A) 1.55
The speed of light in a medium is given by:
[tex]v=\frac{c}{n}[/tex]
where
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light in a vacuum
n is the refractive index of the material
In this problem, the speed of light in quartz is
[tex]v=1.94\cdot 10^8 m/s[/tex]
So we can re-arrange the previous formula to find n, the index of refraction of quartz:
[tex]n=\frac{c}{v}=\frac{3\cdot 10^8 m/s}{1.94\cdot 10^8 m/s}=1.55[/tex]
B) 550.3 nm
The relationship between the wavelength of the light in air and in quartz is
[tex]\lambda=\frac{\lambda_0}{n}[/tex]
where
[tex]\lambda[/tex] is the wavelenght in quartz
[tex]\lambda_0[/tex] is the wavelength in air
n is the refractive index
For the light in this problem, we have
[tex]\lambda=355 nm\\n=1.55[/tex]
Therefore, we can re-arrange the equation to find [tex]\lambda_0[/tex], the wavelength in air:
[tex]\lambda_0 = n\lambda=(1.55)(355 nm)=550.3 nm[/tex]
