Final answer:
The separation of slits for a diffraction grating with 678 rulings per millimeter is calculated by taking the reciprocal of the number of rulings per meter, which results in a slit separation of 1475 nanometers.
Step-by-step explanation:
The student is asking about the separation of slits in a diffraction grating that has 678 rulings per millimeter. To find the separation between the slits, or the slit separation (d), we need to take the reciprocal of the number of rulings per unit distance. Since there are 678 rulings per mm, we can convert this number to rulings per meter by multiplying 678 by 1000, giving us 678,000 rulings per meter. The separation d is then the reciprocal of this number.
d = 1 / (number of rulings per meter)
d = 1 / 678,000 rulings/m
d = 1.475 x 10-6 meters
d = 1475 nanometers (nm)
Therefore, the separation of slits for this diffraction grating is 1475 nm.