What is the resolving power of a diffraction grating that is capable of just distinguishing between two wavelengths of 568.20 nm and 569.60 nm? (1 nm = 10−⁹ m) A)1.10 B)406 C)487 D)812 E)568.9

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Quizplus · Accepted Answer

The resolving power of a diffraction grating is given by the formula $R = \frac{\lambda}{\Delta \lambda} = mN$, where $R$ is the resolving power, $\lambda$ is the wavelength, $\Delta \lambda$ is the difference in wavelengths, $m$ is the order of diffraction, and $N$ is the number of lines per meter on the grating. Here, $\lambda = 568.90$ nm (the average of the two wavelengths), and $\Delta \lambda = 569.60 nm - 568.20 nm = 1.40$ nm. Without knowing $m$ and $N$, we directly calculate $R = \frac{\lambda}{\Delta \lambda} = \frac{568.90}{1.40} \approx 406$, assuming the calculation is done in the first order ($m = 1$).

What Is the Resolving Power of a Diffraction Grating That