14. Circle of light
Made by Katarína
Problem
When a laser beam is aimed at a wire, a
circle of light can be observed on a screen
perpendicular to the wire. Explain this
phenomenon and investigate how it depends
on the relevant parameters.
hypothesis
• H1: material
• H2: angle between a laser beam and a wire
• H3: distance of meeting point of the laser beam and the wire from a
shield
• H4: a shape of a wire’s cross-section
• H5: surface of a wire
• H6: surrounding
• H7: shield
• H8: thickness of a wire
Equipment
• Laser, wires of different thickness and cross-section, shield
(board/polystyrene), protractor
Pmax < 2.2mW
λ=630-675nm
Pmax < 1.0mW
λ=635-660nm
equipment - wires
sample
material
diameter of cross-section
[mm]
shape of cross-section
0
textile
0.20
circle
1
iron
2.50
circle
2
iron
2.10
circle
3
iron
1.70
circle
4
iron
1.30
circle
5
iron
0.50
circle
6
copper
0.50
circle
7
copper
0.20
circle
8
copper
0.10
circle
9
copper
0.05
circle
10
aluminium
2.95
circle
11
ron
7.80
square
measuring apparatus
wire
laser
laser
α
wire
shield
shield
Theory
x
β
y
a = (- sinα; 0; cosα )
x
laser
α
y
x
β
z
y
b = (-ax cos 2β ; ax sin 2β ; az ) = (sinα cos 2β ; sinα sin 2β ; co
b = (-ax cos 2β ; ax sin 2β ; az ) = (sinα cos 2β ; sinα sin 2β ; cosα )
x = 0 + bx l = l sinα cos2β
y = 0 + by l = l sinα sin2β
z = 0 + bz l = l cosα
Tienidlo - v rovine z=A
A = l cosα
+
cos2 2β + sin2 2β = 1
r = A tanα
material
• any glossy material
Measuring the radius of the circle
sample 0
sample 1
sample 2
sample 3
sample 4
sample 5
A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm
α [°]
r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm]
70
0,0
0,0
2,6
5,0
2,7
5,1
2,5
5,1
2,7
5,0
2,5
5
50
0,0
0,0
1,0
2,1
1,1
2,1
1,2
2,3
1,1
2,4
1,1
2,2
30
0,0
0,0
0,5
1,1
0,6
1,1
0,5
1,2
0,4
1,3
0,5
1,2
sample 6
sample 7
sample 8
sample 9
sample 10
sample 11
A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm A=1cm A=2cm
α [°]
r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm] r [cm]
70
2,6
5,1
2,6
5,1
2,5
5,1
2,7
5,2
2,6
5
2,5
5,2
50
1,1
2,2
1,2
2,1
1,2
2,2
1,1
2,3
1,1
2,1
1
2,2
30
0,6
1,1
0,6
1,2
0,6
1,2
0,5
1,3
0,6
1,3
0,6
1,1
tan70°=2,7
tan50°=1,2
tan30°=0,6
shapes of the cross-section
• influence only at the
brightness of the
circle
• circle cross-section –
uniform brightness
• different cross-section
– diversified
brightness
roughness of the wire’s surface
surrounding
• No influence at a reflection of light from a wire – still circle
water
oil
shield
•
properties of the circle are dependent
on:
•
roughness of the shield
•
surface light-reflecting
Fraunhofer diffraction
• At wires with a small diameter
• Laser going through double slit – diffraction and
interference of the light
• Maxima and minima (picture)
• Visible when distance A is longer
CONCLUSIO
N
• H1: material
• H2: angle between a laser beam and a wire
• H3: distance of meeting point of the laser beam and the wire from a
shield
• H4: a shape of a wire’s cross-section
• H5: surface of a wire
• H6: surrounding
• H7: shield
• H8: thickness of a wire
Resources
• http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/imgpho/muls2.gif
• http://en.wikipedia.org/wiki/Fraunhofer_diffraction
• http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslidi.html#c2
• http://www.dep.fmph.uniba.sk/mambo/images/stories/books/PraktikumOptika/uloha-09.pdf
Thank you for your attention