Why do 35mm Camera Lenses Produce Different Focal Length Results When Placed on a Digital Body?

Why is it that a 100mm lens when placed on a digital body—with a small sensor size— effectively becomes a lens with a larger focal length? Nothing changes in the lens; we are simply placing it on the digital body. The lens remains a 100mm lens. But, the effective focal length is longer.

As we all know, cameras come in various format sizes—for example, film cameras of large, medium, 35mm, and APS formats, and, more recently, a number of digital cameras with varying sensor sizes. The 35mm full frame camera has been the most popular camera type and typically is used as the reference point. Let’s take an example and visualize what the scene would look like when viewed through a 100mm lens on a 35mm camera. (Please see Figures 1, 2, and 3.)

The image produced by the lens is circular, known as the Image Circle. The Image Circle fully encompasses the rectangular 35mm film, and a rectangular image is captured on the film. Let us see how the 100mm lens, when placed on a digital body, which has a smaller sensor size than a 35mm frame, changes its effective focal length. Let as imagine that we are taking picture of alphabets.

Lets us first use a 35mm camera with a lens at 100mm focal length, Figure 1. The lens under this focal length produces an Image Circle, which captures G to X. The rectangular 35mm film inside this image circle captures I to V as shown below. When we take a print of this picture we get a picture of alphabets I to V.

Next, Figure 2. a 35mm camera uses a focal length of 150mm. Obviously, the Image Circle will now capture less alphabets than what it did at 100mm—lets say the Image Circle now captures J to V. The rectangular 35mm film inside this image circle captures L to U, as shown above, and we get a picture of alphabets L to U.

Next, lets change the lens focal length back to 100mm and place it on a digital body with a sensor size smaller than 35mm frame. As before the image circle captures G to X, but the sensing chip, which is smaller than 35mm frame, will capture L to U, as shown in Figure 3.

When we place a 100mm lens on a digital body—with a smaller sensor size—it produces a picture that is the same as the picture taken by 35mm frame body with a 150mm lens. This is often called the “digital multiplication factor”, or sometimes also known as “Field Of View Crop Factor”. It is the size of the digital sensor, which decides the effective 35mm equivalent focal length of the lens. Various brand digital cameras have different multiplication factors. These factors work to the advantage of photographers interested in telephoto pictures, but often to their disadvantage when they take wide-angle shots with their digital SLRs.