Diffraction Theory Questions and Answers

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.

Answer: D

The highest resolving power belongs to the Fabry-Perot etalon.

Resolving power \( \lambda/\Delta\lambda \) grows with the number of interfering beams and the path difference between them. A Fabry-Perot etalon works in a very high order (the plate gap is many thousands of wavelengths) with effectively dozens of beams set by the reflectivity, giving resolving powers of order \( 10^{6} \) to \( 10^{7} \) in the visible.

A good grating reaches \( mN \sim 10^{5} \), and a prism, triangular or constant deviation, only about \( 10^{4} \), set by its base length and dispersion. That is why the etalon is used to study hyperfine structure.