(a) [tex]4.74 \cdot 10^{14}Hz[/tex]
The frequency of a wave is given by:
[tex]f=\frac{v}{\lambda}[/tex]
where
v is the wave's speed
[tex]\lambda[/tex] is the wavelength
For the red laser light in this problem, we have
[tex]v=c=3\cdot 10^8 m/s[/tex] (speed of light)
[tex]\lambda=632.8 nm=632.8\cdot 10^{-9} m[/tex]
Substituting,
[tex]f=\frac{3\cdot 10^8 m/s}{632.8 \cdot 10^{-9} m}=4.74 \cdot 10^{14}Hz[/tex]
(b) 427.6 nm
The wavelength of the wave in the glass is given by
[tex]\lambda=\frac{\lambda_0}{n}[/tex]
where
[tex]\lambda_0 = 632.8\cdot 10^{-9} m[/tex] is the original wavelength of the wave in air
n = 1.48 is the refractive index of glass
Substituting into the formula,
[tex]\lambda=\frac{632.8\cdot 10^{-9}m}{1.48}=427.6\cdot 10^{-9}m=427.6 nm[/tex]
(c) [tex]2.02\cdot 10^8 m/s[/tex]
The speed of the wave in the glass is given by
[tex]v=\frac{c}{n}[/tex]
where
[tex]c = 3\cdot 10^8 m/s[/tex] is the original speed of the wave in air
n = 1.48 is the refractive index of glass
Substituting into the formula,
[tex]v=\frac{3\cdot 10^8 m/s}{1.48}=2.02\cdot 10^8 m/s[/tex]
