1. Physics 1202: Lecture 21 Today’s Agenda
Announcements: Team problems today
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #10: due Friday next week
NO HOMEWORK this week.
Midterm 2: solutions in class
Chapter: 27 Optical instruments
Review of the eye
Microscope & telescope
Chapter 28: Physical Optics
Interference
Two-slit experiment 1

2. 27
Optical
Instruments

3. The Mirror/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)

4. 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

5. 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

6. 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

7. 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.

8. 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 \

9. 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.

10. 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:
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11. 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.

12. 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

13. 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 focus
the object has a larger angular size

14. 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

15. Compound Microscope I1 I2 Lnp=N Objective Eyepiece (fob< 1cm)
meye=N/feye
Objective
(fob< 1cm)
fob
L=i1+feye
Eyepiece
(feye~5cm)
feye o1 h O h1 I1 i1 I2 h2
Magnification:

16. 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.

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

18. 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.

19. 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.

20. © 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.

21. Interference Diffraction
28- Physical Optics
Interference
Diffraction

22. 28-1 Superposition and Interference
If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.

23. Superposition What happens when two waves collide ?
They add point by point
Why?
Because the wave equation is linear.
This is the principle of superposition.

24. Interference
Light waves interfere with each other much like mechanical waves do
All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine
Destructive interference
Constructive interference

25. Lecture 21 – Act 1
If you added the two sinusoidal waves shown in the top plot, what would the result look like ?

26. Conditions for Interference
For sustained interference between two sources of light to be observed, there are two conditions which must be met
The sources must be coherent
They must maintain a constant phase with respect to each other
The waves must have identical wavelengths
Incoherent light beams pass through each other, with no obvious interference.
Although white-light interference is observed under certain conditions, it’s easier to see interference when sources are monochromatic.

27. Wavefronts: slit acts like point source
A wave through a slit
Wavefronts: slit acts like point source
Rays

28. A wave through two slits (two coherent point sources)

29. Add Amplitudes! (electric fields or magnetic fields)
Intensity
What happens when two light waves are present at the same point in space and time?
What will we see? Intensity!
Add Amplitudes! (electric fields or magnetic fields)
Brightness ~ <Amplitude2> ~ ½ E02

30. Lecture 21 – Act 2 Which of the following statements are true?
Suppose laser light of wavelength l is incident on the two-slit apparatus as shown below.
Which of the following statements are true?
(A) There are new patterns of light and dark.
(B) The light at all points on the screen is increased (compared to one slit).
(C) The light at all points on the screen is decreased (compareed to two slits).

31. A wave through two slitsq d l2 L
Screen
Assume L is large, Rays are parallel

32. A wave through two slits
In Phase, i.e. Maxima when DP= l2 - l1 = d sinq = ml
Out of Phase, i.e. Minima when DP = d sinq = (m+1/2)l d q
DP= l2-l1 = d sinq
Screen

33. A wave through two slits
In Phase, i.e. Maxima when DP = d sinq = ml +
Out of Phase, i.e. Minima when DP = d sinq = (m+1/2)l +

34. Waves and Interference
Note that you could derive the reflectance equation (qi=qR) using a particle model for light.
Bouncing balls.
You could also derive Snell’s Law for particles.
n1sin (qi)=n2sin(q2)
The particles change speed in different media
(Newton did just this)
You cannot get a particle model for these interference effects. You would have to magically create particles at the bright spots and annihilate them at the dark spots.
Interference effects mean that light must be made up of waves.

35. 28-2 Young’s Two-Slit Experiment
In this experiment, the original light source need not be coherent
it becomes so after passing through the first very narrow single slit
Thomas Young first demonstrated interference in light waves from two sources in 1801
Light is incident on a screen with a narrow slit, So
The light waves then pass through two narrow, parallel slits, S1 and S2
The bright areas : constructive interference
The dark areas : destructive interference
© 2017 Pearson Education, Inc.

36. 28-2 Young’s Two-Slit Experiment
The light on the screen has alternating light and dark fringes, corresponding to constructive and destructive interference.
The path difference is
Therefore, the condition for bright fringes (constructive interference) is:

37. 28-2 Young’s Two-Slit Experiment
This diagram illustrates the numbering of the fringes.
The dark fringes are between the bright fringes; the condition for dark fringes is:
© 2017 Pearson Education, Inc.

38. Recap of Today’s Topic :
Announcements: Team problems today
Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis
Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon
Homework #10: due Friday next week
NO HOMEWORK this week.
Midterm 2: solutions in class
Chapter: 27 Optical instruments
Review of the eye
Microscope & telescope
Chapter 28: Physical Optics
Interference
Two-slit experiment