# Depth of Field and Lens Equivalents Explained

A fundamental aspect of even the most basic lens is that at some point it will produce a sharp image of an object when that object is at a distance of one focal length from the lens. The same principle is used in photography lenses, except that unlike rudimentary lenses, such as magnifying glasses, the image has to be formed on an image sensor. In this video, John P. Hess from Filmmaker IQ elaborates:

#### Focusing Distance

On lenses that have focusing distance indicators, you can verify the distance at which the lens is focused. Let’s say a lens is focused on an object that is 10 feet away. That’s the distance at which the lens is focused. Now the question is, how close do we have to be so that the focus is good enough? In this case, will an object at a distance of 11 feet also be acceptably in focus?

#### Depth of Field

Depth of field signifies how much space we have in front of and beyond the focus plane where an object will be acceptably in focus.

Depth of Field

#### Aperture

Aperture plays a key role in determining the depth of field. A smaller aperture produces a much larger depth of field compared to a wider aperture. We all know this. But how about putting this theory to the test?

For this experiment, Hess used homemade apertures with the above setup. The apertures were nothing more than tennis ball can lids through which he punched holes through which he could focus light.

The first aperture was about equal to f/9 (Aperture = Focal length / Aperture Diameter). In this case, he was using a focal length of 130mm with an aperture that was about 14mm. This aperture produced a depth of field of 14 inches, meaning an increase in depth of field associated with the smaller aperture.

Depth of Field produced by a130mm lens with an aperture of f/9

#### Distance to Subject

Another experiment Hess did was to prove that the distance from the subject to the lens has a bearing on the depth of field. With the same f/9 aperture, Hess brought the light bulb (subject) closer to the lens at about 12 inches. The new depth of field was only 6 inches, as demonstrated by this image:

Depth of field produced when the lens is closer to the subject

At 19 inches, the new depth of field was 9 inches:

DoF changes again when the subject is pushed away from the lens

#### Circle of Confusion

“How sharp is sharp enough?”

This question arises because of a factor called the circle of confusion. There can be only one point in the image where the focus is tack sharp. When we look at an image, however, that theory doesn’t work. There is always a bit of leniency. This is due to the circle of confusion.

“The circle of confusion is the maximum size that spot of light can be to be indistinguishable from a single point to the final viewer.”

Here are some other interesting derivations from Hess’s experiments:

• the higher the resolution, the shallower the depth of field
• smaller sensors produce shallower depth of field, with the lens and aperture remaining the same

#### Crop Factor

If you shoot with a 50mm lens on a crop sensor camera like the Canon 7D, the resulting angle of view is equivalent to that of an 80mm lens on a full-frame camera. Here’s a comparison:

Comparison of angle of view on different sensor sizes

To get the same angle of view applying crop factor you get this:

80mm lens on a full-frame camera to match 50mm on an APS-C camera

As you will notice the bokeh with the longer lens appears more pronounced. This is because when applying crop factor to the focal length you also need to apply that to the f-stop:

With f-stop adjusted for the crop factor

But why is the image so dark? That’s because the crop factor has to be applied to ISO as well:

Hopefully this video has helped you understand how lens equivalents and depth of field work. Let us know what you think in the comments.

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### One response to “Depth of Field and Lens Equivalents Explained”

1. R.G.Menon says:

Very nice article. I had some unclear thoughts about the optics of camera lens. I could never grasp how a zoom will affect the depth of field. The video cleared it. The video says that as the object approaches the focal lenth the image distance retreats from the focal distance. What happens to the image? It would have been nice if you had dealt the maths for this scenario too. It would have been benificial to those like me who are not adept at maths. Mr. Hess may I expect to get a rreply pl. I would be obliged and thankful.

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