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Lenses, Mirrors & the Human Eye
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Concepts • Concave and convex mirrors
– Focus
• Converging and diverging lenses– Lens equation
• Eye as an optical instrument• Far and near points• Corrective lenses
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Lenses• Convex lens bulges
out –converges light• Concave lens caves
in –diverges light
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Focus• Light goes through – focal
points on both sides – F and F’– Always a question which focal
point to choose when ray tracing
• Converging lens:– Parallel beam of light is
converged in 1 point – focal point F
– Real focus: f>0– Key for the focal point choice:
Rays must bend in
• Diverging lens:– Parallel beam of light seems to
be coming out of 1 point F– Virtual focus: f<0– Key for the focal point choice:
Rays must bend out
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Ray tracing for converging lens
3 Easy rays:1. Parallel
through focus F
2. Through focus F’ parallel (reversible rays)
3. Through the center itself
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LENS QUESTIONS
LENSAPPLET
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) Object between F and lens
VirtualErectLarger than objectBehind the object on the same side of the lens
Image formed by a diverging lens
e) Object at F
Characteristics of the image regardless of object postionVirtualErectSmaller than objectBetween object and lens
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Diverging lens
• Same rules, but remember to diverge (bend out)• Parallel projection through focus F• Projection through F’ parallel• Through the center goes through
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Lens equation
• d0 – distance to object
• di – distance to image
• f –focus
f1
d1
d1
io
f1
P
• P – power of lens, in Dioptry (D=1/m)
• f must be in m
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Sign convention for lenses and mirrors
d0>0
h0>0
di>0 – real image
Opposite side from O
di<0 - virtual image
Same side with O
hi>0 – upright image
hi<0 - inverted image
f>0 – concave mirror
f<0 – convex mirror
f>0 – converging lens
f<0 – diverging lens
o
i
o
i
dd
hh
m •hi>0di<0 – upright image is always virtual•hi<0di>0 – inverted image is always real
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• Converging lens, concave mirror
• d0>2f – (real, inverted), smaller• 2f>d0>f – (real, inverted), larger• d0<f – (virtual, upright), larger
• Diverging lens, convex mirror
• Image is always
(virtual, upright), smaller.
Images in lenses and mirrors
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System of lenses
• Image of the 1st lens of object for the 2nd lens.
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Spherical mirrors
• Convex mirror bulges out – diverges light• Concave mirror caves in – converges light
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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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Ray tracing3 Easy rays:
1. Parallel through focus
2. Through focus parallel (reversible rays)
3. Through the center of curvature C itself
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Magnification
• h0 – object height– h0>0 - always
• hi – image height– hi>0 – upright image– hi<0 – inverted image
• m=hi/h0 - magnificationo
i
o
i
d
d
h
hm
|m|>1 –image larger than object|m|<1 –image smaller than object
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Mirror equation
• d0 – distance to object– d0>0 - always
• di – distance to image– di>0 – real image– di<0 – virtual image
fdd io
111
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Convex mirror
• Virtual focus – parallel beam focuses behind the mirror:
f<0• Same rules for ray
tracing.
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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
o
i
o
i
d
d
h
hm •hi>0di<0 – upright image is always virtual
•hi<0di>0 – inverted image is always real
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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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Eye as an optical instrument• Eye is a converging lens• Ciliary muscles are used to
adjust the focal distance.– f is variable
• Image is projected on retina – back plane.– di stays constant
• Image is real (light excites the nerve endings on retina) inverted (we see things upside-down) – di>0, hi<0
• Optic nerves send ~30 images per second to brain for analysis.
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Far and near points for normal eye
• Relaxed normal eye is focused on objects at infinity – far point
f0=eye diameter =~2.0 cm
• Near point – the closest distance at which the eye can focus - for normal eye is ~25cm. Adjusted focus:
f1=1.85 cm
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Corrective lenses• Nearsighted eye
– far point<infinity– diverging lens f<0 P<0
• Farsighted eye – near point > 25 cm – converging lens f>0 P>0
• Lens+eye = system of lenses
• Nearsighted eye Far point = 17 cm di =-0.17m
Need to correct far point
Object at “normal far point” =infinity
• Farsighted eye Near point = 70 cm di =-0.70m
Need to correct near point
Object at “normal near point” =25cm
• Corrective lenses create virtual, upright image (di<0 !) at the point where the eye can comfortably see
od mdo 25.0
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• Converging lens - for farsighted
• d0>2f – (real, inverted), smaller• 2f>d0>f – (real, inverted), larger• d0<f – (virtual, upright), larger
• Diverging lens - for nearsighted
• Image is always (virtual, upright), smaller.
Images in lenses
Image in corrective lenses is always virtual and upright
di<0 and hi>0
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Corrective lenses
• Nearsighted eye
Far point = 17cm
Near point = 12 cm
P-?
new near point -?
Diverging lens projects infinity to 17 cm from the eye
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Real and virtual imageMirrors:I and O – same side
I and O –opposite sides IO M
IO L
IO M
IO L
Lenses:I and O –opposite sides
I and O – same side
Real, invertedlight goes through
Virtual, uprightlight does not go through
Real, invertedlight goes through
Virtual, uprightlight does not go through