Final answer:
The spacing between slits, s, for a diffraction grating with 200 slits per millimeter is 5 x 10^-6 meters or 5 micrometers. This measurement is fundamental in multiple slit diffraction for calculating the diffraction pattern of light.
Step-by-step explanation:
If a diffraction grating has 200 slits per millimeter, this means that there are 200,000 slits per meter because 200 slits per mm is the same as 200,000 slits per meter (since 1 mm is 1/1000th of a meter). To find the spacing between the slits, s, which is also referred to as the slit separation distance d, we need to take the inverse of the number of slits per meter. Therefore, d = 1 / 200,000 m, which simplifies to d = 5 x 10-6 m or 5 micrometers.
Understanding this is crucial for predicting the pattern of light when it passes through the slits, which is based on principles of wave interference and diffraction. This calculation forms the basis for solving problems in multiple slit diffraction such as finding the angles at which various wavelengths of light will constructively or destructively interfere, leading to the bright and dark fringes observed in diffraction patterns.