Optics: Reflection, Refraction
05/25/2006
Reflections and Refractive Offset
• Let’s consider a thick piece of glass (n = 1.5), and the
light paths associated with it
– reflection fraction = R = [(n1 – n2)/(n1 + n2)]2
– using n1 = 1.5, n2 = 1.0 (air), R = (0.5/2.5)2 = 0.04 = 4%
n1 = 1.5 n2 = 1.0
incoming ray
(100%)
96%
image looks displaced
due to jog
8% reflected in two
reflections (front & back)
A lens, with front and back curved surfaces,
bends
light twice, each diverting incoming ray towards
centerline.
Follows laws of refraction at each surface.
Parallel rays, coming, for instance from a specific
direction (like a distant bird) are focused by a
convex
(positive) lens to a focal point.
object
pinhole
image at
film plane
In a pinhole camera, the hole is so small that light hitting any particular point
on the film plane must have come from a particular direction outside the camera
(infinite depth of field)
object
image at
film plane
lens
4%
92% transmitted
0.16%
4%
The Eye
• Eye forms image on retina, where light is sensed
– Cornea does 80% of the work, with the lens providing slight
tweaks (accommodation, or adjusting)
Refractive indices:
air:
1.0
cornea:1.376
fluid: 1.336
lens: 1.396
Central field of view (called fovea)
densely plastered with receptors for
high resolution & acuity. Fovea
only a few degrees across.
Lecture 16
Cameras
Applications of Optics
Curved lenses refract as flat interfaces, using local surface normal
Placing film at this point would record an image of
the distant bird at a very specific spot on the film.
Lenses map incoming angles into positions in the
focal plane.
In a camera with a lens, a point on the film plane corresponds to a point on
the object, other distances being “out of focus”. Lenses, however, have the
important advantage of collecting more light than the pinhole.
Wave Optics
Quick Quiz
The wave nature of light is needed to explain various
phenomena
Interference
Diffraction
Polarization
The particle nature of light was the basis for ray
(geometric) optics
• Why do things look blurry to us when under water
unless we use goggles?
• A. Because of waves and other disturbances in the
water
• B. Because fish move faster than our eyes can move
• C. Because the index of refraction of the lens in the
eye is almost equal to that of water
• D. Because water is bad for humans
Interference
Light waves interfere with each other much like
mechanical waves do
All interference associated with light waves arises
when the electromagnetic fields that constitute the
individual waves combine
Optics: Reflection, Refraction
05/25/2006
For Interference to Occur
The sources must be coherent
They must maintain a constant phase with respect
to each other-wave go up and down together in
time
The waves must have identical wavelengths
Thomas Young first demonstrated interference
in light waves from two sources in 1801
Light is incident on a screen with a narrow slit,
So
The light waves emerging from this slit arrive
at a second screen that contains two narrow,
parallel slits, S1 and S2
Fringe Pattern
The fringe pattern formed
from a Young’s Double
Slit Experiment would
look like this
The bright areas
represent constructive
interference
The dark areas represent
destructive interference
Thomas Young first
demonstrated interference
in light waves from two
sources in 1801
Light is incident on a
screen with a narrow slit,
So
The light waves emerging
from this slit arrive at a
second screen that
contains two narrow,
parallel slits, S1 and S2
• Why is a single wave used to illuminate the two slits in the
experiment, producing the interference pattern?
• A. Light sources are expensive and difficult to hook up
• B. It is a good way of producing two waves with the same
frequency, amplitude, and phase
• C. Some things don’t matter
• D. Light is a particle, not a wave
Bright bands
Interference Patterns
http://h2physics.org/?cat=48
Lecture 16
Quick Quiz
Young’s Double Slit Experiment
Constructive interference
occurs at the center point
The two waves travel the
same distance
Therefore, they arrive
in phase-a bright fringe
The upper wave travels onehalf of a wavelength farther
than the lower wave
The trough of the bottom
wave overlaps the crest of the
upper wave
This is destructive interference
A dark fringe occurs
The upper wave has to travel farther than the lower
wave
The upper wave travels one wavelength farther
Therefore, the waves arrive in phase
Bright fringes occur when the path length differs by
exactly mλ
Quick Quiz
What is the difference in path
lengths for the dark bands?
A.mλ
B.(m+1) λ
C.(m+½) λ
D.(m+¾) λ
E.Can not be predicted