I have various magnifying glasses and I'm using them when I take macro photos with a phone or a camera. I want to group/label my magnifying glasses by their magnification power. And by magnification power I mean something like 10x.

Lens magnificationmicroscope

An Allen wrench, in its turn, is a separate manual tool. However, both a hex bit and an Allen wrench have the same hexagon shape (if to look at the front side).

When you have a lens with a given focal length then you have two equations with three unknown. So, when you want to calculate the magnification you would not have a unique solution. However manufactures probably want to add a label to their lenses which a layman can understand. For this they probably will use eyepiece magnification,

Macrolens magnification

where $f$ is the focal length of the lens, $v$ is the distance from the object to the lens and $b$ the distance from the lens to the image of the object. This is demonstrated in the image below, including three principal rays (these only apply for thin lenses).

Have you ever assembled furniture? Or maybe you spend hours in your garage? Then you definitely used this tool. Some call it a hex key, others - an Allen wrench.

where the numerator is equal to the least distance of distinct vision, which is roughly 250 mm for a human with normal vision.

where $n$ is the refractive index of the lens material, $d$ the thickness of the lens, $R_1$ and $R_2$ the radius of curvature of the two sides of the lens.

Cameralens magnification

With a ball end hex key, the fastener access angle can be varied, there is no need to approach the fastener directly at a 90° angle, which is very convenient.

Allen wrenches are compact, portable, and lightweight, you can take them with you wherever you need to go. In addition, using them reduces fatigue, increasing your productivity.

Zoomlens magnification

Here $\text{F}_1$ and $\text{F}_2$ are the two focal points of the lens, with $f_1$ and $f_2$ as their respective focal lengths (these are often equal to each other, which is also assumed in the first equation).

So, Allen vs hex head? Now you know there’s no difference. On Mega Depot, you can find hex keys that come in an array of sizes (measured by across-flats - the distance between the opposite ends of the flat side). Note that if your Allen wrench is bigger than it should be, the fastener or instrument may be damaged.

Maximummagnificationcameralens

The tips of a hex screwdriver and an Allen key are the same but the difference lies in the shapes of these tools. Typically, an Allen key is L-shaped and a screwdriver is straight with a handle for more convenience.

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Make an optical setup aimed at the wall so that the flashlight is static and exactly 90 degrees to the center of your lens (make sure that you know how close your lens is to the wall!).

Take a flashlight and tape a cross to it(make sure you don't let any light through the taped section, this is very important).

(1) I didn't calculate it, I just drew the magnifying glass in Illustrator with its actual values Index of refraction doesn't matter. The result doesn't have to be 100% correct. 1.52 can be used as the index.

Lens magnificationcalculator

For more than a century, people have been using these instruments, they are affordable and popular among many users the world over, including professional mechanics as well as those who need these tools for home use.

These instruments are essentially L-shaped wrenches with 6 sides. They are used to drive hexagon-shaped recessed holes. Greek "hex" means "six". Hence the name.

I believe that the difference between the radius of curvature and the thickness is great enough to use the thin lens equation [if not I have another formula at the end that will work with this method].

Hex keys with a ball end have one undeniable benefit - they are perfect for hard-to reach places, or, for example, if the bolt is located close to the obstruction on one of the sides. In this case, using a ball end hex key is more effective than using a regular hex key. With a ball-shaped end, it is easier to slide your key into the receiving slot. You will save your time, that’s for sure!

Lens magnificationChart

However, using a ball end hex key is not the best option when it comes to high-torque applications as you will lose some fastener engagement.

To calculate their magnification power, I've read several Wikipedia pages, Lens (Optics) for calculating focal length, and Magnification for calculating magnification power, but I end up with wrong results. I must be doing something wrong.

At the beginning of the 20th century, William G. Allen patented a cold drawing process for making hex socket set screws. Wrenches for turning such screws became widely popular. "Allen" is a registered trademark, however, even wrenches by other manufacturers are sometimes called Allen wrenches.

The resulting magnification, $M$, will be equal to the ratio between $h_1$ and $h_2$, which when expressed in terms of $v$ and $b$ looks as follows,

At the very least, even if the lens isn't thin enough to utilize the thin lens criterion, you will be able to calculate a magnification, by dividing the image's distance to the lens into the cross' distance to the lens (unless you used the height method I gave you first). After you have the magnification, you can use the relationship to calculate the focal length by the relationship: Magnification = (focal length)/(focal length - cross' distance from the lens). You have 1 equation and 1 unknown now. I am curious as to what you measure the focal length to be with each method. If you get different results, the lens was likely too thick to use the thin lens equation, however, you will still be able to calculate the focal length no matter what, and can therefore calculate the power by dividing that into 1 and multiplying it by 100.

I figured the focal length of magnifying glass by experimenting with a light source, but I want to calculate it on a paper.

Lens magnificationformula

It is important to mention that a hex key with a ball end makes point contact with the screw. A hex key with a straight end, in its turn, makes the line contact. Keep that in mind.

A lens does not have have one specific magnification, it depends on the positioning of the lens. When neglecting aberrations, the workings of a lens can be simplified with the following equation,

On our website, there are tools made by various manufacturers, choose the best Allen wrenches that meet your needs. It is possible to buy hex keys separately or in sets.

Nowadays, there are many hand tools to choose from. But this article is aimed to help you figure out the difference between an Allen wrench and a hex key.