An eyepiece graticule includes a scale marked into 100 divisions. A stage micrometer is marked with 50 divisions, and the separation between each division is $0.040\,\text{mm}$. When a $\times 40$ objective lens is used, the full length of this stage micrometer scale coincides with 15 divisions on the eyepiece graticule. What is the true length of the 100 division scale on the eyepiece graticule?
- A$1.3\,\text{mm}$
- B$13\,\text{mm}$
- C$75\,\mu\text{m}$
- D$750\,\mu\text{m}$