How a -2.5 diopter myope with 3.5 diopters of accommodation can see clearly from about 16.7 cm to 40 cm

Understanding the range of clear vision in uncorrected myopia is a neat little puzzle that connects math, physiology, and everyday sight. If you’ve ever wondered how a doctor reasons through figures like far points and accommodation, you’re in good company. Here’s a clear, practical walk-through using a classic example from visual optics: a −2.5 diopter myope with an accommodation amplitude of 3.5 diopters. The takeaway? The range of uncorrected clear vision lands from about 16.7 cm up to 40 cm in front of the eye. Let me explain why.

What those numbers mean in plain language

• Myopia in diopters (D) tells you how strongly the eye bends light. A −2.5 D myope has trouble seeing distant objects, because their eye’s focusing power isn’t enough to bring distant light rays to the retina.

• The far point is the furthest distance at which light from a distant object can still be brought into focus by the uncorrected eye. For our −2.5 D myope, that far point sits at 40 cm in front of the eye.

• Amplitude of accommodation (A) is how much extra focusing power the eye can summon when you actively try to see something closer. Here, that reserve is 3.5 D.

• The range of clear vision without corrective lenses is then the span from the closest distance at which you can still focus (near point, NP) up to the far point (FP) for distance objects.

So how do we get NP and FP in numbers?

1. Far point distance (FP)

• For myopia, FP in meters is the reciprocal of the myopia’s magnitude: FP = 1 / |M|. Here, |M| = 2.5 D, so FP = 1 / 2.5 = 0.40 meters, i.e., 40 cm.

• In everyday language: without glasses, this person can clearly see things that are as close as 40 cm or closer, but anything farther away tends to blur.

2. Near point with accommodation (NP)

• When you use your accommodation, you add power. The eye can push its total focusing power up by the accommodation amount A. Since the myopic base is 2.5 D, adding the full 3.5 D yields a maximum effective power of 2.5 + 3.5 = 6.0 D.

• The closest distance you can clearly see with that maximum power is NP = 1 / (|M| + A) = 1 / 6.0 ≈ 0.1667 meters, which is about 16.7 cm.

3. The range

• Put those two ends together: NP ≈ 16.7 cm on the near side, FP = 40 cm on the far side. Between these distances, light can be focused onto the retina without correction; farther than FP or closer than NP, it won’t be in sharp focus.

Why this is a tidy, intuitive result

• It’s a nice demonstration of how myopia and accommodation work hand in hand. The eye’s baseline power (the myopia) sets a “default” point where things at distance start to blur. The accommodation reserve acts like a dimmer switch, letting you pull in closer objects by increasing the total power.

• The 16.7 cm figure isn’t arbitrary. It comes straight from the added power you can summon (3.5 D) plus the existing myopic demand (2.5 D). Add them and you’ve got 6.0 D of total focusing power, which corresponds to a nearest point of about 16.7 cm.

A quick mental model you can carry to real life

• Think of your eye as a little camera. If the camera has a fixed focal length that’s too short for infinity, you can compensate by changing the lens power—but only up to a point (your accommodation saturation). For our example, you can zoom in (focus on nearer things) until you hit about 16.7 cm. Beyond that, the eye runs out of spare focusing power.

• That explains why many people with uncorrected myopia see things clearly at arm’s length or closer, but struggle with anything beyond a few tens of centimeters. The exact numbers depend on how strong the myopia is and how much accommodation a person can muster.

A few real-world tangents that fit this topic

• Reading distance and devices: If you’re myopic and you’re staring at a phone or a book, you’re often within that NP range—unless you push the text a little too close. As screens get smaller and text gets crisper, we end up hovering at a distance that’s comfortable and within the eye’s available accommodation.

• Age matters: Amplitude of accommodation tends to decline with age. A younger reader might hit a smaller NP and cover more of the near-to-far span without glasses; an older reader might find that range narrower, and the numbers shift a bit. That’s why many people switch to corrective lenses as years go by.

• What would glasses do here? If this person wore a −2.5 D lens correction (glasses that push the overall power toward normal vision for distance), the FP for distant objects would shift. Corrective lenses don’t erase the basic relationship between M and A; they simply change the coordinate system—distance becomes easier to see because you’re shifting the eye’s effective power toward the right value to land images on the retina.

A simple, practical summary

• FP for uncorrected −2.5 D myopia: 40 cm

• NP with accommodation 3.5 D: about 16.7 cm

• Range of clear vision without correction: roughly 16.7 cm to 40 cm

• The math actually hinges on adding the myopic magnitude and the accommodation: NP = 1 / (|M| + A), FP = 1 / |M|.

That’s the core idea in a compact package. It’s one of those little calculations that sneaks into daily life more often than you’d think: reading menus at a cafe, glancing at a street sign from across the corner, checking the clock on the wall while you’re at a desk. All of these moments ride on the same basic principle: how the eye’s focusing power lines up with the distance of what you’re trying to see.

If you’re curious, you can test this concept in a safe, hands-on way (with an eye care professional present, of course). A simple far point demonstration—using a chart at a known distance and a bit of accommodation—can illuminate how far your own NP and FP drift with age or as you try different focal tasks. It’s a gentle reminder that vision is a living system, not a single static number.

A final thought

Numbers like 40 cm and 16.7 cm aren’t just trivia; they’re meaningful clues about how your eyes balance power and purpose. The more you understand that balance—the dance between far points and near points, between baseline myopia and accommodative reserve—the more you’ll see how the eye adapts to daily life. And if you ever want to poke around a bit deeper, you’ll find the same relationships repeat themselves, just with a few decimals shifted by the strength of the myopia and the size of the accommodation reserve.

If you’re revisiting this topic, keep the key takeaway handy: FP = 1 / |M| and NP = 1 / (|M| + A). For our example, that’s 40 cm and 16.7 cm, respectively, stitching together a practical range of clear vision that fits neatly between them. It’s a small equation, but it unlocks a lot about how we actually see the world—close, far, and everything in between.