Answer:
The difference in the pulses times of arrival at the detector is  [tex]\Delta t = 0.79*10^{-8} \ s[/tex]
Explanation:
From the question we are told that
  The distance of the detector from the source is [tex]d = 7.65 \ m[/tex]
  The index of refraction of ice is  [tex]n_i = 1.309[/tex]
 Â
Generally the speed of light is  a constant with a value  [tex]c = 3. *10^{8} \ m/ s[/tex]
So the time taken for the first light source through air is Â
   [tex]t_a = \frac{d}{c}[/tex]
substituting value
    [tex]t_a = \frac{7.65}{3.0 *10^{8}}[/tex]
    [tex]t_a = 2.55 *10^{8} \ s[/tex]
The time taken to travel through ice is
   [tex]t_i = \frac{d}{\frac{c}{n_i} }[/tex]
substituting values
   [tex]t_i = \frac{7.65}{\frac{3.0*10^{8}}{1.309} }[/tex]
    [tex]t_i = 3.34 *10^{-8}[/tex]
The in pulses time arrival is mathematically evaluated as
   [tex]\Delta t = t_2 - t_1[/tex]
 substituting values
   [tex]\Delta t = (3.34 - 2.55)*10^{-8}[/tex]
   [tex]\Delta t = 0.79*10^{-8} \ s[/tex]
