A glass slab consists of multiple thin uniform layers of progressively increasing refractive indices such that the R.I.(refractive index) of any layer is $\mu +\mathrm{m}\Delta \mu .$ Here $\mu$ and $\Delta \mu$ denote the RI of $0^{\text{th }}$ layer and the difference in R.I. between any two consecutive layers, respectively. The integer $\mathrm{m}=0,1,2\dots$ denotes the number of the successive layers. A ray of light from the upper most layer enters the consecutive layer at an angle of incidence of $30°$. After undergoing the ${\mathrm{m}}^{\text{th }}$ refraction, the ray emerges by grazing the interface. If $\mu =1.26$ and $\Delta \mu =0.012,$ the value of $\mathrm{m}$ is_____.