1. Physics 1202: Lecture 18 Today’s Agenda
Announcements: Team problems today
Team 10: Alisha Kumar, Adam Saxton, Alanna Forsberg
Team 11: Riley Burns, Deanne Edwards, Shauna Bolton
Team 12: Kervell Baird, Matthew  George, Derek Schultz
Homework #8: due Friday
Midterm 2:
Tuesday April 10: covers Ch
Office hours if needed (M-2:30-3:30 or TH 3:00-4:00)
Chapter 26:
Review of Refraction
Total internal reflection
Refraction and polarization
Equation for lenses
Dispersion & rainbows 1

2. o i f h’ h
26.5

3. EM wave at an interface
What happens when light hits a surface of a material?
Three Possibilities
Reflected
Refracted (transmitted)
Absorbed
Snell’s Law q2 q1
incident
ray
reflected
ray qr
MATERIAL 1: n1
MATERIAL 2: n2
refracted
ray

4. 26-5 Refraction: Basic properties
Light may refract into a material where its speed is lower
angle of refraction is less than the angle of incidence
The ray bends toward the normal
Light may refract into a material where its speed is higher
angle of refraction is more than the angle of incidence
The ray bends away from the normal
If n1 = n2 Þ no effect
If light enters normal Þ no effect

5. Lecture 18, ACT 1
Which of the following ray diagrams could represent the passage of light from air through glass and back to air?
(a)
(b)
(c)

6. Optical effect
Refraction can make objects immersed in water appear broken
Refraction can create mirages

7. Lecture 18, ACT 2 (a) (b) (c) (d)
Which of the following ray diagrams could represent the passage of light from air through glass and back to air?
(a)
(b)
(c)
(d)

8. Total Internal Reflection
Consider light moving from glass (n1=1.5) to air (n2=1.0)
incident
ray
reflected
refracted q2 q1 qr
GLASS
AIR n2 n1
ie light is bent away from the normal.
as q1 gets bigger, q2 gets bigger, but q2 can never get bigger than 90° !!
In general, if sin q1  sin qC  (n2 / n1), we have NO refracted ray;
we have TOTAL INTERNAL REFLECTION.
For example, light in water which is incident on an air surface with angle q1 > qc = sin-1(1.0/1.5) = 41.8° will be totally reflected. This property is the basis for the optical fibers used in communication.

9. ACT 3: Critical Angle...
An optical fiber is cladded by another dielectric. In case I this is water, with an index of refraction of 1.33, while in case II this is air with an index of refraction of 1.00.
Compare the critical angles for total internal reflection in these two cases
a) qcI>qcII
b) qcI=qcII
c) qcI<qcII
air n =1.00
glass n =1.5 qc
water n =1.33
Case I
Case II

10. ACT 4: Fiber Optics
The same two fibers are used to transmit light from a laser in one room to an experiment in another. Which makes a better fiber, the one in water (I) or the one in air (II) ?
a) I Water
b) II Air
air n =1.00
glass n =1.5 qc
water n =1.33
Case I
Case II

11. © 2017 Pearson Education, Inc.
26-5 Applications of TIR
Total internal reflection (TIR) is used
in some binoculars
in optical fibers
In other optical devices
© 2017 Pearson Education, Inc.

12. Internal Reflection in a Prism
Submarine Periscopes
to “see around corners”

13. Fiber Optics An application of internal reflection
Plastic or glass rods are used to “pipe” light from one place to another
Applications include
medical use of fiber optic cables for diagnosis and correction of medical problems
Telecommunications

14. 26-5 Refraction & polarization
Brewster’s angle
special angle
light reflected is totally polarized
Reflected light is completely polarized
When angle between reflected and refracted beams is 90o
Polarization is parallel to the reflecting surface
Applications
Remove reflection
Photographs of objects in water …

15. © 2017 Pearson Education, Inc.
26-5 Applications of TIR
Total internal reflection (TIR) is used
in some binoculars
in optical fibers
In other optical devices
© 2017 Pearson Education, Inc.

16. q R h q
R-i
o-R h’ i o
& h i o f h’

17. Mirror – Lens Definitions
Some important terminology we introduced last class,
o = distance from object to mirror (or lens)
i = distance from mirror to image
o positive, i positive if on same side of mirror as o.
R = radius of curvature of spherical mirror
f = focal length, = R/2 for spherical mirrors.
Concave, Convex, and Spherical mirrors.
M = magnification, (size of image) / (size of object)
negative means inverted image R g q a
object b h
image o i

18. 26-6 Ray Tracing for Lenses
A lens is a piece of transparent material shaped such that parallel light rays are refracted towards a point, a focus:
Convergent Lens
light moving from air into glass
will move toward the normal
light moving from glass back into
air will move away from the normal
real focus
Divergent Lens
light moving from air into glass
will move toward the normal
light moving from glass back into
air will move away from the normal
virtual focus

19. 26-6 Types of Lenses Lenses are used to focus light and form images
There are a variety of possible types
We will consider only the symmetric ones
the double concave and the double convex

20. Recall prisms Bends light twice in the same direction
Think of a convex lens as consisting of prisms
light converges at a focal point (if properly shaped)
Concave lens can also be modeled by prisms

21. 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.

22. 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

23. 26-7: The Lens Equation
We now derive the lens equation which determines the image distance in terms of the object distance and the focal length.
Convergent Lens: o h i f h’
Ray Trace:
Ray through the center of the lens (light blue) passes through undeflected.
Ray parallel to axis (white) passes through focal point f.
two sets of similar triangles:
same as mirror eqn
if we define
i > f > 0
eliminating h’/h:
magnification: also same as mirror eqn!!
M < 0 for inverted image.

24. when the following sign conventions are used:
Summary
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)

25. 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

26. Lecture 18, ACT 5 (a) left half of image disappears
object
A lens is used to image an object on a screen. The right half of the lens is covered.
What is the nature of the image on the screen?
lens
(a) left half of image disappears
(b) right half of image disappears
screen
(c) entire image reduced in intensity

27. 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

28. 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!

29. 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

30. 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

31. Lecture 18, ACT 6
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

32. 26-8 Dispersion and the Rainbow
Rainbows are created by the dispersion of light as it refracts in a rain drop.

33. 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.

34. 26-8 More about Rainbows
As the drop falls, all the colors of the rainbow arrive at the eye.

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

36. © 2017 Pearson Education, Inc.
26-8 A second Rainbow !
Two reflection + refraction
Less intense because of loss due to refraction
© 2017 Pearson Education, Inc.

37. © 2017 Pearson Education, Inc.
26-8 The two Rainbows
Why ?
© 2017 Pearson Education, Inc.

38. Recap of Today’s Topic :
Announcements: Team problems today
Team 10: Alisha Kumar, Adam Saxton, Alanna Forsberg
Team 11: Riley Burns, Deanne Edwards, Shauna Bolton
Team 12: Kervell Baird, Matthew  George, Derek Schultz
Homework #8: due Friday
Midterm 2:
Tuesday April 10: covers Ch
Office hours if needed (M-2:30-3:30 or TH 3:00-4:00)
Chapter 26:
Review of Refraction
Total internal reflection
Refraction and polarization
Equation for lenses
Dispersion & rainbows