To determine the output light frequency of the material used before doubling, let's follow these steps:
1. Understand the relationship between wavelength and frequency:
The speed of light [tex]\( c \)[/tex] is related to the frequency [tex]\( v \)[/tex] and wavelength [tex]\( \lambda \)[/tex] by the equation:
[tex]\[
v = \frac{c}{\lambda}
\][/tex]
where [tex]\( c \)[/tex] is the speed of light (approximately [tex]\( 300,000,000 \)[/tex] meters per second).
2. Convert the wavelength from nanometers to meters:
The wavelength of the green light emitted by the laser is given as 532 nm. Since 1 meter is equal to [tex]\( 1,000,000,000 \)[/tex] nanometers, we convert the wavelength from nanometers to meters:
[tex]\[
\lambda_{green} = \frac{532 \, \text{nm}}{1,000,000,000 \, \text{nm/m}} = 5.32 \times 10^{-7} \, \text{meters}
\][/tex]
3. Calculate the frequency of the green light:
Using the relationship [tex]\( v = \frac{c}{\lambda} \)[/tex], we can find the frequency of the green light:
[tex]\[
v_{green} = \frac{c}{\lambda_{green}} = \frac{300,000,000 \, \text{m/s}}{5.32 \times 10^{-7} \, \text{m}} \approx 5.639 \times 10^{14} \, \text{Hz}
\][/tex]
4. Determine the original frequency before doubling:
Since the laser uses a frequency doubler to double the frequency of the emitted light to produce the 532 nm wavelength, the original frequency is half of the calculated green light frequency:
[tex]\[
v_{original} = \frac{v_{green}}{2} = \frac{5.639 \times 10^{14} \, \text{Hz}}{2} \approx 2.819 \times 10^{14} \, \text{Hz}
\][/tex]
5. Compare with the given options:
The original frequency we calculated is approximately [tex]\( 2.8 \times 10^{14} \, \text{Hz} \)[/tex], which matches option B.
Therefore, the output light frequency of the material used before doubling is:
[tex]\[ \boxed{2.8 \times 10^{14} \, \text{Hz}} \][/tex]
