As given on FADGI glossary a bit depth is explained through following example

a typical color image using 8 bits per channel is often referred to as a 24-bit color image (8 bits x 3 channels). Color scanners and digital cameras typically produce 24 bit (8 bits x 3 channels) images or 36 bit (12 bits x 3 channels) capture, and high-end devices can produce 48 bit (16 bit x 3 channels) images. A grayscale scanner would generally be 1 bit for monochrome or 8 bit for grayscale (producing 256 shades of gray). Bit depth is also referred to as color depth.

However depth of field (DOF) is defined as the distance between the nearest and farthest objects in the frame. In order to have the entire image sharp, a large DOF is recommended. In other cases, a small DOF may be useful, focusing the subject while de-emphasizing the other elements of back or foreground. In cinematography, the first case is referred to  deep focus, and the later one is called shallow focus.

Hope it helps

Czechoslovak Journal of Physics, September/October 1993, Volume 43, Issue 9-10, pp 977-981

Peculiar meaning of the concept of the information depth in appearance potential spectroscopy

Also see the above article will help improve this concept.

Happy Learning:)

Thanks madam.