The speed of light is a constant and approximately equal to 300,000,000 meters per second.
Green lasers emit light at a wavelength of 532 nm. However, the material that is used to make most green lasers does not emit light at 532 nm. Instead, it emits light at a different wavelength, and the laser then uses a “frequency doubler.” This doubles the frequency of the emitted light, and the resultant light is the green 532 nm that we observe.
1 meter is equal to 1,000,000,000 nanometers.
What is the output light frequency of the material used before doubling?
The Correct Answer and Explanation is:
To determine the output light frequency of the material used before frequency doubling, we first calculate the frequency of the green light emitted after doubling and then halve this value to find the frequency before doubling.
Step-by-Step Calculation:
- Speed of light formula:
[
c = \lambda \cdot f
]
where:
- ( c ) is the speed of light (( 3.0 \times 10^8 \, \text{m/s} )),
- ( \lambda ) is the wavelength in meters,
- ( f ) is the frequency in hertz (( \text{Hz} )).
- Convert 532 nm to meters:
[
532 \, \text{nm} = 532 \times 10^{-9} \, \text{m}
] - Calculate the frequency of the green light:
Substituting into the formula:
[
f_{\text{green}} = \frac{c}{\lambda}
]
[
f_{\text{green}} = \frac{3.0 \times 10^8}{532 \times 10^{-9}}
]
[
f_{\text{green}} = 5.64 \times 10^{14} \, \text{Hz}
] - Calculate the frequency before doubling:
The frequency before doubling is half the green light’s frequency:
[
f_{\text{original}} = \frac{f_{\text{green}}}{2}
]
[
f_{\text{original}} = \frac{5.64 \times 10^{14}}{2}
]
[
f_{\text{original}} = 2.82 \times 10^{14} \, \text{Hz}
]
Explanation:
Green lasers emit light at 532 nm after frequency doubling. The frequency of light is inversely proportional to its wavelength. Using the speed of light formula, we calculated the frequency corresponding to 532 nm as ( 5.64 \times 10^{14} \, \text{Hz} ). The material’s emitted light undergoes frequency doubling, which doubles the frequency. Hence, the light emitted initially by the material has half the frequency of the green light, calculated to be ( 2.82 \times 10^{14} \, \text{Hz} ). This process allows the laser to achieve green light through precise optical manipulation.