Rank in order the following according to their speeds, from fastest (1) to slowest (5): (i) 425-nm-wavelength light through a pane of glass, (ii) 500-nm-wavelength light through air, (iii) 540-nm-wavelength light through water, (iv) 670-nm-wavelength light through a diamond, and (v) 670-nm-wavelength light through a vacuum.

Answer 1

The speed depends on the refractive index of the substance n
n=c/v
1. vacuum: c=3•10⁸ m/s
2. air n= 1.000293 =>
v= c/n =3•10⁸ /1.000293 =2.999•10⁸ m/s
3. water n=1.333
=> v= c/n =3•10⁸ /1.333 =2.25•10⁸ m/s
4. glass n=1.5
=> v= c/n =3•10⁸ /1.5 =2•10⁸ m/s
5. diamond n=2.42
=> v= c/n =3•10⁸ /2.42 =1.24•10⁸ m/s

Answer 2

the answer is just the actual speeds, no math needed.

so v, ii, iii, i, iv