Saturday, September 15, 2012

The Science of Photography -- Part Seven

In the last episode, we learned the three things that affect depth of field: f/stop, lens focal length, and distance to the subject. In a deeper examination of the impact of focal length, we learned that the size of the film or sensor determines the way the subject being photographed is displayed -- it’s size or field of view--and that this is often referred to based on a central lens size called a “normal lens.” Lenses with focal lengths less than "normal" are considered wide angle and lenses with focal lengths longer than the "normal" value are considered telephoto lenses.

The interesting thing is that the value of focal length that is considered “normal” depends on the sensor size. In the days of film photography, when 97% of cameras used 35mm film, this was not an issue. A 50mm lens was considered "normal."

But in this new age of digital cameras, most sensors are smaller than 35mm, and many are much, much smaller. This changes the lens focal length that is considered this median, normal value, and some old habits and assumptions are not correct. There are advantages to the smaller sensors because they allow for smaller and cheaper optics to work, but there are disadvantages too. As usual, at least in my opinion, knowledge is the key to using these new, smaller cameras and that is the business I’m in -- the knowledge business. So, lean back, grab a hot beverage, and enjoy this chapter of the Science of Photography as we learn more about the impact of different sensor sizes.

The important thing to understand is that, when you buy your camera or camera body, the size of lens that is considered “normal” may be different than you expect, and the ranges of lens focal lengths for wide angle, “normal” and telephoto views is based on the size of the sensor in the camera. I’ll start with a description of what determines a "normal" lens for a camera. Once you know what the normal lens is (and I’ll quit putting the term in quotes from now on), you'll know that any focal length shorter than that is wide angle, and the shorter it gets, the wider-angle it gets, and that anything longer than normal is telephoto, and the longer it gets, the more telephoto.

Figuring out the focal length that determines a normal lens is pretty easy. All you need to know is the size of your film or sensor. The normal lens focal length is generally considered to be equal to the diagonal of the image size.

Lens focal lengths even on small point and shoot cameras are often referred to in terms of their 35mm equivalents, so I am going to start with 35mm film/full frame digital sizes as a reference. In 35mm film cameras, the actual image size is 24mm x 36mm.

Film formats are rectangular or square, and square corners means ninety degrees, so to figure the diagonal, you use the formula for the hypotenuse of a right triangle. You remember: the square root of the sum of the squares of the other two sides. Sure, the Pythagorean Theorem, I remember it well!

It's easy. With 35mm film, add 24 squared (576) plus 36 squared (1,296) and you get 1,872. Take the square root of that number and you get 43.3. That is the size of the normal focal length for a 35mm camera. A lot of 35 mm cameras had a 50mm lens, slightly longer than the 43mm calculated as the size of the normal lens.

We will repeat this calculation for smaller sensors, and you may wish to calculate the normal lens focal length for your camera and sensor size. Do be careful if you do this with a simple calculator. If you enter the first number, and then press the x-squared key, that’s fine. If you then press the plus key and enter the second number and then press x-squared, you won’t get the second number squared, but you’ll get the first number squared plus the second number, that entire sum squared. I suggest you square each number individually and write down the values. Then add those squares and take the square root of the sum. You can also use parentheses on the fancy calculator or use calculator memory to save values. I just wanted to warn you about a common calculator mistake. If you’re not sure, you can even do the squares by hand. You may find the square root calculations a little hard to do manually, although it can be done and the method was taught, around sixth or seventh grade. But, now we have calculators. Thank God for calculators! I also link to several web sites which will help you find the length of the diagonal for your camera’s sensor.

So what is the significance of all this ancient cameras and more ancient mathematics -- whether from sixth grade or the much older greek method of determining the hypotenuse? Most 35mm film SLRs came with a 50mm lens as the normal lens, slightly longer than the 43mm calculated above. A 50mm lens was typically the standard lens installed on cameras in those days. A few compact film cameras came with 35mm, 40mm, or 45 mm lenses.

Anything shorter than 43mm would be a wide angle lens, anything longer telephoto (actually, 50mm is hardly telephoto, just sort of a long normal).

One of my early cameras was a Konica C35 rangefinder camera. It had a 35 mm lens, and was a good example of these smaller cameras with a slightly wide angle lens. It had a built-in exposure meter and shutter speeds from 1/30 to 1/650 of a second automatic tied to the exposure meter. You would set the aperture f/stop and the camera automatically set shutter speed for correct exposure. It had an f/2.8 lens and a dial to set the film speed. It would calculate exposure for film speeds from ASA 25 - 400. ASA was an early American predecessor of the current, international ISO value.

As I asked earlier, what is the significance of all this ancient math and normal lens focal length? Why would we care? It is because, in this day and age, most digital cameras have sensors smaller than the 24mm X 36mm area of 35mm film. In fact, that size is huge compared to most small cameras today. DSLRs have larger sensors, but even most DSLR cameras don’t have senors as big as the old 35 mm film. Only the top, professional, and expensive models have full sized sensors.

So assuming that 43mm or even 50mm is the dividing line between wide angle and telephoto is not correct. With smaller sized sensors, the normal lens size is smaller -- maybe a lot smaller.

Both of my  digital SLRs have APS size sensors, about 2/3 the size of 35mm film. APS stands for “Advanced Photo System,” a late attempt at a simple consumer film format for those for whom loading and rewinding 35mm was too complex. The typical tiny compact digital point and shoot camera has even smaller -- actually tiny sensors, and cell phone cameras have teeny-tiny sensors.

You can check the technical reference data in your cameras manual or on the web to see what size sensor is in your camera. Remember, a smaller format sensor or film is going to take a shorter lens to be normal, and shorter focal lengths have greater depth of field.

I’ll save you the calculations and list a few common camera’s sensor size and resultant normal focal length. What I haven’t mentioned so far is that, in the days of film, there were cameras with film size larger than 35mm such as the Hasselblad two and a quarter inch camera. This is true today too, with some expensive cameras having very large sensors such as the professional Hasselblad digital camera. I’ll list those too.

(Unfortunately, FB Notes does not have good table formatting, so you’ll just have to bear with this and make the best that you can of the following list.)

Camera                                Sensor Size                    Normal Lens

Speed Graphic Press             4” x 5”                                  162mm
Film Camera                        101.6mm x 127mm  

Hasselblad Film Camera       2 1/4 inch squared                 85mm
                                            60mm x 60mm  

Hasselblad Digital                36.8mm x 49.1mm                 61mm

35mm film                           24mm x 36mm                       43mm

Nikon D3                             23.9mm x 36.0mm                  43mm

Canon 5D                            23.9mm x 35.5mm                  43mm

Canon 60d                          16.7 x 25.1mm                        30mm

Nikon D7000                      15.6mm x 23.6mm                   28mm

Canon T2i                           14.9mm x 22.3mm                   27mm

Olympus PEN and                13.0mm x 17.3mm                   22mm
Panasonic Lumix                 4/3” Micro Sensor

Canon G12                          1/1.7”                                      9.5mm
                                           5.7mm x 7.6mm

Small Canon                        1/2.3”                                      7.7mm
                                           4.12mm x 6.16mm

iPhone                                 2.68mm x 3.58mm                 4.5mm    

Finally, I just read of an experimental sensor produced by Canon and billed as the world’s largest (and the most sensitive). It is 202mm x 205mm for a normal lens focal length of 288mm. I suspect that sensor will be put into an astronomical telescope or some sort of CIA satellite. Only the government could afford the cost of the lens needed to match that sensor!

If you would like to read more about sensor size, view a few more common camera sensors, and even see representations of these sensors -- drawings of just how big they actually are (although it does depend on the size of your computer screen) -- then check out this web site:

I also found this to be a good site for reference:

You can look up your personal camera on the internet and find the sensor size and calculate its normal lens depth of field and compare to the above table. Now for the application. Remember, the shorter the focal length, the greater the depth of field. Tiny cameras like those in cell phones have such short normal lenses, and you can assume these fixed lens cameras probably have normal focal length lenses, that they have a giant depth of field. As I’ve said before, that’s how they can get away with not having any focus adjustment. But, with those cameras, you are not going to be able to operate with a narrow depth of field and be able to have part of your picture be out of focus. That eliminates a lot of artistic effects.

Not only are these calculations good for determining what size lens is normal, but a lot of modern zoom lenses are specified with their “35mm camera equivalent focal lengths.” That can be confusing, especially if you don't notice the distinction between actual focal length and the equivalent lengths.

Here is a web site with a focal length comparison tool to allow you to make that kind of comparison:

For example, the Canon The EF-S 55-250mm f/4-5.6 IS, which -- as it says -- is a 55-250 mm lens intended for use with APS sensors. In the Canon technical description it states the 35mm camera equivalent zoom is 88-400 mm. So you old time photographers who considered a 400mm lens as pretty long glass, notice that this 250mm max zoom lens is equivalent when used with a small, APS sensor.

There is more to say. Now that we’re on the subject of sensors, what about the sensor resolution? You know, those megapixels you’re always hearing about. What about them? At this rate I may never get this series on the “Science of Photography” done.

OK, I’ll explain about sensor resolution and the science behind that modern wonder. I’ll have to write fast because this is changing all the time. So, wait until tomorrow to hear more about sensors. Their size and other goodies. Until then, TTFN.

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