Measure object depth with ray_cast There is a template script:
operator_modal_view3d_raycast.py
That show how use the ray_cast() to find the the coordinates of hit face.
But I want to measure the distance of the opposite face from the hit face.
The depth of the object from the 3d view.
You can use mathutils.geometry.intersect_ray_tri to check any intersections with object triangles.
You can use the raycast method and then again with normals inverted to get the opposite face