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- R. J. Wilkes
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Physics 116 Lecture 17 Refraction and lenses Oct 27, 2010 R. J. - - PowerPoint PPT Presentation
Physics 116 Lecture 17 Refraction and lenses Oct 27, 2010 R. J. - - PowerPoint PPT Presentation
Physics 116 Lecture 17 Refraction and lenses Oct 27, 2010 R. J. Wilkes Email: ph116@u.washington.edu Lecture Schedule (up to exam 2) Today 2 Simple case: Refraction at a plane surface Last time: Light bends at interface between
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Simple case: Refraction at a plane surface
- Light bends at interface between refractive indices
– bends more the larger the difference in refractive index – can be effectively viewed as a “least time” behavior
- get from A to B faster if you spend less time in the slow medium
– Object at B appears to be at location B’
- Fish in tank appears to be displaced
- Put your feet in the lake and they seem bent
n2 = 1.5 n1 = 1.0 A B 1 2 Exact formula: n1sin1 = n2sin2 B’
Last time:
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- In a thick piece of glass (n = 1.5), the light paths are as shown
– About 4% of light energy is reflected from the surface (mirrorlike)
- Same thing happens at back surface (4% of that gets re-reflected
from the inside front surface, and ends up going out the far side also…)
n1 = 1.5 n2 = 1.0 n0 = 1.0
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Reflections, and refractive optical illusion
incoming ray from object (100%) 4% ~ 4% 96% 92% transmitted 0.16% 8% reflected in two reflections (front & back)
- bject appears displaced
due to jog inside glass
Apparent direction to object
A B
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FYI: Fermat’s principle here too
- Fermat’s Least-Time principle
– Pierre de Fermat, French mathematician, 1601-1665
- Best known for “Fermat’s Last Theorem”
- Wrote a friend just before he died “I have discovered a truly
remarkable proof which this margin is too small to contain” – but he never got to explain
- F’s Last Theorem was finally proven true in 1994 (by A. Wiles,
Princeton U.)
Least-time principle applies to refraction also:
Actual path is quickest path, taking into account changes in light speed! Has solutions (Pythagoras) Never works, if N>2 But
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Underwater refraction: Total Internal Reflection
- Looking up toward air from under water, refraction bends light
rays away from normal (going from higher to lower n)
- For large angle of incidence, angle of refraction becomes >90° !
– 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 greater incidence angles (look at sky from underwater…can’t see out!) – Same principle is used to confine light within optical fibers
n2 = 1.5 n1 = 1.0 42° At critical angle, refracted ray hugs surface At steeper angles, rays are 100% reflected Shallow-angle rays escape
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Polarization by reflection
- David Brewster (1781-1868):
Found that when !T - !R = 90deg reflected light is polarized parallel to surface (perpendicular to plane of incidence) By Snell's Law: Brewster (polarizing) angle: e.g., air/glass has !B = tan -1(1.5)= 57deg Reason: – incident light has E components parallel and perpendicular to plane of incidence – reflected light can only have component perpendicular to plane of incidence for !R = !T + 90deg
- Parallel component would have to be along propagation direction = longitudinal
wave! n1 n2
!T !R !I 90deg
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Refraction at curved surfaces: Lenses
- Lenses = medium with higher n than air, with curved surfaces
- Convex (positive or converging ) lens: thicker at center than edges
– Positive lens (by convention, we say its focal length f is positive) focuses parallel incoming rays to a point at distance f behind it
Lens with curved surfaces front and back (double-convex) bends light twice, each time refracting incoming ray towards normal line. Snell’s law of refraction applies at each surface. (One curved/one flat surface = plano-convex; inward cuving = concave lens) Focal length may be given in m or mm. Optometrists instead specify “refracting power” in diopters: higher power = shorter f F (in diopters) = 1/(f in meters) +1 diopter lens has f=1 m +2 diopter lens has f=1/2 m
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Diverging lenses
- Concave (negative or diverging ) lens: thinner at center than
edges
– Negative lens (we say its f is negative) makes parallel incoming rays bend outwards, so it seems as if light were coming from a point in front of the lens (focal point)
- Meniscus lens: has both sided curved in the same direction, but
- ne surface is more sharply curved than the other
– Commonly used for eyeglasses – Can be either positive or negative (thicker at center, or thinner) f Meniscus lenses
Diverging (-) Converging (+)
Negative lens
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Ray tracing rules for lenses
Ray tracing rules for a (simple, thin) lens are: 1) Rays arriving parallel to the axis emerge to pass through the back focal point 2) Rays passing through the front focal point emerge parallel to the axis 3) Rays through center of the lens are undeviated
image
- bject
f 3 2 1
- Object distance
dO Image distance dI
Focal pt
This lens setup could be used as a camera, or a slide projector
- Focal pt
Rays from object tip re-converge at a point, forming a real, inverted, magnified image there
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When object is close to converging lens
1) Rays arriving parallel to the axis emerge to pass through the back focal point 2) Rays through center of the lens are undeviated 3) Rays do not re-converge – image is virtual
image
- bject
f 2 1
- Object distance
dO Image distance dI
Focal pt
This lens setup could be used as a magnifying glass
- Focal pt
Gazing through the lens toward the object, we see rays appearing to emerge from a virtual, erect, magnified image
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Diverging lens, distant object
1) Rays arriving parallel to the axis emerge as if they came from the focal point 2) Rays through center of the lens are undeviated 3) The intersection of these rays shows image location, orientation, and size
image
- bject
f 2 1 Object distance dO Image distance dI
Focal pt
This lens could be used in eyeglasses for a nearsighted person
- Gazing through the lens toward
the object, we see rays appearing to emerge from a virtual, erect, demagnified image that is closer than the object
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Diverging lens, nearby object
1) Rays arriving parallel to the axis emerge as if they came from the focal point 2) Rays through center of the lens are undeviated 3) The intersection of these rays shows image location, orientation, and size
image
- bject
f 2 1 Object distance dO Image distance dI
Focal pt
- Very little difference – image just
moves a bit closer to the lens
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