Final answer:
The resolving power of a diffraction grating with 15,000 rulings for first order is 15,000 and for second order is 30,000.
Step-by-step explanation:
The resolving power of a diffraction grating is given by the product of the total number of lines (N) on the grating and the order number (m). For a diffraction grating with 15,000 rulings in its width, the resolving power in the first order (m=1) is simply 15,000, because the order number does not amplify the number of lines. For second-order (m=2) diffraction, the resolving power would be twice the number of rulings, which is 30,000.
To calculate the resolving power we use the following formula:
Resolving Power (R) = N × m, where N is the number of lines and m is the order of the spectrum.
In this case:
- For first order (m=1): Resolving Power (R) = 15,000 × 1 = 15,000
- For second order (m=2): Resolving Power (R) = 15,000 × 2 = 30,000