1. Physics 1202: Lecture 19 Today’s Agenda
Announcements: Team problems today
Team 12: Kervell Baird, Matthew  George, Derek Schultz
Team 13: Paxton Stowik, Stacey Ann Burke
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #9: due Friday
Midterm 2:
Tuesday April 10: covers Ch
Chapter 26:
Review Equation for lenses
Dispersion & rainbows
Chapter 27:
Eye
Optical instruments 1

2. o i f h’ h
26.5

3. Converging Lens Principal RaysF
Image
P.A.
Object F
1) Rays parallel to principal axis pass through focal point.
2) Rays through center of lens are not refracted.
3) Rays through F emerge parallel to principal axis.
Image is: real, inverted and enlarged (in this case).
Assumptions:
• monochromatic light incident on a thin lens.
• rays are all “near” the principal axis.

4. Diverging Lens Principal RaysF
P.A.
Image
Object F
1) Rays parallel to principal axis pass through focal point.
2) Rays through center of lens are not refracted.
3) Rays toward F emerge parallel to principal axis.
Image is virtual, upright and reduced

5. when the following sign conventions are used:
26-7: The Lens Equation
We have derived, in the paraxial (and thin lens) approximation, the same equations for mirrors and lenses:
when the following sign conventions are used:
Variable
f > 0
f < 0
o > 0
o < 0
i > 0
i < 0
Mirror
concave
convex
real (front)
virtual (back)
Lens
converging
diverging
real (back)
virtual (front)

6. 3 Cases for Converging Lenses
Object
Image
Past 2F
Inverted
Reduced
Real
This could be used in a camera. Big object on small film
Image
Object
Between
F & 2F
Inverted
Enlarged
Real
This could be used as a projector. Small slide on big screen
Image
Object
Inside F
Upright
Enlarged
Virtual
This is a magnifying glass

7. 26-8 Dispersion and the Rainbow
The index of refraction n varies slightly
with the frequency f of light (or wavelength l) of light
in general, the higher f, the higher the index of refraction n
This means that refracted light is “spread out” in a rainbow of colors
This is known as dispersion

8. Prisms A prism does two things,
Index of refraction
frequency
ultraviolet
absorption
bands
1.50
1.52
1.54
A prism does two things,
Bends light the same way at both entrance and exit interfaces.
Splits colors due to dispersion.
white light
prism
split into colors!

9. For air/glass interface, we use n(air)=1, n(glass)=n
Prisms q1 q2
Entering q3 q4
Exiting
For air/glass interface, we use n(air)=1, n(glass)=n

10. Prisms f
The index of refraction for a material usually decreases with increasing wavelength
Violet light refracts more than red light when passing from air into a material

11. Lecture 19, ACT 1
White light is passed through a prism as shown. Since n(blue) > n(red) , which color will end up higher on the screen ? ? ?
A) BLUE
B) RED

12. 26-8 Dispersion and the Rainbow
Rainbows are created by the dispersion of light as it refracts in a rain drop.

13. 26-8 Dispersion and the Rainbow
How does it look ….
Figure The formation of a rainbow seen by an observer standing with the Sun behind his back.

14. 26-8 More about Rainbows
As the drop falls, all the colors of the rainbow arrive at the eye.

15. Sometimes a faint secondary arc can be seen.
LIKE SO!
In second rainbow pattern is reversed
Sometimes a faint secondary arc can be seen.

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26-8 A second Rainbow !
Two reflection + refraction
Less intense because of loss due to refraction
© 2017 Pearson Education, Inc.

17. © 2017 Pearson Education, Inc.
26-8 The two Rainbows
Why ?
© 2017 Pearson Education, Inc.

18. 27
Optical
Instruments

19. The
EYE I2 I1
~fo
~fe L
objective
eyepiece

20. The Eye What does the eye consist of? Sphere (balloon) of water.
- An aperture that controls how much light gets through – the Iris/pupil
- Bulge at the front – the cornea
- A variable focus lens behind the retina – the lens
- A screen that is hooked up to your brain – the retina
Retina
To brain
Iris
Cornea
Lens

21. 27-1 The Human Eye & the Camera
Light
passes through the cornea
is focused by the lens
onto the retina
The ciliary muscles
change the shape of the lens
so it can focus at different distances
The vitreous and aqueous humors are transparent
Rods and cones on the retina
convert the light into electrical impulses
signal travels down the optic nerve to the brain.
© 2017 Pearson Education, Inc.

22. Recall: 3 Cases for Converging Lenses
Object
Image
Past 2F
Inverted
Reduced
Real
This could be used in a camera. Big object on small film
Image
Object
Between
F & 2F
Inverted
Enlarged
Real
This could be used as a projector. Small slide on big screen
Image
Object
Inside F
Upright
Enlarged
Virtual
This is a magnifying glass

23. 27-1 The Human Eye The eye produces
a real, inverted image (usually smaller) on the retina
The brain adjusts the image to appear properly
That’s why things do not look upside down to us

24. 27-1 The Human Eye The ciliary muscles The near point The far point
adjust the shape of the lens to accommodate near and far vision.
The near point
the closest point to the eye that the lens is able to focus
normal vision ~ 25 cm from the eye
it increases with age as the lens becomes less flexible
The far point
farthest point at which the eye can focus
it is infinitely far away, if vision is normal

25. 27-1 The Camera The simplest camera: The camera lens
a lens & film in a light-tight box
The camera lens
cannot change shape
it moves closer to or farther away from the film in order to focus
The f-number characterizes the size of the aperture
The combination of f-number and shutter speed determines the amount of light that reaches the film

26. The Lens Equation
Convergent Lens: h i o f h’

27. 27-2 Lenses in Combination & Corrective Optics
In a two-lens system, the image produced by the first lens serves as the object for the second lens.

28. 27-2 Lenses in Combination & Corrective Optics
To find the image formed by a combination of lenses, consider each lens in turn, starting with the one closest to the object.
The total magnification is the product of the magnifications of each lens.

29. Multiple Lenses
We determine the effect of a system of lenses by considering the image of one lens to be the object for the next lens.
f = +1
f = -4 -1 +3 +1 +2 +6 +5 +4
For the first lens: o1 = +1.5, f1 = +1 \
For the second lens: o2 = +1, f2 = -4 \

30. Multiple Lenses
Objects of the second lens can be virtual. Let’s move the second lens closer to the first lens (in fact, to its focus):
f = +1
f = -4 -1 +3 +1 +2 +6 +5 +4
For the first lens: o1 = +1.5, f1 = +1 \
For the second lens: o2 = -2, f2 = -4 \
Note the negative object distance for the 2nd lens.

31. Multiple Lenses
If the two lenses are thin, they can be touching – i.e. in the same position. We can treat as one lens.
ftotal = ?? ?
For the first lens: o=o1, i1 and f1
For the second lens: o2 = -i1, i2=i, f2
Adding,
As long as,

32. 27-2 Corrective Optics & Human Eye
A nearsighted person: far point at a finite distance
objects farther away will appear blurry: lens focus too strong
so the image is formed in front of the retina.
Use diverging lens
f chosen for a distant object to form image at the far point
Strength of corrective lenses:
© 2017 Pearson Education, Inc.

33. 27-2 Corrective Optics & Human Eye
A farsighted person: see distant objects clearly
but cannot focus on close objects—the near point is too far away
lens not strong enough: image focus is behind the retina.
Use a converging lens
Augment the converging power of the eye
The final image is past the near point
© 2017 Pearson Education, Inc.

34. 27-3 The Magnifying Glass A simple convex lens
makes objects appear bigger by making them appear closer
Similar to a corrective lens for farsightedness
it brings the near point closer to the eye
Angular size of an object
angle it subtends on the retina, and depends both on the size of the object and its distance from the eye
assuming it is small

35. 27-3 The Magnifying Glass
If object is moved closer to the eye, its angular size increases.
If it is placed at the near point, its size is:
Now, place a converging lens
very close to the eye
with f less than N
place object at the focal
the object has a larger angular size

36. 27-4 The Compound Microscope
In its simplest form, made of two converging lenses
One, the eyepiece, is close to the eye
The other, the objective, is close to the object

37. Compound Microscope I1 I2 Objective Eyepiece (fob< 1cm) (feye~5cm)L
Eyepiece
(feye~5cm)
feye o1 h O h1 I1 i1 I2 h2
Magnification:

38. 27-5 Telescopes Similar to microscopes: an objective + an eyepiece
However, objects are at infinity, so the light will be focused at the focal point of the objective
The image formed by the objective is at the focal point of the eyepiece.

39. Refracting Telescope Objective Eyepiece (fob~ 250cm) (feye~5cm) fob 
feye
Star i1 I1 h1
Angular
Magnification:   I2 h2

40. 27-5 Telescopes Objective of a telescope as large as possible
so that it may collect as much light as possible.
Each doubling of its diameter gives four times more light
Very large lenses are difficult to handle
Large telescopes are made as reflectors —objective is a mirror rather than a lens
The mirror has only one surface, can be made very thin, and reflects almost all the light that hits it.

41. 27-6 Lens Aberrations
Spherical aberration: light striking the lens far from the axis does not focus properly.
can be fixed by grinding the lens to a precision, non-spherical shape.
Chromatic aberration occurs when different colors of light focus at different points.

42. © 2017 Pearson Education, Inc.
27-6 Lens Aberrations
Chromatic aberration can be improved
by combining two or more lenses that tend to cancel each other’s aberrations
This only works perfectly for a single wavelength, however.
© 2017 Pearson Education, Inc.

43. Recap of Today’s Topic :
Announcements: Team problems today
Team 12: Kervell Baird, Matthew  George, Derek Schultz
Team 13: Paxton Stowik, Stacey Ann Burke
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #9: due Friday
Midterm 2:
Tuesday April 10: covers Ch
Chapter 26:
Review Equation for lenses
Dispersion & rainbows
Chapter 27:
Eye
Optical instruments