When I look through binoculars, rifle and pistol scopes, I observe some that seem to not be magnified the amount they should be. How can I easily verify the magnification of an optical device?

That’s a good question I’ve wondered about myself.
We could compare two devices side by side at the same nominal magnification setting to see if they agree, but that wouldn’t confirm the actual magnification.

Something to keep in mind is that some designations such as “4-16” are marketing claims like “super powerful” detergent. Reading the actual specifications of optics from reputable companies may reveal that “4-16×50mm” scope is actually 3.8-15.5×. I don’t know how common that is these days, but it’s something I noted years ago.

Your question prompted me to ask the AI Gemini this: “how accurate are manufacturers' riflescope magnification claims”

Part of the answer:
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Manufacturers' claims regarding riflescope magnification are generally accurate but rarely exact. While many users expect a "3-9x" scope to provide precisely 3.0x and 9.0x power, the industry operates with a degree of rounding for marketing purposes and built-in mechanical tolerances.

### 1. Nominal vs. Actual Magnification
Manufacturers typically use "nominal" numbers for product names because they are easier to market. However, the technical specifications (the "Actual Magnification") often reveal slight differences.
* **Marketing Rounding:** A scope sold as a **4-12x** might actually have a range of **4.4x to 11.6x**.
* **The Mark 5HD Example:** For instance, the **Leupold Mark 5HD 3.6-18x44** is specifically listed with an actual magnification of **3.6x to 18.0x**. In this case, the branding matches the technical reality, but in the **VX-3HD 3.5-10x**, the actual magnification is often closer to **3.3x to 9.7x**.

### 2. Industry Tolerance Standards
While there is no single global law governing magnification accuracy, most high-quality manufacturers aim for a tolerance of **±5%**.
* If a scope is set to 10x, a measured magnification between 9.5x and 10.5x is considered within acceptable industry norms.
* Budget-tier optics may have wider variances, sometimes reaching **±10%**, which can be noticeable when trying to use reticle subtensions for ranging on a Second Focal Plane (SFP) scope.

...

Added: I asked Gemini this follow-up question: "is there a way for the user to confirm the actual magnification of the scope." The answer provided some detailed suggestions about methods to confirm the actual magnification, so that may be of use. I will probably try them myself at some point.

Easily is the trick.
Magnification Factor = Apparent Size / Actual Size. If you are at a distance where a yardstick looks like 1/2 a yard to your eyeball, but your scope makes appear 1yd, you have a 2X scope.
You need to be able to measure the apparent size of an object of known size. Getting that measurement precisely enough to be useful can be easier said than done - any measurement error is literally multiplied. An accurate reticle is probably the best you can do if 'Easily' means 'Not a bunch of extra, expensive, equipment that is difficult to set up & use'.
Take an object of known size. Then measure it as accurately as possible* on the device you are trying to verify.
*I would set the lowest magnification & change distance to be able to get the object to line up to reticle lines as closely as possible. Then repeat on highest magnification.

With a cheap digital microscope, I stick a ruler under it & mark 1mm in software, then the software knows the magnification and any measurement I take is accurate as long as I don't touch the focus/magnification and the object is the same distance from the lens.
I've pulled my hair out with a very expensive system that was supposed to be able to do that automatically, but would randomly be off just enough that we wouldn't notice until a lot of data turned into wasted time & compliance failures. Now, every Picture0.jpg that thing spits out is a picture of a ruler + a measurement that should = 1mm+/-0.03. If the user doesn't notice that the software is giving bunk data, at least we can calculate the real measurement. There have been other checks & changes to make sure a colossal fuckup doesn't happen again, but this satisfies 'the show must go on' requirement.

I can think of a relatively easy way, but not laboratory precise. Print out some words at various font sizes, and see what's the smallest font you can read at 5 yards. Then move that out to 50 yards, and the smallest you should be able to read should be the same at 10X. Do the math for other powers.

I am not sure what you are seeking.

Buy reputable optics from reputable vendors.

There is no way in a store that you can verify the magnification.