Lens Depth of Field Scales. 2. Intrapolation and the Infinity Mark

A slight complication of reading a depth-of-field scale is that the focusing scale on a lens is not linear. In other words, equal distances on the focusing scale are not equal distances between the camera and the subject. There is a greater distance between, say, the marks for 2 and 3 metres than between those for 3 and 4, and so on. The corresponding position on the focusing ring of the aperture mark on the depth of field scale has to be estimated by intrapolation because there is not room on the focusing ring for marks at, say, every metre, as the subject distance increases.

The pitch of the thread on the focusing ring, the greater circular distance the ring has to be turned to change the point of focus. With a fine thread more marks can be shown. Even with a lens with a long travel (i.e. a good depth-of-field scale), estimates have to be made between, say, 10 and 15 feet with allowance made for the fact that the distance on the focusing ring will be greater for 10-11 feet, than for each succeeding foot up to 14-15 feet. Beginners unaccustomed to non-linearity have to be made to realise that a point midway between the 10 and 15 foot marks is not 12.5 feet.

The reason that the focusing scale is non-linear is not because there is a circular dial. It is simply because of the laws of physics. The graph shows the lens-film distance as the focused subject is moved from 1 to 100 metres from the camera. In the nearest 10 metres, the lens is moved more than 2 mm but the movement is less than a further 0.5 mm in shifting the focus between 10 and 100 metres for a 50 mm lens.

Lens-film (sensor) distance at different subject distances for a 50 mm lens

At long subject distances, the change in the lens-film distance is so small that virtually anywhere within reason could be chosen as a point of maximum travel for the focusing ring. At long ranges an ∞ mark is not really necessary especially for short and medium focal lengths. The focal length (i.e. when the lens is 50 mm from the film) could be the position of the ∞ mark, since the blue line in the graph hits the focal length when the subject is at ∞. But what is infinity? With a depth-of-field scale an ∞ mark is necessary and its position can easily be set by the lens manufacturer, either at the focal length or near to it.

One way of looking at the ∞ mark is to consider it from the point of view of the depth of field scale. Depending on the circle of confusion (see previous post) the lens is focused on a subject at the at the hyperfocal distance. Then the scale can be marked at the near point of acceptable focus at a particular aperture. The measured distance on the scale between the near point and the hyperfocal distance can then be applied to the opposite side of the scale to indicate the point on the focusing scale to which the ∞ mark can be marked on the focusing ring. In other words the ∞ mark is needed for the depth-of-field scale but its position can be calculated in the first place from the calculated depth-of-field for a lens of a particular focal length at a particular aperture.

Out of interest, I measured as accurately as I could the position of the focusing marks on an old Pancolar 50 mm lens, transformed the values so that I could get a linear relationship to subject distance and then extrapolated the line to estimate what distance the ∞ mark was set at. Infinity was set at approximately 255 feet (78 metres). How far the actual setting is from the 50 mm focal length that could be set as being at infinity I do not know.