A beam of red laser light with wavelength $633\,\text{nm}$ is incident normally on a diffraction grating having $600$ lines per mm. The red beam is then swapped for blue laser light of wavelength $445\,\text{nm}$. A new diffraction grating is selected so that the first-order maximum of the blue light is formed at the same point on the screen as the first-order maximum of the red light from the original laser. What is the number of lines per mm in the replacement diffraction grating?
- A$420\,\text{mm}^{-1}$
- B$470\,\text{mm}^{-1}$
- C$600\,\text{mm}^{-1}$
- D$850\,\text{mm}^{-1}$