Discussion
Light of wavelength 1.5 μm incident on a material with a characteristic Raman frequency of 20 × 1012 Hz results in a Stokes-shifted line of wavelength :
Answer: C
The Stokes line is at 1.67 μm.
Work in frequency. The incident frequency is \(c/\lambda = 3 \times 10^{8}/1.5 \times 10^{-6} = 2.0 \times 10^{14}\) Hz. A Stokes line is shifted down by the Raman frequency:
\[ \begin{aligned} \nu_{s} &= 2.0 \times 10^{14} - 0.2 \times 10^{14} \\ &= 1.8 \times 10^{14}\ \text{Hz} \\ \lambda_{s} &= \frac{3 \times 10^{8}}{1.8 \times 10^{14}} \\ &= 1.67\ \mu\text{m} \end{aligned} \]
1.47 μm would be on the anti-Stokes side (shorter wavelength). 1.57 and 1.77 μm do not correspond to a 20 THz shift.
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