Here is my original report:

For more details, see http://www.truetex.com/raspberrypirkinch wrote:This is my analysis proving the 4mm focal length of the stock lens in the camera module based on my physical measurements and the Omivision OV5647 specs.

Shooting a full-resolution still (2592 x 1944 pixels) displays a field of view about 34.75 inches wide at 38 inches.

By optical principles, this corresponds to a 2*atan(0.5*34.75/38) = 49 degrees horizontal field of view. Likewise the vertical field of view is 37 degrees, and the diagonal 61 degrees.

The sensor chip is 3.674mm wide. Proportioning this by 38/34.75 = 4mm yields the lens focal length.

Comparing to a 35mm film camera (36mm x 24mm frame), the relative sensor size is 36mm/3.674mm = 9.8x, or 10x as an approximate rule of thumb. So the Raspberry Pi camera module with its 4mm lens acts like a 35mm camera with a 40mm lens, in terms of field of view. Depth of field is likewise scaled 10x. The aspect ratios also differ, namely 4:3 (Raspberry Pi) versus 3:2 (35mm film).

For the 1080p video frame, the system uses the center 1920 x 1080 pixel crop, and the field of view is proportionately different from the full frame. The 1920 pixel width corresponds to 2.721mm on the sensor. This cropping is 2952/1920 = 1.35x horizontally and 1944/1080 = 1.8x vertically from the full frame. A sample image shows a field of view 76 inches wide at 112 inches distance. Proportioning 112/76*2.721mm = 4mm focal length, as expected. HD 1080p field of view is 37 degrees horizontally, 21 degrees vertically, and 43 degrees diagonally.

The 35mm lens equivalent for the 1080p video mode would be 36mm/2.721mm*4mm = 53mm.

My microscopic examination of the lens entrance pupil shows it to be about 1.25mm diameter, so the f/number of this 4mm lens is 4mm/1.25mm = f/3.2.