1. Lecture 11 Geometric optics
Physics 114
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2. Principles of geometric optics
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3. Concepts Ray model of light Image formation Reflection Refraction
Dispersion
Total internal reflection
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4. EM waves c – speed of light (m/s) f – frequency (Hz=1/s)
l – wavelength (m)
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5. Ray model of light
Light is an EM wave diffraction (go around obstacles)
This happens on microscopic scale
In everyday life we use straight line approximation for light propagation = Ray model of light  geometric optics
We infer positions of objects assuming light travels in straight lines.
Geometry is important,
Bring ruler and pencil,
make good pictures!!!
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6. Reflection We see objects because
They emit light (Sun, light bulb)
They reflect light (Moon, table)
angle of incidence = angle of reflection:
qi=qr
Rough surface Polished surface.
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7. Formation of image
Eye assumes light propagates in straight lines  image (rays of light crossing) is formed behind the mirror
do – distance to object
di – distance to image
For plane mirror
do= di
No light here
 Virtual image
If light actually goes through the place
where image is formed  real image
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8. Spherical mirrors Convex mirror bulges out – diverges light
Concave mirror caves in – converges light
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9. Focus
Parallel beam of light (e.g. from a very distant object) is converged in 1 point – focal point F
Distance from the mirror to F is called focal distance, or focus
f =r/2
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10. Ray tracing 3 Easy rays: Parallel  through focus
Through focus  parallel (reversible rays)
Through the center of curvature C  itself
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11. Magnification h0 – object height hi – image height
h0>0 - always
hi – image height
hi>0 – upright image
hi<0 – inverted image
m=hi/h0 - magnification
|m|>1 –image larger than object
|m|<1 –image smaller than object
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12. Mirror equation d0 – distance to object di – distance to image
d0>0 - always
di – distance to image
di>0 – real image
di<0 – virtual image
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13. Convex mirror Virtual focus – parallel beam focuses behind the mirror:
Same rules for ray tracing.
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14. Sign convention for mirrors
d0>0
h0>0
di>0 – real image
di<0 - virtual image
hi>0 – upright image
hi<0 - inverted image
f>0 – concave mirror
f<0 – convex mirror
hi>0di<0 – upright image is always virtual
hi<0di>0 – inverted image is always real
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15. Images in curved mirrors
Concave mirror
d0>r – (real, inverted), smaller
r>d0>f – (real, inverted), larger
d0<f – (virtual, upright), larger
Convex mirror
Image is always
(virtual, upright), smaller.
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16. Speed of light in medium
Speed of light in vacuum:
c=3.0x108m/s
Speed of light in media:
v<c
Index of refraction:
n=c/v >1.0
From table 33-1
Vacuum n=1.00
Air n=1.0003
Water n=1.33
Diamond n=2.42
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17. Refraction
The front is slowing down
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18. Refraction, Snell’s law
Bend toward normal
Bend away from normal
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19. Image formation
Eye still assumes light propagates in straight lines  optical illusions
Image is shifted
Pool appears shallower
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20. What if n depends on l?
If n depends on l  angle of refraction depends on l
n(red)<n(green)
A-red, B-green
B- red, A-green A B
Dispersion
This is why rainbow occurs
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21. Total internal reflection
For q>qc - total internal reflection –
no light come out – all light is reflected
Fiber optics
Necessary condition:
from thick to thin media
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22. 1.3 m
2.1 m
2.7 m x
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