Recitations and labs

1
Recitations and labs

• Recitations start this week Wed first day
• If you have not signed up yet please do so asap
• Homework 1 due this week in recitation class
• Labs start next week
• An announcement from physlabs_at_pas.rochester.edu
  will be mailed soon.

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Lenses, mirrors and human eye

• Physics 123, Spring, 2006

3
Concepts

• Concave and convex mirrors
• Focus
• Converging and diverging lenses
• Lens equation
• Eye as an optical instrument
• Far and near points
• Corrective lenses System of lenses

4
Spherical mirrors

• Convex mirror bulges out diverges light
• Concave mirror caves in converges light

5
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

6
Ray tracing

• 3 Easy rays
• Parallel ? through focus
• Through focus ? parallel (reversible rays)
• Through the center of curvature C ? itself

7
Magnification

• h0 object height
• h0gt0 - always
• hi image height
• higt0 upright image
• hilt0 inverted image
• mhi/h0 - magnification

mgt1 image larger than object mlt1 image
smaller than object
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Mirror equation

• d0 distance to object
• d0gt0 - always
• di distance to image
• digt0 real image
• dilt0 virtual image

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Convex mirror

• Virtual focus parallel beam focuses behind the
  mirror
• flt0
• Same rules for ray tracing.

10
Sign convention for mirrors
d0gt0
h0gt0
digt0 real image dilt0 - virtual image
higt0 upright image hilt0 - inverted image
fgt0 concave mirror flt0 convex mirror

• higt0?dilt0 upright image is always virtual
• hilt0?digt0 inverted image is always real

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Images in curved mirrors

• Concave mirror
• d0gtr (real, inverted), smaller
• rgtd0gtf (real, inverted), larger
• d0ltf (virtual, upright), larger

• Convex mirror
• Image is always
• (virtual, upright), smaller.

12
Lenses

• Convex lens bulges out converges light
• Concave lens caves in diverges light

13
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 fgt0
• 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 flt0
• Key for the focal point choice Rays must bend
  out

14
Ray tracing for converging lens

• 3 Easy rays
• Parallel ? through focus F
• Through focus F? parallel (reversible rays)
• Through the center ? itself

15
Diverging lens

• Same rules, but remember to diverge (bend out)
• Parallel ? projection through focus F
• Projection through F ? parallel
• Through the center ? goes through

16
Lens equation

• d0 distance to object
• di distance to image
• f focus

• P power of lens, in Dioptry (D1/m)
• f must be in m

17
Sign convention for lenses and mirrors
d0gt0
h0gt0
digt0 real image Opposite side from O dilt0 - virtual image Same side with O
higt0 upright image hilt0 - inverted image
fgt0 concave mirror flt0 convex mirror
fgt0 converging lens flt0 diverging lens

• higt0?dilt0 upright image is always virtual
• hilt0?digt0 inverted image is always real

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Images in lenses and mirrors

• Converging lens, concave mirror
• d0gt2f (real, inverted), smaller
• 2fgtd0gtf (real, inverted), larger
• d0ltf (virtual, upright), larger

• Diverging lens, convex mirror
• Image is always
• (virtual, upright), smaller.

19
System of lenses

• Image of the 1st lens of object for the 2nd lens.

20
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)
• digt0, hilt0
• Optic nerves send 30 images per second to brain
  for analysis.

21
Far and near points for normal eye

• Relaxed normal eye is focused on objects at
  infinity far point
• f0eye diameter 2.0 cm
• Near point the closest distance at which the
  eye can focus - for normal eye is 25cm. Adjusted
  focus
• f11.85 cm

22
Corrective lenses

• Nearsighted eye
• far pointltinfinity
• diverging lens flt0 ? Plt0
• Farsighted eye
• near point gt 25 cm
• converging lens fgt0 ? Pgt0
• Lenseye system of lenses

• Corrective lenses create virtual, upright image
  (dilt0 !) at the point where the eye can
  comfortably see

• Farsighted eye
• Near point 70 cm ? di -0.70m
• Need to correct near point
• Object at normal near point 25cm

• Nearsighted eye
• Far point 17 cm ? di -0.17m
• Need to correct far point
• Object at normal far point infinity

23
Images in lenses

• Converging lens - for farsighted
• d0gt2f (real, inverted), smaller
• 2fgtd0gtf (real, inverted), larger
• d0ltf (virtual, upright), larger

• Diverging lens - for nearsighted
• Image is always (virtual, upright), smaller.

Image in corrective lenses is always virtual and
upright
dilt0 and higt0
24
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

25
Real and virtual image
Mirrors I and O same side I and O opposite
sides
Real, inverted light goes through
Virtual, upright light does not go through
I
O
M
Lenses I and O opposite sides I and O same
side
Real, inverted light goes through
I
O
L
Virtual, upright light does not go through
I
O
L