The speed of light in a certain material is 1.6 × 108 m/s. Express the speed of light in (a) feet per nanosecond (ft/ns) and (b) millimeters per picosecond (mm/ps).
To express the speed of light in feet per nanosecond (ft/ns) and millimeters per picosecond (mm/ps), we need to convert the given speed of light (1.6 × 10^8 m/s) into the desired units. Here's how you can do it:
(a) To convert meters (m) to feet (ft) and seconds (s) to nanoseconds (ns), we can use the following conversion factors:
1 m = 3.28084 ft
1 s = 1,000,000,000 ns
First, let's convert meters to feet:
Speed of light in ft/s = 1.6 × 10^8 m/s × 3.28084 ft/m
Now, let's convert seconds to nanoseconds:
Speed of light in ft/ns = Speed of light in ft/s ÷ 1,000,000,000 ns/s
(b) To convert meters (m) to millimeters (mm) and seconds (s) to picoseconds (ps), we can use the following conversion factors:
1 m = 1,000 mm
1 s = 1,000,000,000,000 ps
First, let's convert meters to millimeters:
Speed of light in mm/s = 1.6 × 10^8 m/s × 1,000 mm/m
Now, let's convert seconds to picoseconds:
Speed of light in mm/ps = Speed of light in mm/s ÷ 1,000,000,000,000 ps/s
By plugging in the values and performing the calculations, you can find the speed of light in the desired units.