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Physics 101- Learning Object 9
Transcript
Physics 101- Learning Object 9
Side Note:
by looking at the Figure, we can use trigonometry to solve for:
if you notice that the 2 fringes are located too close together ....
you can increase in the space in between...
by either :
keep angle constant, and increase the distance to the screen.
A:
OR
increase the angle with by rearranging:
d sin = m
λ
Ө
B:
λ
to get ...
λ
increase the
angle will decrease
"d" and
increase " "
m
d
sin = -----
Ө
λ
Now that we have solved for "d"
we can achieve this by
setting = 90 degrees
Ө
we want to calculate the MAXIUM number
of fringes on either side
... and solving for "m"
Ө
d sin (2.7 X 10^-6) Sin (90)
(4.73 X 10 ^-7)
m = ------ = ----------------- =
5.71
λ
now we can answer our question:
Ө
How many bright fringes are on the screen?
m = 5.71
This means there are 5 fringes on each side of the central zero-order maximum.
There are 2 sides, and therefore a total
of
10 fringes.
the angle we want
(work in degrees)
0.0057 m
0.0057 m
0.032 m
------- = 0.178 m
tan =
Ө
Plugging information into Equation (28-5) and solve for :
d
d *sin = m
λ
Ө
what do we have now?
Ө
rearrange equation...
m = 1
= tan ^-1 (0.178)
= 10.09 degrees
λ
d = ------ = ---------------
D = 0.032 m
y = 0.0057 m for m=1
= 4.73 X 10^-7 m
λ
m 1 X (4.73 X 10 ^-7)
sin sin (10.09)
Ө
= 10.09 degrees
Ө
= 2.70 X 10 ^-6 m
since D =0.032 m
the adjacent side of
will also be 0.032 m.
Ө
what do we have?
= 4.73 X 10^-7 m
λ
D = 0.032 m
y = 0.0057 m
m = 1
convert from mm --> m :
wavelength:
0.1 cm 0.01 m
1 mm 1 cm
----- X -----
0.000473mm X
= 4.73 X 10 ^-7 m
what do we need to find in order to solve "how many bright fringes are on the screen?" ?
Distances:
convert from km --> m :
0.000032 km X
1000 m
1 km
----- = 0.032 m
d = ?
= ?
Ө
convert from cm --> m:
can be found
through trigonometry
use to find d
Ө
0.01 m
1 cm
0.57 cm X
----- = 0.0057 m
let's begin by ...
converting units
The Question:
A laser beam with a wavelength of 0.000473mm illuminates a double slit and produces an interference pattern on a screen located 0.000032km away. Fringe m=0 and fringe m=1 is separated by a distance of 0.57 cm.
--> How many bright fringes are present on the screen?
28-3 Double-Slit Interference
Jeanny Chang
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