Answer :
The question requires us to calculate how many inches light would travel through glass in 458.9 nanoseconds, given that the speed of light in glass is 2.00x10^8 m/s.
To solve this problem, we'll need to go through the following steps:
1) Calculate the speed of light in inches / nanoseconds, considering that 1 nanosecond = 10^-9 s and 1 meter = 39.37 inches;
2) Calculate how many inches light would travel through glass in 458.9 nanoseconds.
Next, we'll go through the steps above to solve the problem:
1) We can convert the speed of light from meters per second (m/s) to inches per nanosecond (in/ns) in two steps: first, let's calculate the speed of light in in/s:
1 m --------------------------------- 39.37 in
2.00 x 10^8 m ---------------- x
Solving for x, we'll have:
[tex]x=\frac{(2.00\times10^8m)\times(39.37in)}{(1m)}=7.87\times10^9in[/tex]Therefore, 2.00 x 10^8 m/s corresponds to 7.87 x 10^9 in/s.
Now, let's convert the value obtained in in/ns:
1s -------------------- 7.87 x 10^9 in
10^-9 s = 1 ns ------------ y
Solving for y, we'll have:
[tex]y=\frac{(10^{-9}s)\times(7.87\times10^9in)}{1s}=7.87\text{ in}[/tex]Therefore, 2.00 x 10^8 m/s corresponds to 7.87 in/ns.
2) Now, we can use the value for speed of light in in/ns to calculate how many inches light would move in 458.9 nanoseconds:
1 ns -------------------- 7.87 in
458.9 ns ------------ z
Solving for z, we'll have:
[tex]z=\frac{(458.9ns\text{)}\times(7.87in)}{(1ns)}=3.61\times10^3in[/tex]Therefore, light would travel 3.61 x 10^3 inches in 458.9 ns through glass.
