A carbon dioxide laser is an infrared laser. A CO2 laser with a cavity length of 48.4 cm oscillates in the m=100,000.0 mode.
1. What is the wavelength of the laser beam?
2. What is the frequency of the laser beam?
1. wavelength = (cavity length)/50,000
(50,000 is the number of half waves between the mirrors)
2. frequency = (speed of light)/wavelength
To calculate the wavelength and frequency of the laser beam, we can use the formula:
λ = 2L / m
where λ is the wavelength, L is the cavity length, and m is the mode of oscillation.
1. Calculating the wavelength:
Given:
L = 48.4 cm
m = 100,000.0
Substituting these values into the formula:
λ = 2 * 48.4 cm / 100,000.0
= 0.0968 cm
Therefore, the wavelength of the laser beam is 0.0968 cm.
2. Calculating the frequency:
The frequency (f) can be calculated using the equation:
c = λ * f
where c is the speed of light and λ is the wavelength.
Given:
λ = 0.0968 cm
c = 2.998 x 10^10 cm/s (speed of light in cm/s)
Substituting these values into the equation:
2.998 x 10^10 cm/s = 0.0968 cm * f
Rearranging the equation to solve for f:
f = (2.998 x 10^10 cm/s) / 0.0968 cm
= 3.09 x 10^11 Hz
Therefore, the frequency of the laser beam is 3.09 x 10^11 Hz.
To find the wavelength and frequency of the laser beam in a carbon dioxide (CO2) laser, we can use the formula:
c = λ * f
Where:
c = speed of light in vacuum (approximately 3 x 10^8 m/s)
λ = wavelength of the laser beam
f = frequency of the laser beam
1. To find the wavelength (λ), we can rearrange the formula as:
λ = c / f
Substituting the known values:
λ = (3 x 10^8 m/s) / 100,000.0
Calculating:
λ ≈ 3 x 10^3 m/s
Therefore, the wavelength of the laser beam is approximately 3 x 10^3 m.
2. Now, to find the frequency (f), we can rearrange the formula as:
f = c / λ
Substituting the known values:
f = (3 x 10^8 m/s) / (3 x 10^3 m)
Calculating:
f ≈ 1 x 10^5 Hz
Therefore, the frequency of the laser beam is approximately 1 x 10^5 Hz.
1) wavelength= 2L/m
m=100000
L=48.4/100=0.484m
wavelength= 9.68x10^-6m
2) fn=n(speed of light)/wavelength
speed of light =299,792,458 m/s
fn= 100000(299792458)/9.68x10^-6
= 3.10x10^28 Hz