2. You would like to build an atomic emission spectrometer to measure the two D

Question

2. You would like to build an atomic emission spectrometer to measure the two D lines from sodium with a prism. Given a BK7 prism with a base length L = 2 cm and an apex angle of 60 degrees,

1) calculate the refractive index at two different wavelengths 580nm and 590nm using the Sellmeier equation listed in the lecture notes.

2) calculate the maximum spectral resolving power of the prism. Would you be able to resolve the D lines?

Hint: you can use n/ as an approximation for dn/d.

3) is it possible to use a prism with another glass material to separate the D lines?

Hint: check the refractiveindex.info website to find the Sellmeier equation for different glasses. Generally speaking, the higher the refractive index, the larger the angular dispersion of the prism.

Explanation / Answer

1) n2() = 1 + (B12 / 2 - C1) + (B22 / 2 - C2) + (B32 / 2 - C3)
   where n is the refractive index
For BK7, B1 = 1.0396 ; B2 = 0.2318 ; B3 = 1.0105 ; C1 = 6.0006*10-3 m2
C2 = 2.0018*10-2 m2 ; C3 = 1.0356*102 m2
At =580 nm = 580*10-3m
Just plug in all values in the equation,
n2(580 nm) = 1+1.05848+0.24646-3.29316*10-3
n2 = 2.3016539
refractive index at 580 nm , n = 1.5171
Similarly perform calculations for 590 *10-3 m using the same equation,
n2(590 nm) = 1 + 1.057835+0.245943-3.408086*10-3
refractive index at 590 nm , n = 1.5166

2) Maximum resolving power of the prism, R
   Rmax = base * |dn/d| = (2 cm) * | (1.5171-1.5166) / (580*10-7-590*10-7) |
  Rmax = (2) * 500 = 1000

3) Yes, it is possible to use other glass materials like silica to separate D lines.

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