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).
kujh
To convert the speed of light in a certain material to feet per nanosecond (ft/ns), we need to know the conversion factors for feet and nanoseconds.
1 meter = 3.281 feet
1 second = 10^9 nanoseconds
Given that the speed of light in the material is 1.6 × 10^8 m/s, we can calculate:
(a) Conversion to feet per nanosecond (ft/ns):
Speed of light in feet per nanosecond = (Speed of light in meters per second) x (Conversion factor from meters to feet) x (Conversion factor from seconds to nanoseconds)
Speed of light in feet per nanosecond = (1.6 × 10^8 m/s) x (3.281 ft/m) x (10^9 ns/s)
= 524,800 ft/ns
Therefore, the speed of light in this material is 524,800 ft/ns.
To convert the speed of light in a certain material to millimeters per picosecond (mm/ps), we need to know the conversion factors for millimeters and picoseconds.
1 meter = 10^3 millimeters
1 second = 10^12 picoseconds
Given that the speed of light in the material is 1.6 × 10^8 m/s, we can calculate:
(b) Conversion to millimeters per picosecond (mm/ps):
Speed of light in millimeters per picosecond = (Speed of light in meters per second) x (Conversion factor from meters to millimeters) x (Conversion factor from seconds to picoseconds)
Speed of light in millimeters per picosecond = (1.6 × 10^8 m/s) x (10^3 mm/m) x (10^12 ps/s)
= 1.6 x 10^23 mm/ps
Therefore, the speed of light in this material is 1.6 x 10^23 mm/ps.
To express the speed of light in different units, we need to use conversion factors. Let's begin:
(a) To express the speed of light in feet per nanosecond (ft/ns), we need to convert meters to feet and seconds to nanoseconds. We can use the following conversion factors:
1 meter = 3.281 feet (conversion factor for meters to feet)
1 second = 1 × 10^9 nanoseconds (conversion factor for seconds to nanoseconds)
Now, let's go step by step:
1. Convert the speed of light from meters per second to feet per second.
Speed of light in feet per second = Speed of light in meters per second × conversion factor
Speed of light in feet per second = 1.6 × 10^8 m/s × 3.281 ft/m
Speed of light in feet per second ≈ 5.249 × 10^8 ft/s (approx.)
2. Convert the speed of light from feet per second to feet per nanosecond.
Speed of light in feet per nanosecond = Speed of light in feet per second × conversion factor
Speed of light in feet per nanosecond = 5.249 × 10^8 ft/s × 1 ns/1 × 10^9 s
Speed of light in feet per nanosecond ≈ 0.525 ft/ns (approx.)
Therefore, the speed of light in the given material is approximately 0.525 ft/ns.
(b) To express the speed of light in millimeters per picosecond (mm/ps), we need to convert meters to millimeters and seconds to picoseconds. We can use the following conversion factors:
1 meter = 1 × 10^3 millimeters (conversion factor for meters to millimeters)
1 second = 1 × 10^12 picoseconds (conversion factor for seconds to picoseconds)
Now let's proceed with the conversions:
1. Convert the speed of light from meters per second to millimeters per second.
Speed of light in millimeters per second = Speed of light in meters per second × conversion factor
Speed of light in millimeters per second = 1.6 × 10^8 m/s × 1 × 10^3 mm/m
Speed of light in millimeters per second ≈ 1.6 × 10^11 mm/s (approx.)
2. Convert the speed of light from millimeters per second to millimeters per picosecond.
Speed of light in millimeters per picosecond = Speed of light in millimeters per second × conversion factor
Speed of light in millimeters per picosecond = 1.6 × 10^11 mm/s × 1 ps/1 × 10^12 s
Speed of light in millimeters per picosecond ≈ 0.16 mm/ps (approx.)
Therefore, the speed of light in the given material is approximately 0.16 mm/ps.