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Level 184

Geometrical Optics


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θ_r=θ_i
Law of Reflection
specular reflection
Reflection of light off a smooth surface
Diffuse reflection
if a surface is rough, the reflected light is sent out in a variety of directions
plane mirror
..., A flat mirror that produces an upright, virtual image the same size as the object
Properties of Mirror Images Produced by Plane Mirros
A mirror image is upright, but appears reversed right to left
Spherical mirrors
has the same shape as a section of a sphere.
convex mirror
..., a mirror with a surface that curves outward
concave mirror
..., a mirror with a surface that curves inward
Center of Curvature
the center of the sphere with radius R of which the mirror is a section
principal axis
an imaginary line, parallel to the tangent of a curved mirror that meets it at the vertex, on which the focal point, and generally the object, is placed
focal point
..., the point at which light rays parallel to the optical axis meet when reflected or refracted
f=0.5*R
Focal Length for a Convex Mirror of Radius R
f=-0.5*R
Focal Length for a Concave Mirror of Radius R
P ray
reflects through the focal point
F ray
reflects parallel to the axis
C ray
reflects back along its incoming path
(1/d_o)+(1/d_i)=(1/f)
The Mirror Equation
m=h_i/h_o=-d_i/d_o
Magnification, m
Focal Length
Sign Conventions for mirrors
refraction
a wave is bent due to a change in speed
v=c/n
Index of Refraction, n
n₁sinθ₁=n₂sinθ₂
Snell's Law
Qualitative Features of Refraction
When a ray of light enters a medium where the index of refraction is increased, and hence the speed of the light is decreased, the ray is bent toward the normal
Total internation reflection
for angles of incidence greater than the critical angle, it is observed that all the light is reflected back into the water
sin θ_c=n₂/n₁
Critical Angle for Total Internal Reflection, θ_c
Brewste's Angle, θ_B
Reflected light is completely polarized when the reflected and refracted beams are at right angles to one another. The direction of polarization is parallel to the reflecting surface.
Imaging Characteristics of Concave Lenses
Object location Image orientation Image Size Image type
m=-d_i/d_o
Magnification, m
Focal Length
Sign Conventions for Lenses
total internal reflection occurs if
the light passes medium with higher refraction index into a medium with lower refraction index
isosceles
prism with equal base angles
light ray
A line on a diagram representing the direction and path that light is traveling
wave front
a series of adjacent points that connect identical wave displacements
propagate along the same line as incident way
if incident light ray is pointed towards the center of the curvature of spherical mirror, then the reflected will
the greater the index of refraction of a medium
1.the slower the speed of light in the medium
porro prism
used in binoculars
unity and one
plane mirror has a magnification equal to
focal point is equal to
half of the radius of the curvature
Concave
A mirror whose rays will be reflected and converge to a focus
vertex
middle point of a curved mirror
the center of curvature (C)
geometrical center for the curved surface of the sphere-shaped mirror
real objects and images
mirror sign image convention: positive object and image distances corresponds
Positive
Object distance (do) are always _______
thin lens
if the axial thickness of a lens is small compared to the radii of curvature r1 and r2 of its surfaces, then lens is treated as
positive thin lenses
thicker in the middle than at the edges
are reflected and pass through the mirror's focal point
if parallel rays of light from a distant star are incident on a concave mirror, the rays of light
light gathering power of the lens
the f-number and numerical aperture of a lens are both indicators
when light beam passes from water into air
total internal reflection at the water/air can occur
when a narrow beam of white light passes through a prism, beam?
is dispersed and emerges as beams of separate colors varying from red and blue
dispersion
physical process in which substances break into small pieces that spread throughout the solvent
Frequency
#cycles/second
specular
if parallel incident light rays reflect as parallel reflected waves, then reflection is
focal length of a lens
lens maker formula used to calculate
capable of expanding beam of light
diverging lens and beam expanding collimator
defraction
spectrum of all colors is made from white light after passing through a prism
pinhole produces a diffraction pattern
concentric rings and one disk in center
soap bubble colorful
multiple reflections from its inner and outer surface, various thickness of soap layer the bubble makes
HEBBAR coatings
for antireflection over broader wavelength regions
V coatings
coating used to reduce reflectance to zero at one specific wavelength
diffraction grating
aperture with thousands of slits, equal separated
light rays are perpendicular to wave fronts
relationship between light ray and a wave front
principle of superposition
2 or more wave pass through a given point in space at the same time, and the displacements of individual waves are added together to arrive at resultant displacement
destructive interferance
2 waves of exactly opposite phase pass through a given point, wave condition at that point
collimated red laser beam passes diffraction grating on screen will see
set of separated red spots formed on either side of a central red spot
greater the index of refraction of a medium
the greater the light ray is bent in going from air into medium, the slower the speed of light in the medium
Real object= (-)
Real object vs virtual object
Real images= +
Real images vs virtual images
Lateral Magnification
m= u'/u
Vergence
curvature of the wavelength of light
SSRI
Single Spherical Refracting Interface
Concave/Convex Convention of SSRI
Concave interface= ALWAYS a diverging interface, wraps around the LOWER n medium
Primary Focal point
Finding U when U' = infinity
Secondary Focal point
Finding U' when U= infinity
Flat Surface and Apparent Depth
Since r= infinity, F= 0, therefore,
Total Internal Reflection
Sin(critical angle)= n2/n1
Thin Lenses
Total Lens = power of SSRI + power of SSRI or
Effective Vergence
Downstream Vergence
Successive Imaging
2 thin lenses seperated by some material of index n = index of the lens
Gauss System and Cardinal Pts
Black box system and 6 Cardinal pts (2 focal pts, 2 nodal pts, and 2 principal pts).
2 focal pts (Cardinal pts)
lengths associated with these focal pts = "equivalent" focal lengths= location of these focal pts are relative to PRINCIPAL PLANE (not the lens).
2 nodal pts (Cardinal pts)
same as before but with added complexity. A ray that strikes the first nodal pt N at an angle with respect to the optical axis will leave the second nodal pt N' at and a…
Seconadry Principal Plane
Consider incident rays parallel to the axis, outgoing rays will pt to the focal pt, F'. Extending the incident ray and the outgoing ray and see where they intersect which is the P'. P'…
Primary Principal Plane
rays from F will leave system as plane waves. The primary principal plane P is the plane containing the intersection of these parallel rays (extended backwards, if needed) and the rays leaving F (extended if needed).
Aperture stop
PHYSICAL ENTITY which limits the AMT OF LIGHT passing into an optical system when viewing an object
Field stop
Limits the SIZE of the object that can be imaged by the system.
Entrance Pupil
image of the APERTURE STOP formed by the lens in FRONT of the the aperture stop.
Exit Pupil
Image of the Aperture stop formed by lenses BEHIND it.
Using Cardinal points for Thick lens system
Similar to using 2 SSRI, Find out the vergence of incident light as it hits P. Find out the vergence of exiting light as it leaves P'. Then use U'=F-U except replace the U's …
Back Vertex Power
The vergence of light exiting the optical system given that plane waves entered the system.
Equivalent Power
Feq= F1+F2-(t/n)F1F2
as long as n1=n3
Finding the nodal point location
Focal Ratio
f/#= f/D
Ports
Images of the field stop formed by the lenses in front or behind the stop
Entrance port
image of the field stop formed by lenses in FRONT of it
Exit port
image of the field stop formed by lenses behind it.
Kepler Telescope
(+) ocular lens, the exit pupil is outside the telescope (closer to pt's eye)
Galilean telescope
(-) ocular lens, the exit pupil is inside the telescope
Depth of focus
interval surrounding RETINA, if light is focused in this interval, the object will be focus
What do pinholes do?
Increase depth of focus!
Depth of Field
Interval surrounding the fixation plane without accommodation.
large depth of field
Short focal length leads to large/small depth of field
Decrease depth of field and decrease depth of focus
Increase in aperture size leads to increase/decrease depth of field? increase/decrease depth of focus
Field of View
extent of the object plane that is imaged
Minus lens will increase/decrease field of view
increase, positive lens will decrease field of view.
Field of Fixation
Angle made from the optical axis by the entrance port as measured at the center of rotation of the eye. Note difference from Field of view since the center of rotation of the ey…
Stigmatic system
point source produces a point image
Astigmatic system
characterized by not a single focal point but by a pair of focal lines.
Contraocular view
view doctor has looking at the pt
COLC
point of best focus for a lens, where the image is distorted equally in each meridians (thus finding the spherical equivalent so that the colc would fall on the retina)
Interval of sturm
distance btw 2 foci of principal meridians
Pantoscopic tilt of a minus lens induces an axis 180/90?
Pantoscopic tilt of a minus lens induce an axis 180
Pantoscopic tilt of a plus lens induces an axis 90/180?
Pantoscopic tilt of a positive lens induce an axis 90
true!
T/F a spherical lens can induce spherical and cyl power by pantoscopic tilt
Mirrors
Remember they are lie thin lens and SSRI problems!
n1=-n,
n for mirror problems
Radius of curvature
r is (-)= convex mirror-> power is negative
F=2n/r
Power of a mirror