Is the formula for object image size given focal length, etc. independent of sensor size?

Question

I am trying to figure out how big an object of, say, 50cm height at 100m distance and 600 mm focal length would appear on a camera's sensor. The ubiquitous formula

$$ \textrm{object size in image} = \frac{\textrm{focal length} \times \textrm{object size}}{\textrm{object distance}} $$

yields

$$ \textrm{object size in image} = \frac{\textrm{600 mm} \times \textrm{.5 m}}{\textrm{100 m}} = \textrm{3 mm} $$

What I am wondering: Are these 3mm entirely independent of sensor size?

E.g., a specific superzoom model has a 1/2.3" sensor (= 4.55mm height according to one source) and a maximum zoom quoted to have a "35mm equivalent focal length of 600mm". Would the object actually cover 3/4.55 = approx. 66% of this sensor's height = 66% of the image, or does the relation between the sensor size and the "35mm equivalent" have to be taken into account somehow?

(My apologies if this has been asked before - I have found many related questions, but not this one.)

Answer 1

The answer to your question generally is yes. However as you mention, the ratio of how much of the overall image your subject takes up will depend on your sensor size. What you do have to watch out for is that the "35mm equivalent focal length" should not be used but the actual focal length as quoted on the camera specs - this is usually something in the single digits of millimetres.

The 35mm equivalent is for comparison purposes only because it reflects the equivalent area of 35mm film (or a full-frame digital sensor) - i.e. 36 x 24mm. People tend to be most familiar with the range of focal lengths at this sensor size e.g. 24mm is wide, 50mm is normal, anything about 100mm is telephoto and so on. This is simply the real focal length multiplied by a factor that represents the ratio between the camera's real sensor size and the nominal 35mm sensor size.

Answer 2

Yes, they are independent of sensor size. Even if the subjects appear to be bigger or nearer on a smaller sensor because of the larger pixel density, the subject's size on the sensor is the same regardless of sensor size.

To elaborate: If a subject occupies 3mm of a sensor, it will occupy 3mm even if you change the sensor size, given that you keep the distance, focal length and subject size unchanged.

The "size on sensor" is often referred to as the reproduction ratio and is widely used in macro photography. E.g., a reproduction ratio of 1:1 means that the subject is the same size in real life as on sensor.

http://en.wikipedia.org/wiki/Macro_photography

Answer 3

Don't forget about the "35mm equivalent" (or fullframe) clause on lenses.

Focal length in your equation is actual focal length. Its because of this issue specifically that they will say for example that a 50mm focal length lens on a 4/3" sensor is equivalent to what a 100mm lens would produce if your sensor were fullframe.

The 50mm lens produces the same sized image whether the sensor is fullframe or smaller, but because that image is a larger proportion on a smaller sensor, the lens has a "35mm equivalent" of a longer focal length.

Answer 4

It depends on how size is measured. If it is with a ruler, then the image formed at the sensor plane will be the same regardless of sensor size.

However, because it is common to measure sensor sizes and image sizes in pixels, and the size at which images are displayed and printed is often related to the quantity of pixels, there is an important sense in which the image formula is misleading.

For example, consider a 3mm x 3mm feature captured on a 24 mega-pixel 3:2 format sensor. If the sensor is 24mm x 36mm the image will cover 250,000 pixels. On a 16mm x 24mm sensor it will cover more than twice as many pixels. Likewise the feature in the image made with the smaller sensor will cover more screen real estate if naively displayed.

Answer 5

I think that the image size formed in the sensor is the same, only the angle of view is variable with the sensor size.