Discussion
Resolving power of a 2 \(cm^{2}\) site grating having a rulings of 600 l/mm in order one is approximately :
Answer: D
The resolving power is approximately \(10^{4}\).
The resolving power of a grating is \(R = nN\), the order times the total number of rulings illuminated. A grating of area 2 \(cm^{2}\) has a ruled width of the order of 1.4 to 2 cm, so with 600 lines per mm:
\[ \begin{aligned} N &\approx 14\ \text{mm} \times 600 \approx 8.5 \times 10^{3} \\ N &\approx 20\ \text{mm} \times 600 = 1.2 \times 10^{4} \end{aligned} \]
Either way, in the first order (n = 1) \(R = N \approx 10^{4}\). The options 10, \(10^{2}\) and \(10^{3}\) are one or more orders of magnitude too small; \(10^{3}\) would correspond to only about 2 mm of ruled width.
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