The formula for vertical measurement by means of the fine adjustment of the microscope,
n2/n1 x measured depth = real depth,
is true, where n2 is the refractive index of the object and n1 is that of the immersion medium of the objective lens. The refractive index of the mountant is unimportant.
Several additional complications of this method of measurement suggest that it should not be used unless it cannot be avoided, or rough figures are required quickly.