An optical flat is used to measure the height difference between a reference slip gauge $\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the optical flat using a monochromatic light of wavelength $0.5 \mu \mathrm{m}, 12$ fringes were observed over a length of $15 \mathrm{~mm}$ of gauge B. If the gauges are placed $45 \mathrm{~mm}$ apart, the height difference of the gauges is ____________ $\mu \mathrm{m}$.
(Answer in integer)