A carbon dioxide laser is an infrared laser. A CO laser with a cavity length of 48.6cm oscillates in the m=100,000.0 mode. What is the wavelength of the laser beam?
b). What is the frequency of the laser beam?
Is this a CO laser or a CO2 laser?
I have never heard of a CO laser.
If m is the number of half waves bewtween the cavity mirrors, the wavelength is 48.6 cm/50,000
= 9.72*10^-4 cm
= 9.72*10^-6 m
= 9.72 microns
This is one of several possible CO2 laser wavelengths.
See
http://en.wikipedia.org/wiki/Carbon_dioxide_laser
(b) For the frequency, divide the speed of light by the computed wavelength.
To find the wavelength of the laser beam, we can use the formula:
\[ \lambda = \frac{2L}{m} \]
Where:
- \( \lambda \) is the wavelength
- \( L \) is the cavity length
- \( m \) is the mode of oscillation
Substituting the given values:
\[ \lambda = \frac{2 \times 48.6 \, \text{cm}}{100,000.0} \]
Simplifying the equation:
\[ \lambda = 9.72 \times 10^{-5} \, \text{cm} \]
So, the wavelength of the laser beam is \( 9.72 \times 10^{-5} \, \text{cm} \).
To find the frequency of the laser beam, we can use the equation:
\[ f = \frac{c}{\lambda} \]
Where:
- \( f \) is the frequency
- \( c \) is the speed of light
- \( \lambda \) is the wavelength
The speed of light is approximately \( 3 \times 10^8 \, \text{m/s} \), and \( \lambda \) is given in cm. So we need to convert the wavelength to meters:
\[ \lambda = 9.72 \times 10^{-7} \, \text{m} \]
Substituting the values:
\[ f = \frac{3 \times 10^8 \, \text{m/s}}{9.72 \times 10^{-7} \, \text{m}} \]
Simplifying the equation:
\[ f \approx 3.09 \times 10^{14} \, \text{Hz} \]
So, the frequency of the laser beam is approximately \( 3.09 \times 10^{14} \, \text{Hz} \).