Answer
(a) $t = 3.3~nm$
(b) In water, the light travels $~~0.75~m$
In glass, the light travels $~~0.67~m$
In cubic zirconia, the light travels $~~0.46~m$
Work Step by Step
(a) We can find the time it takes light to travel $1.0~m$:
$t = \frac{d}{c}$
$t = \frac{1.0~m}{3.0\times 10^8~m/s}$
$t = 3.3\times 10^{-9}~m$
$t = 3.3~nm$
(b) We can write an expression for the speed of light in a medium:
$v = \frac{c}{n}$
where $n$ is the index of refraction of the medium.
We can write an expression for the distance traveled by light in a medium in a given time $t$:
$d = v~t$
$d = \frac{c~t}{n}$
We can find the distance that light travels in water in a time of $3.3~nm$:
$d = \frac{c~t}{n}$
$d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{1.33}$
$d = 0.75~m$
In water, the light travels $~~0.75~m$
We can find the distance that light travels in glass in a time of $3.3~nm$:
$d = \frac{c~t}{n}$
$d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{1.50}$
$d = 0.67~m$
In glass, the light travels $~~0.67~m$
We can find the distance that light travels in cubic zirconia in a time of $3.3~nm$:
$d = \frac{c~t}{n}$
$d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{2.16}$
$d = 0.46~m$
In cubic zirconia, the light travels $~~0.46~m$