Optics: Reflection, Refraction
05/25/2006
Consistent with principle of least time
Reflection
• We describe the path of light as straight-line rays
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click” for someone elseelseviolators will loose all clicker pts.
HITT RF Remote Login Procedure:
A
– “geometrical optics” approach
The radio channel number for this room is “09” (zero, nine).
It is STRONGLY recommended to login your remote for every class just
to be sure it is on the correct radio channel and working before class.
• Reflection off a flat surface follows a simple rule:
– angle in (incidence) equals angle out
– angles measured from surface “normal” (perpendicular)
too long
shortest path;
equal angles
B
1.
2.
surface normal
incident ray
same
angle
exit ray
3.
4.
PRESS AND HOLD THE DOWN ARROW KEY until the
GREEN light on the remote turns RED.
PRESS THE “0” KEY and you will see the RED light flash
GREEN.
PRESS THE “9” KEY and you will see the RED light flash
GREEN.
PRESS AND RELEASE THE DOWN ARROW KEY again
and you will see the red light search for the receiver, if it
BLINKS GREEN MULTIPLE TIMES you are logged in.
Thanks to our friends at UCSD for help with the slides
Hall Mirror
Hall Mirror
Quick Quiz
The rays
virtual
doofnot
really
exist-are colored
The
oflight
lightrays-which
that you see
your
image
A.Blue
A.Start at your eyes
B.Orange
B.Start at the part of your body that you see (head or foot)
Curved mirrors
• In your mind, draw in the direction arrows for the real
and virtual rays
• What if the mirror isn’t flat?
– light still follows the same rules, with local surface normal
• Parabolic mirrors have exact focus
– used in telescopes, backyard satellite dishes, etc.
“real”
you
“real”
you
mirror only
needs to be half as
high as you are tall. Your
image will be twice as far from you
as the mirror.
Lecture 16
“virtual”
you
Parallel rays converge on focus
mirror only
needs to be half as
high as you are tall. Your
image will be twice as far from you
as the mirror.
“virtual”
you
To find image draw two rays:
Parallel and thru focus
Optics: Reflection, Refraction
Refraction
• Light also goes through some things
– glass, water, eyeball, air
• The presence of material slows light’s progress
05/25/2006
Refraction at a plane surface
Driving Analogy
• Light bends at interface between refractive indices
– Larger difference in refractive index bends light more
– can be effectively viewed as a “least time” behavior
• get from A to B faster if you spend less time in the
slow medium
• Let’s say your house is 12 furlongs off the road in the middle of
a huge field of dirt
– interactions with electrical properties of atoms
A
• The “light slowing factor” is called the index of
refraction
– glass has n = 1.52, meaning that light travels about
1.5 times slower in glass than in vacuum
– water has n = 1.33
– air has n = 1.00028
– vacuum is n = 1.00000 (maximum speed of light)
n1sinθ1 = n2sinθ2
θ1
• At critical angle, refraction no longer occurs
– thereafter, you get total internal reflection
– for glass, the critical internal angle is 42°
– for water, it’s 49°
– a ray within the higher index medium cannot
escape at shallower angles (look at sky from
underwater…)
incoming ray hugs surface
n1 = 1.0
n2 = 1.5
42°
Larger than 42°
Lecture 16
• this means “refractive index” of the dirt is 5/3 = 1.667
– Starting from point A, you want to find the quickest route:
• straight across (AD)—don’t mess with the road
• right-angle turnoff (ABD)—stay on road as long as possible
• angled turnoff (ABD)—compromise between the two
A
n1 = 1.0
n2 = 1.5
B
C
road
dirt
θ2
D (house)
B
Total Internal Reflection
– you travel 5 furlongs per minute on the road,
but only 3 furlongs per minute on the dirt
Refraction in Suburbia
• Think of refraction as a pair of wheels on an axle
going from sidewalk onto grass
– wheel moves slower in grass, so the direction changes
when first wheel hits grass
Note that the wheels
move faster (bigger space)
on the sidewalk, slower
(closer) in the grass
leg
AB
AC
AD
BD
CD
dist.
7
16
20
15
12
∆t@5
1.4
3.2
—
—
—
AD: 6.67 minutes
ABD: 6.4 minutes: the optimal path is a “refracted” one
ACD: 7.2 minutes
∆t@3
—
—
6.67
5
4
Note both right triangles in figure are 3-4-5
Even gets Total Internal Reflection Right
• Moreover, this analogy is mathematically equivalent
to the actual refraction phenomenon
– can recover Snell’s law: n1sinθ1 = n2sinθ2
Wheel that hits sidewalk starts to go faster,
which turns the axle, until the upper wheel
re-enters the grass and goes straight again
Optics: Reflection, Refraction
Quick Quiz
• What do you think you would see from underwater looking
up at the sky at an angle to the surface normal greater
than 49º?
A. Blue sky
B. Nothing-no light would be seen
C. The surface would be like a mirror reflecting what was in
the water in front and below you.
Lecture 16
05/25/2006
Quick Quiz
• If you want to spear a fish looking from above the water at
an angle less than zero degrees to the normal, should you
aim
A. above the fish?
B. right at the fish?
C. or aim below the fish
(assume the fish won’t move)