Question

The minimum number of lines in a plane diffraction grating required to just resolve the sodium doublet (5890 Å and 5896 Å) in first order is:

• A. 982
• B. 491
• C. 1964
• D. 246

Hint:

To resolve closely spaced spectral lines, the resolving power of a grating must be sufficiently high.

Answer 1

The Correct Option is A

The resolving power \( R \) of a grating is given by:
\[ R = \frac{\lambda}{\Delta \lambda} = N n \] where:
- \( \lambda \) is the average wavelength of sodium doublet: \( \lambda = 5893 \) Å.
- \( \Delta \lambda = 5896 - 5890 = 6 \) Å.
- \( n = 1 \) (first-order spectrum).
\[ N = \frac{R}{n} = \frac{5893}{6} \approx 982. \]