The speed of a wave is given by:
[tex]v=f.\lambda[/tex] (1)
Where [tex]f[/tex] is the frequency and [tex]\lambda[/tex] the wavelength.
In the case of light, its speed is:
[tex]c=f.\lambda[/tex] (2)
On the other hand, the described situation is known as Refraction, a phenomenon in which the light changes its direction when passing through a medium with a refractive index different from the other medium.
In this context, the Refractive index [tex]n[/tex] is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum ([tex]c=3(10)^{8}m/s[/tex]) and the speed of light [tex]v[/tex] in the second medium:
[tex]n=\frac{c}{v}[/tex] (3)
In addition, as the light changes its direction, its wavelength changes as well:
[tex]n=\frac{\lambda_{air}}{\lambda_{glass}}[/tex] (4)
Knowing this, let's begin with the answers:
From equation (2) we can find [tex]f[/tex]:
[tex]f=\frac{c}{\lambda}[/tex] (5)
Knowing that [tex]1nm=(10)^{-9}m[/tex]:
[tex]f=\frac{3(10)^{8}m/s}{632.8(10)^{-9}m}[/tex]
[tex]f=4.74(10)^{14}Hz}[/tex] (6) >>>Frequency of the helium-neon laser light
We already know the wavelength of the light in air [tex]\lambda_{air}[/tex] and the index of refraction of the glass.
So, we only have to find the wavelength in glass [tex]\lambda_{glass}[/tex] from equation (4):
[tex]\lambda_{glass}=\frac{\lambda_{air}}{n}[/tex]
[tex]\lambda_{glass}=\frac{632.8(10)^{-9}m}{1.48}[/tex]
[tex]\lambda_{glass}=427(10)^{-9}m=427nm[/tex] (7) >>>Wavelength of the helium-neon laser light in glass
From equation (3) we can find the speed [tex]v[/tex]of this light in glass:
[tex]v=\frac{c}{n}[/tex]
[tex]v=\frac{3(10)^{8}m/s}{1.48}[/tex]
[tex]v=2.027(10)^{8}m/s[/tex] (8) >>>Speed of the helium-neon laser light in glass
