A laser range finder consists of a laser and a light receiver. It operates by bouncing a laser pulse off a mirror and measuring the time of flight, the time it takes for the pulse to leave the laser, bounce off the mirror and return to the receiver. The speed of light in a vacuum is exactly 299,792,458 m/s, so the accuracy of the distance measurement depends strictly on accuracy of the time measurement. Using a laser range finder, an engineer measures the time of flight to be 3.45 (plus or minus) 0.03 microseconds.

A. Derive a formula for the distance between the mirror and the laser/receiver, and calculate the distance using the measured time of flight

B. What is the fractional uncertainty and the percentage uncertainty of the time of flight?

C. What is the fractional uncertainty and the percentage uncertainty in the distance measured?

D. What is the uncertainty in meters in the distance between the mirror and the laser/receiver?

E. The speed of light in air is 0.02925% slower than in a vacuum. If a correction were applied to account for this, is it correcting for systematic or random error?

F. Do you think it necessary to correct the reported distance measurement because the speed of light in air is slightly slower than in a vacuum?