Prisms and Dispersion

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Prisms and Dispersion
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• What would the index of refraction of a material
• have to be to make the speed of light half of its
• speed in vacuum?

V C/2
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2. A light ray traveling in air intersects a
glass block (n 1.500) at an angle of 18o to the
normal. Without using a calculator or table of
sines, calculate the angle of refraction.
1.000 X 0.1p 1.500 X qr
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• A crystal has an index of refraction of 5.000.
• What is the speed of light in the crystal.
• (b) What is its critical angle?

V 0.6 X 108 m/sec
qc sin-1 (0.2) 11.54o
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• A ray of light is incident on a piece of glass at
  an
• angle of 45?. If the angle of refraction is
  25.27?, find
• (a) the refractive index and (b) the critical
  angle.

1.00 X sin (45) nr X sin (25.27)
0.707 nr (0.427)
nr 1.656
qc sin-1 (0.604) 37.14o
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REFRACTIVE PRISMS
Prisms bend rays toward the base.
Prism Diopter
Displacement of ray (cm) 100 cm from prism. E.g.
XD
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Calculating Prism Diopters--Example
4.5 prism diopters or 4.5 cm?
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EXPERIMENT 4
Measure prism power in diopters of a prism.
mark beam height w/o prism
base-down prism in lens holder
diode laser
mark ht. w/ prism
measure
(about 10 cm)
Calculate deflection at 100 cm (1 m).
What happens when prism is rotated?
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PRISM DEFLECTION
a
a
d1
q1
q2
Want to determine D in terms of q1, q2, and a.
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Prism deflection
1
d2
d1
d2
d2
d1
total deviation, D d1 d2
q1
2
q2
Find d1 and d2
d1 q1 q1
d2 q2 q2
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Prism deflection
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Find a in terms of q1 and q2
Already know
90 (90 q1) a/2 180
d2
d1
a/2 q1
d2
d1
similarly,
a/2 q2
q1 q2 a/2 a/2
90-q1
a q1 q2
q2
q1
q2
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Prism deflection
Solve for D in terms of qs
We now know
D q1 q1 q2 q2
D q1 q2 q1 q2
D q1 q2 (q1 q2)
a q1 q2
D q1 q2 a
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a 20?
D q1 q2 a
D
qr 10.26?
qi 20?
D 20 10.26 20 10.26?
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Prism Tilt and Beam Deviation
Minimum total deviation, D, occurs when q1 q2
(equal bending at each prism face)
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Total Deflection (deg)
q2
15.1o
10.2o
Angle of Incidence, q1
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EXPERIMENT 5
3/8 wood strip
screen
hole
mark beam position
prism on pivot
determine angle of minimum deviation
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Prism Combinations
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cos 90o 0
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(No Transcript)
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EXPERIMENT 6
Prism combination
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RISLEY PRISM
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Prism image shift Image always shifts toward
apex
laser beam from fovea
fovea
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Prism displacement as prism rotated around line
of sight
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PRENTICES RULE
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REFLECTIVE PRISMS
total internal reflection
Total internal reflect when
qi gt qc
sin qc
1.00
qc 38.7o
sin qc
0.625
1.60
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Ernst Abbe
1840 -1905
Doctorate in physics, University Gottigen 1861
Professor of mathematics and physics, University
of Jena
Partner in Karl Zeiss. Made fundamental
discoveries in optics of microscopy
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Color Dispersion
qi
n 1
qD
C
F
D
n
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qD
qF - qC
F
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Dispersive Index (Abbe Number)
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Abbe Number Example
Spectacle Crown Glass
C
F
D
486.1
589.2
656.3
n
l (nm)
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The smaller the Abbe Number, the more Dispersive
the material
 
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PRISM DISPERSION--SPECTRA