Mathematics or Illusion, 

That is the Question here!

 

Article #: 27

Note to the Reader: I receive an average of 5 email questions a week. Top that with 25 to 30 business related emails per day and I find myself bogged down. Although I have been able to answer all questions within a timely manner on a personal level, I have been doing a very poor job of keeping this portion of the web site up to date. I apologize and will work harder to improve this situation. You will note however, that I can now add graphics to the articles.

Dear Charlie:

Thought I would give your email question a try. So here goes. With our ever-shrinking chip size, I'm finding it hard to match lenses with cameras. For instance, I am working on a site that has 1/4" cameras with 6.5mm-65mm zoom lenses. I want to add a 1/3" camera to the site. Will a 5mm-50mm zoom lens give me the same views? Is there a formula to figure this out?

I sure could use your expertise, Charlie. Please give me an e-mail at your convenience.

Thanking you in advance, Sign me,

Signed: More or Less in the image

Dear More or Less,

This is an excellent question and a very common problem. The good news is that there are ways to calculate the differences between the various formats of cameras and lenses. To really understand the solution however, you will need a basic understanding of what it is all about. I put together a couple of graphics to help explain the differences that you are encountering.

It starts with an understanding of the different formats of lenses. Wide angle, Standard, Telephoto. Wide angle lenses give us a very wide view and are used for, (as a rule) image reproduction of areas that are close to the cameras view. Usually for objects that are within 0 to 15 feet of the cameras range. Standard lenses reproduce an image equivalent to what the human eye sees at the same distance. The key difference here is that the lens does not have the peripheral range that the eye does. Telephoto lenses, of course, are used for long range areas.

When we talk about the different lenses, i.e.; 16 mm, 25 mm, et cetera, we are referring to the focal length of the lens. This is determined by the distance between the major optics within the lens as measured in millimeters (mm). If a lens has a space between the main optics of 16 mm, it will be a 16 mm lens. If the space is 120 mm, it will be a 120 mm lens. We also know that the larger the space or the longer the lens, the more telephoto the lens will be and in retrospect, the small the space or shorter the lens, the wider the angle of view will be. The focal length of the lens determines the field of view or how wide and tall the image will be.

The next step is to understand that the lens format size must meet or exceed the camera format size and that each camera format size has it's own standard lens or starting point. Format size however, has nothing to do with the image size (See fig. 1)

. For example, I can use a 2/3 inch lens on a « inch formatted camera and still have a full image. I cannot however, use a « inch lens on a 2/3 inch camera as the focused image will not completely cover the chip or sensor, causing a black ring around my image. I repeat that the format size of the lens has nothing to do with the size of the image.

The standard lens for a one inch camera is 25 mm. This means that if we have a one inch formatted camera with a 25 mm lens, we will reproduce an image equivalent to what the human eye sees at the same distance. This is the first step to calculating the differences between the various format sizes of cameras and their standard lenses. If you know the standard for a one inch camera, everything from there is simple math.

What is the difference between a one inch camera and a 1/4 inch camera? Simple. The 1/4 inch camera is 1/4 the size of the one inch camera. Therefore, basic logic would tell us that the standard lens for the 1/4 inch camera would be 1/4 as much as the one inch camera (See Fig. 2).  Therefore, 25 mm divided by 4 equals 6.25 mm. So if I have a one inch camera with a 25 mm lens and a 1/4 inch camera with a 6.25 mm lens, sitting side by side, the images on the two monitors should look equal ... and they will.

The same would be true with the 1/3 inch camera. 25 mm divided by 3 equals 8.33 mm (we round this up to 8 mm for the 1/3 inch standard). Also with the « inch camera. 25 mm divided by 2 equals 12.5 mm lens as standard for the « inch camera.

To calculate the difference between a 1/3 inch camera and a 1/4 inch camera (as in your example) would be as follows:

1/4 inch lens X 4 = 1 inch equivalent / 3 = 1/3 inch equivalent

6.5 mm - 65 mm zoom X 4 = 26 mm - 260 mm / 3 = 8.67 mm to 86.7 mm zoom

In other words, your 1/3 equivalent would be rounded to the nearest lens which would be an 8 mm - 80 mm zoom. The use of a 5 mm - 50 mm zoom on your 1/3 inch camera will result in a wider view and a shorter zoom. To compensate, you could mount your camera closer to the scene.

Based upon your 1/4 inch camera (with 6.5 mm - 65 mm lens) being mounted 25 feet away from your wide angle subject, your field of view would be about 12 feet wide. To accomplish the same with the 1/3 inch camera with a 5 mm - 50 mm lens, you would need to mount the camera at about 17 feet from the wide angle scene. But this is a whole separate math lesson for the next time around.

I hope that this helps you out. If you have any additional questions or need any further assistance, please feel free to holler at any time. I am in your service.

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