1. Refraction and Lenses

2. refraction: the bending of light as it travels at an
angle from one transparent medium into another
less
When light goes from a… dense medium
more
more
to a… dense medium,
less
toward
it bends… the normal.
away from
It has been found that light obeys
the principle of least time.

3. angle of incidence, Qi normal incident ray refracted ray
AIR (less dense)
incident ray
refracted ray
Qi for 2nd boundary
angle of refraction, Qr
GLASS (more dense)
AIR (less dense)
Qr for 2nd boundary

4. “ZAP!” “LASER…” “Costing one MILLION dollars…” AIR (less dense)
GLASS (more dense)
“LASER…”
AIR (less dense)
“Costing
one MILLION
dollars…”

5. Index of Refraction
n = index of refraction;
c = 3.00 x 108 m/s;
v = velocity of light in mat’l (m/s)
In general...
n >
Snell’s Law
incident
medium (ni) Qi
refracting
medium (nr) Qr

6. Light in air is incident on diamond (n = 2.419)
at 43.0o. Find the angle of refraction.
43.0o
n = 1.000
n = 2.419 Qr
= o

7. Light in water is incident on cubic zirconia at 31.5o.
Angle of refraction is 18.5o. Water’s index of refraction
is Find velocity of light in cubic zirconia.
31.5o
n = 1.333
nr = nc.z. = ?
18.5o
= x 108 m/s

8. Examples of Refraction
atmospheric refraction
We continue to see the Sun after it has set.
image
actual path
of light
Earth
object
…n increases in lower atmosphere,
so light bends more and more

9. Examples of Refraction (cont.)
mirages
object
actual path of light
image
…not an optical illusion;
can be photographed
…“water” on road is an image of sky

10. Lenses Types of Lenses converging lenses diverging lenses
double convex double concave
plano-convex plano-concave
concavo-convex convexo-concave

11. Lens Ray Diagrams
First… 1. Draw a centerline vertically through lens.
2. Draw two F’s on the P.A. F F
Rules:
If ray comes in…
then it is refracted…
parallel to P.A.
through F
through lens’ center
through F
parallel to P.A.
“NOT!”

12. real image: rays actually intersect; can project it
on a screen
virtual image: rays appear to intersect, but don’t;
cannot project it on a screen
p = object dist.  always on LEFT; always +
q = image dist.  RIGHT,+,REAL; LEFT,–,VIRTUAL
h = object height  always UPRIGHT; always +
h’ = image height  UPRIGHT,+; INVERTED,–
f = focal length CONVERGING,+
R = radius of curvature DIVERGING,–

13. q can be + (on right, real)
Lens Equations
Sign Conventions
Converging Lens
Diverging Lens
f is +
f is –
q can be + (on right, real)
or – (on left, virtual)
q is always –
(on left, virtual)
h’ can be – (inverted)
or + (upright)
h’ is always +
(upright)
Thin Lens Equation and Magnification

14. Diverging lens has focal length
10.0 cm. A wiener-dog puppy
15.0 cm tall is 22.0 cm from lens.
Describe image.
(f = –10.0 cm;
h = 15.0 cm;
p = 22.0 cm)
Diverging lens? “SUV.”
= – 6.88 cm =
 h’ = (15)
= cm
SMALLER; UPRIGHT; VIRTUAL; on the left

15. Converging lens has focal length 7.7 cm.
A 0.38 cm-tall real image of a thimble is
formed 9.1 cm from lens. How far from
lens is thimble? How tall is thimble?
(f = +7.7 cm;
h’ = –0.38 cm;
q = +9.1 cm)
= cm
–0.38 cm
= –0.18
h = 2.1 cm

16. Correcting Vision with Lenses
farsighted nearsighted
What is in focus?
cornea
retina
incoming
rays from
nearby objects
incoming
rays from
distant objects

17. What is blurred?
nearby
objects
distant
objects
How do we correct the condition?
converging lens
diverging lens

18. Total Internal Reflection
Light traveling through water (n = 1.333) is incident
on the water/air boundary at o. Find angle
of refraction.
= 90.0o

19. The Critical Angle, Qc 
the Qi for which Qr = 90o
refracted rays
normal
(LESS
dense
medium)
boundary Qc
(MORE
dense
medium)
reflected ray

20. total internal reflection
-- light is incident from MORE dense medium to
a LESS dense medium at Qi > Qc
-- no light escapes from MORE dense medium
e.g., T.I.R. in fiber optic cables
light exiting
light entering

21. Equation for the Critical Angle
Find critical angle for light traveling from
flint glass (n = 1.900) to crown glass (n = 1.522).
= o
crown
glass
flint

22. Dispersion
 when polychromatic light is
separated into its component ls --
occurs because different ls interact
differently w/matter --
n differs for different ls
-- By convention, the accepted index of refraction
for a material is for l = 589 nm.

23. The various ls traveling through a lens
focus at slightly different points;
resulting blurring =
chromatic aberration
WHITE F F R
589 nm V
-- reduced by...
combining converging and
diverging lenses made from
different types of glass

25. h h