Answer:
Speed:
[tex]2.01x10^{8}m/s[/tex]
Wavelength:
[tex]4.24x10^{-7}m[/tex]
Frequency:
[tex]4.74x10^{14}Hz[/tex]
Explanation:
The speed of the laser as it travels through polystyrene can be determine by means of the equation of the refraction index:
[tex]n = \frac{c}{v}[/tex] (1)
Where c is the speed of light and v is the speed of the laser in the medium.
Therefore, v will be isolated from equation 1
[tex]v = \frac{c}{n}[/tex]
[tex]v = \frac{3x10^{8}m/s}{1.490}[/tex]
[tex]v = 2.01x10^{8}m/s[/tex]
Hence, the speed of the laser has a value of [tex]2.01x10^{8}m/s[/tex]
Frenquency:
Since, wavelength is the only one who depends on the media. Therefore the frequency in both medium will be the same. Â
To determine the frequency it can be used the following equation
[tex]c = \nu \cdot \lambda[/tex] Â (2)
Where c is the speed of light, [tex]\nu[/tex] is the frequency and [tex]\lambda[/tex] is the wavelength
Then, [tex]\nu[/tex] wil be isolated from equation 2.
[tex]\nu = \frac{c}{\lambda}[/tex] Â (3)
Before using equation 3 it is necessary to express [tex]\lamba[/tex] in units of meters.
[tex]\lambda = 632.8nm . \frac{1m}{1x10^{9}nm}[/tex] ⇒ [tex]6.328x10^{-7}m[/tex]
[tex]\nu = \frac{3x10^{8}m/s}{6.328x10^{-7}m}[/tex]
[tex]\nu = 4.74x10^{14}s^{-1}[/tex]
[tex]\nu = 4.74x10^{14}Hz[/tex]
Hence, the frequency of the laser has a value of [tex]4.74x10^{14}Hz[/tex]
Wavelength:
To determine the wavelength it can be used:
[tex]v = \nu \cdot \lambda[/tex]
[tex]\lambda = \frac{v}{\nu}[/tex]
Where v is the speed of the laser through the polystyrene.
[tex]\lambda = \frac{2.01x10^{8}m/s}{4.74x10^{14}s^{-1}}[/tex]
[tex]\lambda = 4.24x10^{-7}m[/tex]
Hence, the wavelength of the laser has a value of [tex]4.24x10^{-7}m[/tex]
