An observer uses a 10 sided mirror to measure the speed of light. A clear image occurs every one-tenth of a rotation when the mirror is rotating at 4.31x10^2 rev/s. The total path of the light pulse is 60 km, measured from the light source to the mirrors and reflected back to the observer. What is the speed of light calculated from this data?
a. 3.87x10^-9 m/s
b. 2.59x10^5 m/s
c. 1.39x10^2 m/s
d. 2.59x10^8 m/s
N= 0.1 rev
n= 4.31•10² rev/s
t=N/n = 0.1/4.31•10² = 2.32 •10⁻⁴ s
v=s/t =60000/2.32•10⁻⁴=2.59•10⁸ m/s
Ans. d
To calculate the speed of light, we can use the formula:
Speed of light = (Total path traveled by light) / (Time taken for one complete rotation)
Total path traveled by light is given as 60 km, which is equivalent to 60,000 meters.
To find the time taken for one complete rotation, we can use the given information that a clear image occurs every one-tenth of a rotation when the mirror is rotating at 4.31x10^2 rev/s.
One-tenth of a rotation is equal to 360 degrees / 10 = 36 degrees.
The time taken for one-tenth of a rotation can be found by dividing the angle in degrees by the rotational speed in degrees per second:
Time taken for one-tenth of a rotation = (36 degrees) / (4.31x10^2 rev/s) = (36 degrees) / (4.31x10^2 degrees/s)
Now, we can calculate the speed of light by substituting the values into the formula:
Speed of light = (60,000 meters) / (Time taken for one-tenth of a rotation)
Calculating this value will give us the answer.
To find the speed of light using the given data, we can consider the time it takes for light to travel the total path.
First, let's calculate the total time taken for the light pulse to travel the distance of 60 km. We can use the formula:
Speed = Distance / Time
Since the observer sees a clear image every one-tenth of a rotation, the time taken for one rotation must be the reciprocal of the rotation frequency:
Time for one rotation = 1 / (rotation frequency)
Using the given rotation frequency of 4.31x10^2 rev/s, we can find:
Time for one rotation = 1 / (4.31x10^2 rev/s)
Now, we need to calculate the total time taken for the light pulse to travel the distance of 60 km. Since there is a clear image every one-tenth of a rotation, the total time is (1/10) times the time for one rotation:
Total time = (1/10) * Time for one rotation
Now, we can calculate the speed of light:
Speed = Distance / Total time
Plugging in the values:
Speed = 60,000 m / Total time
Calculating the total time:
Total time = (1/10) * (1 / (4.31x10^2 rev/s))
Speed = 60,000 m / [(1/10) * (1 / (4.31x10^2 rev/s))]
Simplifying the equation:
Speed = 60,000 m * (4.31x10^2 rev/s) * 10
Speed = 60,000 m * 4.31x10^3 rev/s
Now, we need to convert revolutions per second to meters per second. Since one revolution corresponds to the circumference of the circular mirror (which is 2πr), we can find the distance traveled per revolution. In this case, the radius of the mirror is not given, so we can't determine the actual value of the speed of light.
Therefore, it is not possible to calculate the speed of light from the given data. None of the answer choices (a, b, c, or d) are correct.