# I Microscope Magnifications

#### JFS321

Perhaps this should be in the Biology forum, but I'm thinking that you physicists can give a more reliable answer here.

The magnification equation for microscopes is: M = I/A (image size divided by actual size). This seems very easy and intuitive. By this equation, if the image size was equal to the actual size, your magnification would be 1x. Cake.

However, here are just two examples of info from what might be considered by some as reliable websites:
www.sciencing.com: "A 1x magnification power is a 100 percent increase in the magnified object’s size. For example, a 1-inch object at 1x would appear to be 2 inches."

The Glamox Company: "100% magnification = 1X magnification, i.e. the object appears to be twice its actual size."

What gives??? Thanks for the clarification.

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#### davenn

Gold Member
The magnification equation for microscopes is: M = I/A (image size divided by actual size). This seems very easy and intuitive. By this equation, if the image size was equal to the actual size, your magnification would be 1x. Cake.
that is not the usual way to work out the magnification of an optical system

this is the usual way ......
"How is the total magnification of a microscope determined?
Total Magnification is determined by multiplying the eyepiece power (usually 10x) by the objective lens in place. For example, a 10x eyepiece and a 4x objective yields a total magnification of 40x (40 power)."

However, here are just two examples of info from what might be considered by some as reliable websites:
www.sciencing.com:

that link doesn't go to what you are talking about ... definitely not a reliable site

"A 1x magnification power is a 100 percent increase in the magnified object’s size. For example, a 1-inch object at 1x would appear to be 2 inches."
Not sure if that is the correct interpretation ?

100% generally refers to actual size, ie, magnification of 1 ( think printing a document from PC, a photocopier copy, image size on PC screen etc). In all those cases, 100% is ACTUAL size
50% or 0.5 is half size of image/view
200% is double the size

100% and 100x (x100) have two very different meanings
@Andy Resnick is a good lad for this sort of stuff. He will correct us both where necessary

Regards
Dave

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#### JFS321

Dave, thanks. I do think both websites, although they are saying the same thing, are incorrect.

I am good with total power. The magnification formula I give would only be used (I'm assuming) when you need to determine magnification of a printed image with a scale bar, and the total power wasn't given up front.

#### sophiecentaur

Gold Member
Not sure if that is the correct interpretation ?
It's down to the difference in meaning between "Increased By' and 'Increased To'.

In general, Magnification of something is a Ratio of final/initial value and not an Amount Added. Certainly that would apply in Science, even if there is a lot of sloppy talk in the rest of the world. If an Image appears to be twice the size of the object, I would say that the magnification is 2X, which is 200%.
In the Money world, it's true to say that 10% profit means 1/10 more than you start with but that, as a 'magnification' would strictly be 110% (i.e. times 1.1).

Having said that, if a website declares its definition at the start then you should be able to follow its line of argument safely through to the end. Just watch it more carefully and makes sure the arguments are all consistent. If an article uses consistent Maths then it's probably safe.

#### OmCheeto

Gold Member
I've been contemplating buying a microscope for a while, and have been very confused by the products available: Items for sale for $13 seem to have the same magnification(x1600) as$1000+ items.
?????

Anyways, I ended up finding a youtube microscope channel, with a bazillion videos, which answered pretty much all my questions, including this thread's.

Microscope magnification demystified | Microscopy

I attempted to find corroboration of his "250 mm" standard distance, but quickly lost interest, as, in the end, I realized, it really didn't matter at all.

#### Tom.G

I attempted to find corroboration of his "250 mm" standard distance, but quickly lost interest, as, in the end, I realized, it really didn't matter at all.
Yup, 10 inches is the US standard for viewing distance. That's the limiting close-focusing distance of a 'young person.' (are there any on this site?)

The Chinese often use a somewhat larger distance (don't recall what it is) that allows them to advertise a higher power than we do for the same focal length magnifier.

Here is an excerpt from the Edmond Optics site, one of the decades old 'go-to' companies for optical stuff.

Magnification:

10" is assumed to be the closest distance the human eye can focus for comfortable vision. An object only 1" from your eye would be 10 times larger, but out of focus. A magnifier's function is to assist your eye in focusing closer. Since a 1" focal length lens brings clear vision down to 1" from the eye, an object at this distance is clearly seen and appears to be 10 times closer than it does when viewed from 10" away. Such a magnifier is commonly called a 10X or 10 power. Using this definition, the magnifying power of a lens can be approximated as follows: MP = 10/FL if the focal length is specified in inches. If the focal length is specified in mm, the formula will be MP=250/FL.

Actual magnifying power will vary slightly, depending upon working distance, eye relief distance and the characteristics of the observer's eye.
Cheers,
Tom

"Microscope Magnifications"

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