Answer
We can rank them in order of the time it takes light to traverse the tanks, from greatest to smallest:
$e \gt d \gt a \gt f \gt c \gt b$
Work Step by Step
We can find an expression for the speed of light in a substance:
$v = \frac{c}{n}$
Let $d$ be the length of a tank. We can find an expression for the required time $t$ for light to traverse each tank:
$t = \frac{d}{v} = \frac{d}{c/n} = \frac{d~n}{c}$
We can find an expression for the required time for light to traverse each tank:
(a) $t = \frac{d~n}{c} = \frac{(5/4)(1~m)}{c} = \frac{5}{4}~\times \frac{1}{c}$
(b) $t = \frac{d~n}{c} = \frac{(1)(4/5~m)}{c} = \frac{4}{5}~\times \frac{1}{c}$
(c) $t = \frac{d~n}{c} = \frac{(1)(1~m)}{c} = 1~\times \frac{1}{c}$
(d) $t = \frac{d~n}{c} = \frac{(3/2)(1~m)}{c} = \frac{3}{2}~\times \frac{1}{c}$
(e) $t = \frac{d~n}{c} = \frac{(3/2)(5/4~m)}{c} = \frac{15}{8}~\times \frac{1}{c}$
(f) $t = \frac{d~n}{c} = \frac{(3/2)(4/5~m)}{c} = \frac{6}{5}~\times \frac{1}{c}$
We can rank them in order of the time it takes light to traverse the tanks, from greatest to smallest:
$e \gt d \gt a \gt f \gt c \gt b$
