From thick model to pin-hole model : the nodal points influence

The pin-hole model merely consists of using only one optical ray through an equivalent point called the optical center. The extension of the optical model to different media indices, shows that the role of the optical center will be played by the fusion of the two nodal points that conserve the angular magnification.

In the vision community the focal length is defined by the distance between the CCD sensor and the optical center. It can be seen in figure (2.2) that this distance is equivalent to $N_iF_i$ if the object is at infinity.

$$N_iF_i=N_iH_i+HiF_i= \frac{(n_1-n_2)}{k} + \frac{n_2}{k} = \frac{n_1}{k} = f_o$$

$$f_o=N_iF_i= n_1 \frac{r_2}{(n_2-n)} = n_1*Ct$$ (11)

This last relation is a major one for our purpose. It can be noticed that the (vision community) 'focal length' is directly proportional to the object medium index $n_1$, because $n$ (glass index), $n_2$ (CCD medium index $n_2=1$) and $r_2$ are constant.

When the camera is underwater, the focal length is equivalent to the value measured in air multiplied by a factor $1.333$.