Answer
(a) $t = 1.5\times 10^{-11}~s$
(b) In the same amount of time, light could travel through water with a thickness of 3.5 mm
Work Step by Step
(a) We can find the speed of light as it travels through glass. The index of refraction of glass is $n = 1.5$
$v = \frac{c}{n}$
$v = \frac{3.0\times 10^8~m/s}{1.5}$
$v = 2.0\times 10^8~m/s$
We can find the time to travel through 3.0 mm of glass.
$t = \frac{d}{v}$
$t = \frac{3.0\times 10^{-3}~m}{2.0\times 10^8~m/s}$
$t = 1.5\times 10^{-11}~s$
(b) We can find the speed of light as it travels through water. The index of refraction of water is $n = 1.3$. Therefore;
$v = \frac{c}{n}$
$v = \frac{3.0\times 10^8~m/s}{1.3}$
$v = 2.3\times 10^8~m/s$
We can find the distance that light could travel through water in a time of $1.5\times 10^{-11}~s$:
$d = v~t$
$d = (2.3\times 10^8~m/s)(1.5\times 10^{-11}~s)$
$d = 3.5\times 10^{-3}~m$
$d = 3.5~mm$
In the same amount of time, light could travel through water with a thickness of 3.5 mm.
