Please answer and explain following questions. Thank you so much for your help!
ID: 3280379 • Letter: P
Question
Please answer and explain following questions. Thank you so much for your help!
1. A group takes data to measure the speed of light as in Lab 1. The scope trace appears as in the figure below when the mirror is a distance d 1.0 m from the laser and detector: Type Delta Cursor 1 0000s Cursor 2 When measuring the time of the detector pulse, instead of placing the cursor half-way down the detector in the figure, the group decides to mark the detection time ti at the point when the detector pulse falls by 0.1 V. They then move the mirror to d2 4.0 m from the laser, and the detector pulse moves correspondingly by time However its amplitude has decreased according to 1 d2, and pulse as shown the group still measures the detection time t2 at the point when the detector pulse falls by 0.1 V (a) By how much does the group's value of t2-t1 miestinate the value of t? Approximate the signal from the detector as a Gaussian of amplitude-1.0 V and width = 10.0 ns, and assume that the arrival of light at the detector occurs with a constant time offset relative to the mean of the Gaussian. Express your answer in n anoseconds. (b) Using just these two measurement points, the group computes c 2(d2 -d)/(t2 t). By how much would this measurement of c be biased? Express your answer as a percentage.Explanation / Answer
The amplitude of the pulse falls by 1/16 as distance has increased from 1m to 4 m
The pulse is a Guassian shape with 1V amp and 10 ns width.
The peak width from start is 5 ns
Intially the marker is at 0.1v i.e. 0.5ns from 0 offset
now after the distance is increased, the pos. of the marker shall be at 0.5/16
instead it is put at the same pos.
the error is 0.5*15/16 = 0.47ns
The error in (t2-t1) = 0.47 ns
pct.error = 0.47*100/(t2-t1) = 47/(t2-t1)
pct error in C = 47(t2-t1)