1. Up-right or Upside-down
Ex A concave mirror has a 30 cm radius of curvature.
If an object is placed 10 cm from the mirror, where will the
image be found?
f = R/2 = 15 cm, p = 10 cm
1/p + 1/q = 1/f  1/10 + 1/q = 1/15
3/30 + 1/q = 2/30
1/q = -1/30
q = -30 cm
Case 5: p < f
Real or Virtual
Magnified or Reduced
Up-right or Upside-down
q < 0
M = -q/p = 3

2. Q. An upright image that is one-half as large as an object is
needed to be formed on a screen in a laboratory experiment
using only a concave mirror with 1 m radius of curvature.
If you can make this image, I will give you $10. If you can’t
you should pay me $10. Deal or no deal? Why?
1/p + 1/q = 1/f = 2/R > 0
M = -q/p = ½ > 0
should be a real image: q > 0
M = -q/p cannot be positive, if q > 0.
No deal!!!

3. Refraction and Lenses
Optical illusion: the pencil is not bent at the air-water boundary.
caused by non-trivial passage of light rays.

4. Refraction Details, 1
Light may refract into a material where its speed is lower
The angle of refraction is less than the angle of incidence
The ray bends toward the normal

5. Refraction Details, 2
Light may refract into a material where its speed is higher
The angle of refraction is greater than the angle of incidence
The ray bends away from the normal

6. The Index of Refraction
When light passes from one medium to another, it is refracted because the speed of light is different in the two media
The index of refraction, n, of a medium can be defined

7. Index of Refraction, cont
For a vacuum, n = 1
For other media, n > 1
n is a unitless ratio

8. Frequency Between Media
As light travels from one medium to another, its frequency does not change
Both the wave speed and the wavelength do change
The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

9. Index of Refraction Extended
The frequency stays the same as the wave travels from one medium to the other
v = ƒ λ
The ratio of the indices of refraction of the two media can be expressed as various ratios

10. All three beams (incident, reflected, and refracted) are in one plane.
Snell’s Law
All three beams (incident, reflected, and refracted) are in one plane. q1
q1 q2
v: speed of light in a medium
n = c/v :index of refraction
n > 1
v1 = c/n1, v2 = c/n2
n1sinq1 = n2sinq2

11. material n = c/v n depends on l. Index of Refraction vacuum 1.00 air
for l = 589 nm
vacuum
1.00
air
water
1.33
ice
1.31
typical glass
1.52
polycarbonate
1.59
diamond
2.42
n depends on l.
Dispersion

12. q1
q1
q1> q2 q2
water

14. Total Internal Reflection
Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction
Ray 5 shows internal reflection

15. Critical Angle
A particular angle of incidence will result in an angle of refraction of 90°
This angle of incidence is called the critical angle

16. Critical Angle, cont
For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary
This ray obeys the Law of Reflection at the boundary
Total internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

17. Total internal reflection when q2 = 90
n1 (> n2) q1
n1sin(q1) = n2sin(q2)
Total internal reflection when q2 = 90
sin(qc) = n2/n1
< 1
qc: critical angle

18. qf = 2qc Fish vision qc = sin-1(1/1.33) = 49
How could fish survive from spear fishing?
Fish vision
qf = 2qc
qc = sin-1(1/1.33)
= 49

19. ncore nclad
>

20. Q. What is the critical angle for a glass to air surface if the
Index of refraction for glass is 1.5.
sinqc = na/ng
= 1.0/1.5
= 0.667
qc = 42

21. q1()
q2() 10
7.5 20
14.9 30
22.0 40
28.8 50
35.0 60
40.5 70
44.8 80
47.6
sinq1/sinq2
1.33
v1 = c/n1, v2 = c/n2
n1sinq1 = n2sinq2 q1 q2
air
water

22. A fish swims below the surface of the water
A fish swims below the surface of the water. Suppose an observer is looking at the fish straight above the fish. The observer sees
the fish at a greater depth than it really is.
the fish at the same depth.
the fish at a smaller depth than it really is.
no fish due to total internal reflection.

24. nIIsinqII = nIIIsinqIII
There are three layers of different media as shown in the figure.
A beam of light bends as shown in the figure when it passes through
the media. What can we say about the materials?
nIsinqI = nIIsinqII
qII > qI  nI > nII I
nIIsinqII = nIIIsinqIII II
qIII > qII  nII > nIII
III
nI > nII > nIII

25. Dispersion of Index of Refraction for Glass
wavelength (nm) n
361 (near UV)
1.539
434 (dark blue)
1.528
486 (green)
1.523
589 (yellow)
1.517
656 (red)
1.514
768 (dark red)
1.511
1200 (IR)
1.505
2000 (far IR)
1.497

28. In glass
n (red) ≈ 1.51
n (purple) ≈ 1.53