## N.A. Re-visit

Everything relating to microscopy hardware: Objectives, eyepieces, lamps and more.
Message
Author
linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### N.A. Re-visit

I'm probably not the first person who didn't find understanding N.A. a no-brainer. Let alone even understanding why it's printed on the objectives. For what purpose?

Until I found this nifty formula in my Zeiss manual:

Maximum useful magnification = N.A. (1000)

So, for me:

4x = 100
10x = 250
40x = 650
100x = 1250

But what does this mean? If I am looking at a diatom with my 10x, that means that it is 100 times larger than it would be if I looked at it with the naked eye. But according to the formula it is 250 larger. So I don't understand.

My only guess is that the above references maximum theoretical magnification (not "empty" magnification) and not actual magnification.

Can anyone explain what is going on?
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler

BramHuntingNematodes
Posts: 828
Joined: Tue Jan 21, 2020 1:29 am
Location: Georgia, USA

### Re: N.A. Re-visit

It would be 250x with a 25x eyepiece.
1942 Bausch and Lomb Series T Dynoptic, Custom Illumination

dtsh
Posts: 310
Joined: Wed May 01, 2019 6:06 pm

### Re: N.A. Re-visit

As I understand it, that's a general rule for what magnification you can expect before reaching empty magnification.
With the usual 10x eyepieces one is typically well within the useful range of the objective allowing you to swap in higher mag eyepieces to get more. For example, if you have 40x objective and no 60x, the 40x (0.65 NA or so) is good to 650x (0.65*1000), so a pair of 15 eyepieces would get you that 600x.

linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### Re: N.A. Re-visit

@Bram . . .

I already calculated the N.A. for my objectives (which I left out). It depends on one's specs.
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler

linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### Re: N.A. Re-visit

@dtsh

O.K. so the magnification I do achieve is a function of my ocular multiplier. So based on a given objectives's NA(1000), that gives me maximum possible magnification (and concomitant resolution). If I want to exceed my actual magnification, I can change the eyepiece, re-multiply, and if I don't exceed a given objective's NA(1000) I have useful magnification without loss of resolution.

If that's the case, is it common practice to have a range of oculars available?

@Bram . . .

I think you're right. I missed your point.
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler

linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### Re: N.A. Re-visit

This would explain why N.A. is printed on objectives. Two arithmetic calculations tells you if changing the eyepiece can give you magnification/resolution that is useful provided that you do not have the necessary objective. Changing the ocular multiplier is another parameter we have at our disposal but you need the N.A. for each objective.

first calculation: maximum useful magnification = NA (1000) on a given objective. Note that value.

second calculation: say, 15x eyepiece times objective. If the result does not exceed the above vallue, your magnification is useful.
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler

75RR
Posts: 7753
Joined: Sun Oct 12, 2014 2:34 am
Location: Estepona, Spain

### Re: N.A. Re-visit

Useful magnification:

There is a formula (well a rule of thumb really) to calculate this: Range of Useful Magnification (500-1000 x NA of Objective)

In which the 500 x NA (Numerical Aperture) is the minimum necessary for the detail present in an image to be resolved,
and anything over 1000 x NA gives empty magnification.

as an example:
For a Plan 40/0,65NA Objective
the range would be between
500 x 0,65 = 325 and
1000 x 0,65 = 650 so
below 325x total magnification, detail will not be resolved
above 650x total magnification, no additional detail will be resolved

best Useful Magnification Range for this objective is between 325x and 650x

A quick test is to multiply the NA of an objective by 1000,
then multiply the magnification of the objective by the magnification of the eyepiece,
if the second figure is higher then using that objective with that eyepiece will result in empty magnification.

Another useful test is to divide the max magnification by the objective's magnification, this gives you the max eyepiece magnification for that objective.
In this case 650/40 = 16. Therefore a 16x eyepiece would be ok (just) but a 20x eyepiece would give empty (too much) magnification with this objective.
Zeiss Standard WL (somewhat fashion challenged) & Wild M8
Olympus E-P2 (Micro Four Thirds Camera)

Voyager-1
Posts: 26
Joined: Fri Mar 12, 2021 7:48 pm

### Re: N.A. Re-visit

75RR,

Thanks! You made something that was insurmountable very easy to understand!
What a revelation, thanks again 75RR!

V

pippo1234
Posts: 56
Joined: Thu Dec 24, 2020 8:21 am

### Re: N.A. Re-visit

What does the lower bound in that formula imply for micrography? Let’s say 2.5x relay lens and full frame camera and plan 40x,0.65 objective: .65 x 500 = 325 >> 100 = 40 x 2.5.

Does it mean that some detail that could be resolved is not? But is it present and can it be resolved just by magnifying the photo?

TIA

Scarodactyl
Posts: 1299
Joined: Sat Mar 03, 2018 9:09 pm

### Re: N.A. Re-visit

Putting aside the difference between the size and nature of the retina vs a camera sensor, your eye has a wide angle ~23mm lens in front of it which significantly reduces the final magnification of the image. So comparing the magnification there can be tricky.

linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### Re: N.A. Re-visit

@75RR
@Voyager-1
@pippo1234
@Scarodactyl

Thanks to 75RR for your robust post! On further reflection, I don't see the need for the lower value of 500. According to my Zeiss manual, the formula is NA(1000) = maximum useful magnification.

So, to give an actual example, I wanted to purchase an eyepiece > 10x. The only eyepiece by Zeiss that fit my eyetube was a 16x. I decided to check my 40x objective. It's NA is 0.65, so moving the decimal three places to the right, I get 650 maximum useful magnification. Any value > will not permit that objective. Any value < will permit that objective. So 40(16), multiplying my ocular with the 40x I get 640, so, yes, I can use that objective. That was a mandatory calculation prior to purpose.
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler

linuxusr
Posts: 52
Joined: Sun Jun 24, 2018 9:00 pm

### Re: N.A. Re-visit

I left out part of the formula for NA.

It is:

N.A. = n(sin)(theta)

n = refraction rate between specimen and objective lens

n=1 for air
n=1.515 for oil
Nikon AlphaPhot 2 < Zeiss Primostar 3, Full Koehler