# How does depth of field work optically?

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How is it that a camera is able to focus on a set distance, yet blurring things both closer and farther? Whats the difference between a near small image and a far large image?

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The rays of light emanating from an object need to be narrowed down to a single point for them to be picked up by the human eye or a camera sensor as a clear picture. That’s what the lens in your eye/in your camera is for. Without that, the image would be entirely blurry

Light from objects at different distances comes at different angles, which require lenses of different focal length. The focal length is simply a measure of how strongly the light we receive is converged. Thankfully, the human eye’s lens can contract and dilate to change the focal length, and cameras have small motors that shift the position of the lens to focus as well.

Typically there’s a circular lens and the image it forms sees the world from every point on the surface of the lens. The right edge of the lens will see the world from a slightly different point of view than the left edge. Focusing can correct the discrepancy, but only for objects at a limited range of distances from the lens. It’s fundamentally an issue of geometry. Pin-hole cameras, with just a single point of view, have infinite depth of field.

You can experiment yourself by looking at a scene where near objects appear in front of far objects. If you cover one eye and then the other then the image you see will change as each eye has a slightly different point of view. If your eyes converge to look at a near object then far objects no longer line up and you can see a double image of them.

Imagine you have a single convex lens. At a certain distance the object is in front of the lens, there will be a perfect image formed somewhere, at a certain distance behind the lens. This distance is dependent on something called the focal length of the lens. There is also a magnification associated with the image. If you move slightly away from that perfect image distance (while keeping the object distance from the lens the same), the image will look blurry.

The reverse is also true; if you keep the image distance the same but change the object distance, the image will look blurry. The depth of field characterizes the approximate small range of the object distance where the quality of the image is still sharp. Let’s say you shift the object distance from the lens slightly. The distance from the lens where a perfect image is located will also change. Thus, if you change any one of the object or image distance from the lens, the other has to also change to get a sharp image. The magnification will change too.

We know this is how lenses work due to some math involving modelling light as rays.