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To determine the output light frequency of the material used in green lasers before frequency doubling, follow these steps:
1. Recall the given variables and constants:
- Speed of light [tex]\( c = 300,000,000 \)[/tex] meters per second.
- Wavelength of green light [tex]\( \lambda_{\text{green}} = 532 \)[/tex] nanometers (nm).
2. Convert the wavelength from nanometers to meters:
[tex]\[ 1 \text{ nm} = 10^{-9} \text{ meters} \][/tex]
Hence,
[tex]\[ \lambda_{\text{green}} = 532 \times 10^{-9} \text{ meters} \][/tex]
3. Calculate the frequency ([tex]\( v \)[/tex]) of the green light using the formula:
[tex]\[ v = \frac{c}{\lambda} \][/tex]
Substituting the values:
[tex]\[ v_{\text{green}} = \frac{300,000,000 \text{ meters/second}}{532 \times 10^{-9} \text{ meters}} \][/tex]
Simplify this expression to find the initial frequency:
[tex]\[ v_{\text{green}} \approx 563,909,774,436,090.1 \text{ Hz} \][/tex]
4. Given that the material's output frequency is doubled to produce the green light, determine the initial frequency before doubling:
[tex]\[ \text{frequency before doubling} = \frac{v_{\text{green}}}{2} \][/tex]
Substituting the calculated frequency:
[tex]\[ \text{frequency before doubling} = \frac{563,909,774,436,090.1 \text{ Hz}}{2} \approx 563,909,774,436,090.1 \text{ Hz} \][/tex]
5. Compare the calculated frequency before doubling with the options provided:
[tex]\[ A. 1.8 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ B. 2.8 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ C. 5.6 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ D. 1.1 \times 10^{15} \text{ Hz} \][/tex]
From the options, the frequency calculated is approximately [tex]\( 5.6 \times 10^{14} \text{ Hz} \)[/tex], matching option C.
### Conclusion:
The output light frequency of the material used before frequency doubling is:
C. [tex]\( 5.6 \times 10^{14} \text{ Hz} \)[/tex]
1. Recall the given variables and constants:
- Speed of light [tex]\( c = 300,000,000 \)[/tex] meters per second.
- Wavelength of green light [tex]\( \lambda_{\text{green}} = 532 \)[/tex] nanometers (nm).
2. Convert the wavelength from nanometers to meters:
[tex]\[ 1 \text{ nm} = 10^{-9} \text{ meters} \][/tex]
Hence,
[tex]\[ \lambda_{\text{green}} = 532 \times 10^{-9} \text{ meters} \][/tex]
3. Calculate the frequency ([tex]\( v \)[/tex]) of the green light using the formula:
[tex]\[ v = \frac{c}{\lambda} \][/tex]
Substituting the values:
[tex]\[ v_{\text{green}} = \frac{300,000,000 \text{ meters/second}}{532 \times 10^{-9} \text{ meters}} \][/tex]
Simplify this expression to find the initial frequency:
[tex]\[ v_{\text{green}} \approx 563,909,774,436,090.1 \text{ Hz} \][/tex]
4. Given that the material's output frequency is doubled to produce the green light, determine the initial frequency before doubling:
[tex]\[ \text{frequency before doubling} = \frac{v_{\text{green}}}{2} \][/tex]
Substituting the calculated frequency:
[tex]\[ \text{frequency before doubling} = \frac{563,909,774,436,090.1 \text{ Hz}}{2} \approx 563,909,774,436,090.1 \text{ Hz} \][/tex]
5. Compare the calculated frequency before doubling with the options provided:
[tex]\[ A. 1.8 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ B. 2.8 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ C. 5.6 \times 10^{14} \text{ Hz} \][/tex]
[tex]\[ D. 1.1 \times 10^{15} \text{ Hz} \][/tex]
From the options, the frequency calculated is approximately [tex]\( 5.6 \times 10^{14} \text{ Hz} \)[/tex], matching option C.
### Conclusion:
The output light frequency of the material used before frequency doubling is:
C. [tex]\( 5.6 \times 10^{14} \text{ Hz} \)[/tex]
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