Physic 30 – Electromagnetic Radiation Concept Check 3
Concept1.
explain, qualitatively, various methods of measuring the speed of EMR
Describe two of the ways that an experiment can be modified to help measure the
speed of light.
Light travels at a constant velocity, so speed, distance and time are related by
d
v = . You can change the distance the light has to travel, therefore making the
t
time easier to measure (Römer), or you can increase the precision of the device
measuring time so that you can use a shorter distance. (Michelson)
2.
Describe why Galileo failed in his attempt at measuring the speed of light, but
Römer succeeded while using the same method.
Neither had a precise time measuring device, and therefore had to rely on
manipulating distance. Galileo had a very short distance to work (4 miles
between two hills), which made the time much to short to measure. Römer used a
large distance (Earth’s orbital diameter) so had a easily measured time (22
minutes) to work with.
3.
Römer used the diameter of the Earth’s orbit ( 2.98 !1011 m ) to determine the
speed of light. If he determined that light took approximately 22 minutes to travel
that distance, his calculated speed of light was approximately_____
v=
d
t
2.98 !1011 m
v=
60s %
"
$# 22 min!
'
1min &
v = 2.26 !108 m s
4.
To travel to the nearest star , Alpha Centauri, would take approximately
4.4 light years. A light year is the distance that light travels in one year. How
far away is Alpha Centauri in kilometers?
1 year = 365.25 days ×
24hours 60 min 60s
!
!
= 31557600s
1day
1hour 1min
d = vt
d ≈ (3.00 × 10 8 m s)(31557600s × 4.4)
d ≈ 4.17 × 1016 m
d ≈ 4.17 × 1013 km
Concept5.
Calculate the speed of EMR, given data from a Michelson-type experiment
What is the definition of period of rotation?
The period of rotation is the time it takes to complete one whole rotation.
! time $
#" 1 cycle &%
6.
How are period and frequency related to each other?
! #cycles $
Frequency is how often some event occurs per unit of time. #
" 1 s &%
It is the reciprocal of the period.
7.
f =
1
T
What is the frequency of rotation in RPM for an object whose period of rotation is
2.3 x 10-4 s?
f =
1
T
1
2.3 !10 "4 s
f = 4.3 !10 3 Hz
f =
8.
What is the time for one third of a rotation for an object rotating at 420 RPS?
One third of a rotation will take one third of the period to occur. The frequency of
420 RPS is the same as 420 Hz.
T=
1
f
1
420RPS
T = 2.4 !10 "3 s
T=
1
t= T
3
1
t = (2.4 !10 "3 s)
3
t = 7.9 !10 "4 s
9.
Michelson used a rotating eight-sided mirror and a flat mirror a set distance away
to determine the speed of light. How did he measure the time it took light to
travel this small distance?
He rotated the mirror fast enough so that while the light travelled to the flat mirror
and back, the mirror would rotate 1/8 of a revolution. This would cause the
mirror to be in the same orientation as it was originally. By measuring the
frequency of rotation and determining the period, he was able to measure the
time.
10.
Determine the speed of light if an eight sided mirror rotates at 585 Hz in a
Michelson-type experiment. The stationary mirrors are 30 km away.
T=
1
f
1
585Hz
T = 0.00171s
T=
11.
1
t= T
8
1
t = (0.00171s)
8
t = 2.1!10 "4 s
d
t
(2 ! 30000m)
v=
2.1!10 "4 s
v = 2.8 !108 m s
v=
Determine the minimum frequency of rotation of a six-sided mirror in a
Michelson-type experiment if the fixed mirrors are 40 km away. What is the next
highest frequency that the mirror could rotate?
f =
1
, so need to find the period T .
T
d
v
(2 ! 40000m)
t=
3.0 !108 m s
t=
"4
t = 2.7 !10 s
1
t= T
8
T = 8t
T = 8(2.7 !10 "4 s)
T = 2.1!10 "3 s
f =
1
T
1
2.1!10 "3 s
f = 469Hz
f =