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Physics 1161: Lecture 24
Rainbows, Fiber Optics, and Sun Dogs
• section 26-8
Total Internal Reflection
Recall Snell’s Law: n1 sin(q1)= n2 sin(q2)
(n1 > n2  q2 > q1 )
q1 = sin-1(n2/n1) then q2 = 90
q2
“critical angle”
Light incident at a larger angle will
only have reflection (qi = qr)
For water/air:
n1=1.33, n2=1
q1 = sin-1(n2/n1)
= 48.80
n2
n1
qr
qi
qc
q1
normal
Preflight 24.1
Can the person standing on the edge of the pool be prevented from seeing the light by
total internal reflection ?
1) Yes
2) No
58%
42%
“There are millions of light ’rays’ coming
from the light. Some of the rays will be
totally reflected back into the water,
but most of them will not.”
10
8
Fiber Optics
Fiber Optics
Indices of Refraction
What is the critical angle of a
diamond-air boundary?
q c  sin
1
q c  sin
1
q c  sin
1
 n2 


 n1 
 n air 


 n diam ond 
1
 1 
o

sin
0
.4
1
3

24




 2.42 
Internal Reflection in Diamond
• The critical angle for
diamond in air is
24.5 o.
• Any ray which strikes
the inside surface at
an angle greater than
24.5o will be totally
internally reflected.
The diagrams show incident rays approaching a
boundary with a second medium. The relative indices
of refraction of the two media are indicated. In which
diagram will total internal reflection occur, providing
the angle of incidence exceeds the critical angle?
31%
29%
26%
1.
2.
3.
4.
Diagram A
Diagram B
Diagram C
None of these
14%
1
2
3
4
The diagrams show incident rays approaching a
boundary with a second medium. The relative indices
of refraction of the two media are indicated. In which
diagram will total internal reflection occur, providing
the angle of incidence exceeds the critical angle?
51%
1.
2.
3.
4.
Diagram A
Diagram B
Diagram C
None of these
31%
11%
6%
1
2
3
4
Dispersion
The index of refraction n depends on color!
In glass: nblue = 1.53
nblue > nred
nred = 1.52
prism
White light
Blue light gets deflected
more
23
Rainbow:
Preflight 24.5
Which is red?
Which is blue?
Skier sees blue coming up from the
bottom (1), and red coming down from
the top (2) of the rainbow.
Blue light is deflected more!
Rainbow
Rainbow Zoom
Double Rainbow
Double Rainbow on Way to School
Alexander’s Dark Band
• Sky is light inside primary
rainbow
• Dark between primary
and secondary bows
• Light beyond the
secondary rainbow
• Dark region between is
called Alexander’s Dark
Band
Green Flash
http://www.faqs.org/faqs/astronomy/faq/part3/section-13.html
Does moon halo predict bad weather?
22o Halo
Diameter less
than 20.5
micrometers
Randomly oriented
hexagonal ice
crystals
• A halo is a ring of light
surrounding the sun or
moon.
• Most halos appear as bright
white rings but in some
instances, the dispersion of
light as it passes through
ice crystals found in upper
level cirrus clouds can
cause a halo to have color.
Sundogs
• Sundogs or parhelia
on right and left of
sun
Hexagonal ice
crystals
Flat faces
horizontally
oriented
Diameter
greater than 30
micrometers
Sundog
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