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Sunday, 7 February 2010

Focal length and angle of view

The focal length is the measurement from the lens to the sensor in millimetres which determines the angle of view; with 50mm focal length (on a full frame/35mm camera) being the accepted standard angle of view to the way we see. Due to a person’s peripheral vision it’s not an exact comparison though, and would be somewhere in the region of 40-50mm on a full frame camera.

The course notes indicated that the simple guide to finding the standard focal length is roughly the same as the diagonal measurement across the sensor:

  • A full frame sensor of 36mm x 24mm therefore would calculate a standard focal length of 43.3mm, which ties in with the agreed ‘standard’ between 40-50mm
  • So in my camera with a sensor size of 22.5mm X 15mm, would calculate out a standard focal length of 27mm.

I then thought back to what I found in the camera’s manual; taking the ‘focal length multiplier’ (1.6) into consideration.

Using this as a calculation I found the following:

  • For my camera to show the same angle of view as 50mm standard focal length it would work out as 31.25mm
  • I then took the calculated result of 43.3mm as being the standard from my first investigation with the 1.6 factor the result all fell into place with the 27mm result for my sensor!

The calculation in the course notes ties in exactly to what I found in the manual! Indicating my standard focal length being approximately 27mm 

Both of these methods appear to be in line with the course text and all other references I could find in books and the internet.

Having worked on some of the theory it was time to test this in line with the exercise.

NOTE: Unless relevant, (as in this exercise) I won’t routinely convert the values in relation to the FLM (Focal Length Multiplier); i.e. the focal length on my lens/EXIF may state 50mm; and although this relate to an angle of view of 80mm as used by a full frame camera. I will still write it as 50mm in my notes for continuity throughout the course.

The first part of the exercise states

‘Point the camera at any scene, and keep both eyes open – one eye looking through the viewfinder, the other looking directly at the scene. If the lens is approximately standard in focal length you should notice that the objects seen through one eye should appear to be about the same size as through your other eye. This is what is meant by standard.

However this is not what I found.

I first mounted the camera onto a tripod and set my 18-55mm (28-88mm equivalent) - lens to the ‘standard focal length’(as calculated earlier); There is a small dot on my lens that is marked at 28mm, which if taking into consideration the ‘calculations’ is approximate enough for the exercise.

Note: Not the most interesting of viewpoints (my back garden) but the ISO was fixed at 100 for all images in the exercise and the focus point was the right hand half coconut from the bird table.

I noted that looking through the viewfinder with one eye and keeping my other eye open on the scene I could see that objects in the viewfinder were NOT the same size. (below)

28mm Image

Aperture f/5.60

Shutter 1/8 sec 

Then Keeping the camera in the exact position on a tripod I increased the focal length to 55mm and checked the viewfinder again. This time objects ....appeared to be roughly the same size (An equivalent focal length of 88mm)!

The angle of view was smaller and the bird table appeared closer (below)

55mm Image

Aperture f/5.60

Shutter 1/6 sec 

I found the results from the first 2 shots interesting; as the theory (as well as all references I could find in my books and on the internet) from earlier indicated that my equivalent focal length would be approximately 27mm. The question text however suggested that ‘If the lens is approximately standard in focal length you should notice that the objects seen through one eye should appear to be about the same size as through your other eye; however that didn’t happen until the focal length was set at 55mm (88mm equivalent!) contradictory with the theory that my standard focal length would be about 27mm.

I continued with the exercise. Again leaving the camera in the same position I changed the focal length to its shortest focal length of 18mm, equivalent full frame focal length of 28.8mm (below)

18mm Image

Aperture f/5.60

Shutter 1/15 sec 

This was how I expected it. 18mm is the widest angle of view of this lens.

After taking these 3 shots, I printed them out onto A4 size plain paper. Then standing in the exact position that I took the images, I held them at eye level at a distance where the image appears to be the same size and noted the distance

18mm (28.8mm)

Holding the A4 size image at eye level and standing at the same position I found that I had to hold the image very close to my face around, 5-7 Inches, for it to be roughly the same size as what I could actually see.

Angle of view more and object further away

28mm (44.8mm)

This image was held at approx 12-14 inches from my face, which for me was the most comfortable / natural viewing distance; about the same as I would use for reading.

Angle of view natural

55mm (88mm)

For this image to appear the same size as the view I had to hold it at arms length, (even then it was still slightly ‘bigger’ on the A4 image). This was around 26-30 Inches from my face.

Angle of view less and object was closer

I found this exercise quite interesting. Maybe spending more time on it than necessary; however the question suggested (deliberate or not) something that didn’t fit with my initial findings around the ‘standard’ focal length.

Using the printed images established, (for me) that the image with the most comfortable (natural) viewing was taken at my standard focal length of 28mm (approximate to the calculated exercise of 27mm).

Difficult to tell conclude exactly because of peripheral vision, but I don’t believe that A standard focal length makes objects appear the same size in the camera's viewfinder as they appear through the other eye; I believe that the standard focal length is the angle of view similar (or most natural) to the way we see, which is what I found during the exercise.

Final conclusion: I’ve also added a composite of 3 shots on layered on top of each other, each taken at various focal lengths to demonstrate the ‘angle of view’ at different focal lengths. 

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