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 will be mailed soon.
1/1/2019
Lecture II

2. Lenses, mirrors and human eye
Physics 123, Spring, 2006
1/1/2019
Lecture II

3. Concepts Concave and convex mirrors Converging and diverging lenses
Focus
Converging and diverging lenses
Lens equation
Eye as an optical instrument
Far and near points
Corrective lenses System of lenses
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Lecture II

4. Spherical mirrors Convex mirror bulges out – diverges light
Concave mirror caves in – converges light
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Lecture II

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
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Lecture II

6. Ray tracing 3 Easy rays: Parallel  through focus
Through focus  parallel (reversible rays)
Through the center of curvature C  itself
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Lecture II

7. 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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Lecture II

8. 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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Lecture II

9. Convex mirror Virtual focus – parallel beam focuses behind the mirror:
Same rules for ray tracing.
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Lecture II

10. 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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Lecture II

11. 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.
1/1/2019
Lecture II

12. Lenses Convex lens bulges out –converges light
Concave lens caves in –diverges light
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Lecture II

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: 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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Lecture II

14. Ray tracing for converging lens
3 Easy rays:
Parallel  through focus F
Through focus F’ parallel (reversible rays)
Through the center  itself
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Lecture II

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
1/1/2019
Lecture II

16. Lens equation d0 – distance to object di – distance to image f –focus
P – power of lens, in Dioptry (D=1/m)
f must be in m
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17. Sign convention for lenses and mirrors
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
hi>0di<0 – upright image is always virtual
hi<0di>0 – inverted image is always real
1/1/2019
Lecture II

18. Images in lenses and mirrors
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.
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Lecture II

19. System of lenses Image of the 1st lens of object for the 2nd lens.
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Lecture II

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)
di>0, hi<0
Optic nerves send ~30 images per second to brain for analysis.
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Lecture II

21. 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
1/1/2019
Lecture II

22. Corrective lenses Farsighted eye Nearsighted eye 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
Corrective lenses create virtual, upright image (di<0 !) 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
1/1/2019
Lecture II

23. Images in lenses 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.
Image in corrective lenses is always virtual and upright
di<0 and hi>0
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Lecture II

24. Corrective lenses Nearsighted eye Far point = 17cm Near point = 12 cm
new near point -?
Diverging lens projects infinity to 17 cm from the eye
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Lecture II

25. Real and virtual image Mirrors: I and O – same side opposite sides I O
Real, inverted
light goes through
Virtual, upright
light does not go through O M I
Lenses:
I and O –
opposite sides
same side
Real, inverted
light goes through O L I
Virtual, upright
light does not go through O I L
1/1/2019
Lecture II