way, just understand the reading. So here 'tis.

Here is what you know going in;
1) Rx
2) Center Thick
3) Lens Analyzer Readout

1) 2.00 1.00 x 075
2) 1.7 mm
3) 2.037 1.027 x 075 (unrounded best)

For this formula cylinder is disregarded, so;

Using a good digital sag gauge (mine is a 40mm ball tip), we measure for TBC and REAR SPHERE (base) values

TBC = 4.26 D (1.631 sag)
REAR = -6.12 D (2.386 sag)

Moving into the formula then.

Frd = ABS(530/4.26)   Frd = 124.41315
Rrd = ABS(530/-6.12)  Rrd = 86.530612
A1 = 124.41315  86.530612  1.7   A1 = 36.182533
B1 = 1000 * (124.41315  86.530612) + (86.530612 * -2.037) * (124.41315  1.7)   B1 = 16252.764
C1 = 1000 * 86.530612 * 124.41315 * -2.037   C1 = -21929416.5

Since Power < 0 (minus), then
INDEX = 1+ (-16252.764 + SQRT(16252.764^2  4 * (36.182533 * -21929416.5))) / (36.182533 * 2)   INDEX =   1.585665109 (or 585.665109 using the original INDEX= from above posting)

Rounded to 3 places past decimal = 1.586. Hence we have a poly lens

Hope this helps. I have now created a small Excel sheet, so my brain can go back to sleep (normal state).

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## haya

:drop:  wow!!!

That is pretty impressive stuff JRS; i will definitely be getting my calculator out to play around with those figures...

a BIG, HUGE thanks, 

haya

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## ziggy

DEAR OPTI-GODS, 
   I just wanted to say thanks too you all. I only stop by this forum when I feel as though I need to get some question solved. But now I can also stop in when I get to thinking that I am one of the great ones. Man do you guys realy know how to bring an (standard) optician to his knees. I should have stayed in school!! 
Paul:drop:

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## Jeff Trail

Paul,

   You could always check out some "on line" classes if you wanted to delve into the side that we "lab rats" have to deal in.
   One of the regular contributors to this board (Laurie) is an instructor at Hillsbourough C.C. and they do offer a wide range of classes that are done via the web (WebCT) ... Since you already have a lic. you could just go for certian classes where you might want to expand in..I really enjoyed Geometric Optics and they do offer four semesters or so of "lab classes" where you get into the formula's behind the optics in the lens part.
    Geo was more along the lines of ray tracing and lens makers formula's but it was fun..
   I also really enjoyed Anatomy and Physiology of the Eye class.. 

   The toughest part for me is I usually just get calls with "here's the problem..what is the answer" and they do not really want to hear the way I came up with it ;) ..Guess that's the "bane" of being a wholesale lab owner, you are great when they need an answer but the fall guy when they need a place to put the blame on :Rolleyes:  

     Find Laurie on the "profile" section and E-M her if you are interested in the Web class...besides a ton of stuff the mail you and get access to on WebCT you get a load of instructional Vid's ...

Jeff

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## John R

Don't know if this will help you but i have done a chart showing the power reduction that is achived by using the Hi-index materials.

You may have to right click and save as to get the file...

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## Optom

It is normally our lab technicians who does this;I will check with them and post it here or email you if it's lenghty.
I think it works out this way-you check total power of lens(F=F1+F2)using lens clock calibrated for refractive index 1.523.
Now check lens in focimeter,there is a chart to work out power(F)difference in ratio which gives you refractive index of lens.It is more of practical method.
I'll re-check & post you correct method soon.
Regards,
Shabbir Kapasi:)

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## Optom

Hello,
Method used in my lab is reading off index of unknown lens from ratio of power difference as given by geneva lens measure and focimeter.Chart is very long to be posted on this tread.Anybody interested can email me as I can scan it for you.
Our technicians told me that there are accurate methods written in following textbooks: Ophthalmic Lenses by Mo Jalie,Essentials of Dispensing by A.H.Tunnacliffe.
Regards,
Shabbir

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## sandeepgoodbole

I suspect other than the Optical methods of calculating RI, it may be possible to conclude by measuring the density. RI goes on increasing as the density. Don't know whether there is a linear pattern or else. Steve, Guru Shanbaum, John R and other Honerable Fathers  may have some thing to enlighten from this angle .

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## shanbaum

> _Originally posted by sandeepgoodbole_ 
> *I suspect other than the Optical methods of calculating RI, it may be possible to conclude by measuring the density. RI goes on increasing as the density. *


While they tend to be linked for a given class of materials, it's possible for a less dense material to have a higher index than a more dense one...  polycarbonate and crown glass come to mind.

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## haya

Me is a mere, humble student and thus, me is trying to absorb a little of the knowledge that you guys have thrown my way!  It is a slow and painful process, :shiner:, BUT, hopefully i can come through this and still hold my head up high!  

haya:hammer: head

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## Pete Hanlin

Now that all the intellectually challanging ways to find your unknown refractive index have been discovered, I will meekly add that I keep a copy of "Lenses" handy and sometimes use it to check the base curve against those used by different manufacturers.  

Actually, this is more useful in identifying the manufactuerer rather than material of the lens, but I've used it for both occasionally.

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## Johns

Jeff:

I took the Hillsborough C.C. course that included Geo w/ Dr. Norm Ross.  We were still on Davis Island at the time, and all I remember was how I never felt so proud of receiving a grade of 76% on a paper.  Talk about brain drain for us mere mortals.

John (and no...I'm not an O.D.)

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## sandeepgoodbole

> _Originally posted by shanbaum_ 
> *
> 
> While they tend to be linked for a given class of materials, it's possible for a less dense material to have a higher index than a more dense one...  polycarbonate and crown glass come to mind.*


Guru devo bhava !!
Is that an exception enough to proove the rule or sufficient to discard the possibility of drawing a curve between RIS and the density.

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## Clive Noble

I wish I hadn't started reading this thread.

I got left behind with the academic stuff,  I didn't really want to get my books out but I probably will now!!

However, it got me thinking.  At least 3 or 4 times a week someone comes to me and asks
"Clive, what's the index of this lens"

My answer is nearly always right.

After establishing the Rx and lens style  it's then a combination of weight,  feel,  smell, chromatic aberration at edges, colour of material, sound when gently dropped and just a general instinct of having lived with this stuff for 12 hours a day, 6 days a week, 49 weeks a year and 35 years.

I'm sure I'm not the only one who can do this!

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## haya

I have to admit, i do think that your reply is very interesting! It calls out to my lazy instinct... I mean, I would love to have those skills but I think that I am a long way off to honing my art to that depth!!!

haya:D 

p.s. Clive, i hope that you are not pulling my leg...  :Eek:

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## Jeff Trail

John,

   I guess I kind of have an advantage since I have worked both sides of the tracks, retail and wholesale and have had to had to learn it "self educated" but I did enjoy the classes. 
   What I can't pound enough into peoples heads is that to really understand an answer in certian lines of optics you have to have the basic principles of optical theory to really get a grasp on this harder stuff.. you have to have that base to build on and it works in layers, knowing a lot of the formula's are great, and having hands on processing of lens is great but you really need to blend the two area's to really get a good grasp on optics.
   I still get a kick out of a lot of opticians who "memorized" things to get by the ABO and NCLE and than when they get that little pc. of paper saying they are certified can't explain things because they have not a clue of the theories behind the answers.. if everyone that came into an optical fit a "true or false" or multiple choice and you had a few selections than life would be so easy.. but since that is not real life they tend to get lost pretty quickly.
    I have probably trained 30 or more people to sit for the boards and probably 90% of them just want the "easy" answer to remember and not the mathmatics behind it to get the answer. Out of all the accounts I have I could probably count on one hand the number of opticians that understand slabs and count again and have fingers left over on that one hand for the number who know HOW to figure the degree of slab! LOL
    Prism is another point where I know a lot of my accounts need help in. 
    I wish more people would take the college classes to bolster their optical knowledge... I know a lot of us on here have a pretty good grasp of optical theory but I tend to think we are the minority NOT the majority in our field.. or so it seems with the people I deal with daily.
     One thing I could never understand on here is some people I have seen post that say that there is not a need for further education in optics and people can learn via sponsorship and on the job training.. but that usually only teaches the basics hands on but not anything on the theoretical side and chances are the majority won't learn much more than the person who sponsored them and I can tell over the last 12 or so years I have owned my lab that as a whole we are going backwards in knowledge while the technical side of optics have been getting more complicated.
    Did you ever notice that the majority of us who go off into the more complicated things are a little older? (OK so I'm 37 and admit it)LOL There is a place for coolie cutter and chain driven optics but it's not all that easy stuff when you get into a private practice or low vision or visual training just to name a few points of interest.
    It would seem to me if opticians who wanted to expand the scope of opticenry sure would want to make that next step of higher education a must NOT an elective if you wanted to prove the point... I know that the school (HCC) has 3 or so semester of refracting on top of all the other stuff required to get the degree..and how could someone be dispensing contacts and not know physiology and antomy of the eye?
    Oh well guess I'm just a lab rat ahead of his time.. :-) BUT a lab rat that can refract both in plus and minus cylinder and can wear out a trial frame set :-)

Jeff "wish more people took that xtra step" Trail

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## TRISH

I AM WONDERING IF THEIR IS SOMETHING OUT THERE THAT PATIENTS CAN SEE WHAT FRAMES LOOK LIKE ON THEM WHEN THEY HAVE THEIR GLASSES OFF AND WHEN THEIR EYES ARE DILATED. I HAVE PATIENTS SEVERAL TIMES A DAY SAY THEY CAN'T TELL WHAT THE FRAME LOOKS LIKE ON THEM. I KNOW THERE MUST BE SOMETHING AVAILABLE OUT THERE. THANKS TO ALL. TRISH

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## chip anderson

Trish:

Get a video camera,  let them try on a selection, then put thier old glasses on and let them see the playback.

Your welcome.

Chip

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