How to calculate the 35mm-equivalent-focal-length of 31.4mm?

[Dominik Seibold]

I tried to reproduce the denoted 35mm-equiv.-focal-length of 31.4mm of the ex1 at full wide with my knowledge about the intercept-theorem, the chip-size of the ex1 and the stated focal-length of 5.8mm. But my results differ a lot.
That's how I'm calculating it by using the diagonal fov as reference:
Typical 35mm-stuff has the dimension of 35mmx24mm.
So the diagonal is: sqrt((35mm)^2+(24mm)^2) = 42.4mm
The diagonal of the ex1-sensors is: 1/2" = 0.5*25.4mm = 12.7mm
So the equivalent 35mm-focal-length using the intercept-theorem is: (42.4mm/12.7mm)*5.8mm = 19.4mm
But that's way too little! What am I doing wrong?

[Eric Pascarelli]

This issue is that the diagonal of the EX1 sensors is not actually 1/2"

Nor is a 2/3" camera actually 2/3"

These are "nominal" sizes based on the diameter of the round video tubes which predate chip based sensors. Tube diameters were bigger than their imaging areas.

I've never seen a published spec for the EX1 sensor size, but 2/3" sensors are 9.6 x 5.4mm, giving them a diagonal of 11mm, which is actually less than 1/2"

Also, 35mm still frames are actually 24x36mm. And FOV comparisons are generally done using the horizontal angle of view, and there is no really elegant way to compare frames with two different aspect ratios anyway!

[George Kroonder]

Eric is right; 2/3" is 11.0 mm diagonal. The diagonal stays the same regardless of 4:3 or 16:9 sensor size, so the sensors dimensions are different. I'm convinced you have the math skills to work them out ;-)

The diagonal value for 35mm is 43.3mm. For the standard 1/2" size that is 8.0 mm, giving a ratio of 1:5.4125.

George/

[Charles Papert]

Remember that "35mm" can refer both to 35mm still photography and 35mm cine photography, and that the dimensions are very different between the two due to the orientation (horizontal vs vertical) of the film in the camera.

[Buck Forester]

This is an obvious question, but what is the 35mm equivalent range of the Sony stock EX1 lens... speaking in terms of 35mm still photography.

[George Kroonder]

Copy/Paste from the Sony brochure:

f = 5.8 to 81.2 mm (equivalent to 31.4 to 439 mm on 35 mm lens)

George/

[Eric Pascarelli]

Originally Posted by Charles Papert

Remember that "35mm" can refer both to 35mm still photography and 35mm cine photography, and that the dimensions are very different between the two due to the orientation (horizontal vs vertical) of the film in the camera.

Correct. Super 35 4-perf is approximately 18x24mm (depending on how you define the image size - full gate, tv transmission, etc.)

8-perf (still or VistaVision) is 24x36mm.

The "35mm equivalents" used in the prosumer video (EX1) and digital SLR specs generally refer to 8-perf FOV's.

[Dominik Seibold]

Fine. But can anybody show me a reasonable calculation resulting in (approx.) 31.4mm?

[David Lorente]

Originally Posted by Dominik Seibold

Fine. But can anybody show me a reasonable calculation resulting in (approx.) 31.4mm?

Easy.

As George said, the diagonal of a 1/2" sensor is 8 mm. The diagonal of an 8-perf 35mm frame is 43.27 mm. So the ratio between both is 1:5.40875.

Now you just have to multiply the focal lenght of the 1/2" lens by 5.4 to obtain the equivalent focal lenght for 35mm. For the wide end of the EX1 zoom, that's 5.8 mm.

5.8 x 5.40875 = 31.37 ≈ 34 mm

If you want to do the inverse thing, that is, to know what focal lenght in 1/2" is equivalent to a certain focal lenght in 35mm, divide it by 5.40875.

Example: a 24 mm wide angle lens in 35mm is equivalent to a 24 / 5.40875 ≈ 4.4 mm lens.

[George Kroonder]

Right.

Just for clarification; you can use the ~5.4 ratio to convert between focal lengths for 35mm and 1/2" equivalents, but as Charles stated for Field of View comparisons you need to take the dimensions of the sensor into account.

The 2/3", 1/2", 1/3", etc. sensor sizes are based on old picture tube sizes. A 1" tube had a image diagonal of 16.0 mm. The inch-sizes are derivative approximations from that base.

If you imagine a 16 mm circle, you can fit different rectangles within its confines to get different sensor dimensions/aspect ratios (4:3 and 16:9 being the most relevant in video). For all possible aspect ratios the diagonal will always be the same as it is that of the confining circle.

If you need to calculate the focal length (equivalent) for some specific Field of View, you need to use the horizontal and/or vertical ratio to account for aspect differences between the different film/sensor sizes.

George/

[George Kroonder]

For your pleasure and because I was bored:

Wikipedia has a comprehensive list of Film formats, so take your pick...

Standard "35mm" size
35mm (43.3 mm)
4:3 = 36.0 x 24.0 (mm)

Standardized sensor dimensions (diagonal):
1" (16.0 mm) - The Base
16:9 = 13.95 x 7.84 (mm)
4:3 = 12.80 x 9.60 (mm)

2/3" (11.0 mm)
16:9 = 9.59 x 5.39 (mm)
4:3 = 8.80 x 6.60 (mm)

1/2" (8.0 mm)
16:9 = 6.97 x 3.92 (mm)
4:3 = 6.40 x 4.80 (mm)

1/3" (6.0 mm)
16:9 = 5.23 x 2.84 (mm)
4:3 = 4.80 x 3.60 (mm)

Jerry, stick a fork in me...I'm done.

George/