Download - Refraction and Lenses
refraction: the bending of light as it travels at anangle from one transparent medium into another
When light goes from a… dense medium less
more
to a… dense medium, less
more
it bends… the normal. away fromtoward
It has been found that light obeysthe principle of least time.
AIR (less dense)
AIR (less dense)
GLASS (more dense)
angle of incidence, i
normal
angle of refraction, r
refracted ray i for 2nd boundary
r for 2nd boundary
incident ray
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...
vc
n
n > 1.000. airspace n1.000n
Snell’s Law
rrii sin n sin n
incidentmedium (ni)
refractingmedium (nr)
i
r
Light in air is incident on diamond (n = 2.419)at 43.0o. Find the angle of refraction.
43.0o
r
n = 1.000
n = 2.419
rrii sin n sin n
i
r
i1-r sin
nn
sin
ir
ir sin
nn
sin
43 sin 2.4191.000
sin 1- = 16.4o
= 1.37 x 108 m/s
Light in water is incident on cubic zirconia at 31.5o. Angle of refraction is 18.5o. Water’s index of refractionis 1.333. Find velocity of light in cubic zirconia.
31.5o
18.5o
n = 1.333
nr = nc.z. = ?
c.z.c.z. v
c n
rc.z.iOH sin n sin n2
rc.z.
iOH sin vc
sin n2
iOH
rc.z. sin n
sinc v
2
31.5) (sin 1.333
18.5) (sin m/s 10 x 3.00 v
8
c.z.
Examples of Refraction
atmospheric refraction
We continue to see the Sun after it has set.
…n increases in lower atmosphere,
so light bends more and more
Earth
image
object
actual pathof light
Examples of Refraction (cont.)
mirages
actual path of light
object
image
…not an optical illusion; can be photographed
…“water” on road is an image of sky
Lenses
Types of Lenses
converging lenses diverging lenses
double convex double concave
plano-convex plano-concave
concavo-convex convexo-concave
Rules:
Lens Ray Diagrams
If ray comes in… then it is refracted…
parallel to P.A.
through F
through lens’ center
through F
parallel to P.A.
“NOT!”
First… 1. Draw a centerline vertically through lens.
2. Draw two F’s on the P.A.
F F F F
f = focal length CONVERGING,+
R = radius of curvature DIVERGING,–
real image: rays actually intersect; can project iton 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,–
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
f1
q1
p1
pq-
hh'
M
Diverging lens has focal length10.0 cm. A wiener-dog puppy15.0 cm tall is 22.0 cm from lens.Describe image.
(f = –10.0 cm; h = 15.0 cm; p = 22.0 cm)
f1
q1
p1
p1
- f1
q1
p1 f
11
q
22
1 10-1
1
= – 6.88 cm
pq-
M 226.88 - -
= 0.313 h’ = 0.313(15)= 4.70 cm
SMALLER; UPRIGHT; VIRTUAL; on the left
Diverging lens? “SUV.”
Converging lens has focal length 7.7 cm.A 0.38 cm-tall real image of a thimble isformed 9.1 cm from lens. How far fromlens is thimble? How tall is thimble?
(f = +7.7 cm; q = +9.1 cm) h’ = –0.38 cm;
f1
q1
p1
q1
- f1
p1
q1 f
11
p
9.1
1 7.71
1
= 50. cm
pq-
M 509.1 -
= –0.18h = 2.1 cm
hh'
–0.38 cm
Correcting Vision with Lenses
farsighted nearsighted
What is in focus?
retina cornea
incomingrays fromdistant objects
incomingrays fromnearby objects
What is blurred?
How do we correct the condition?
nearbyobjects
distantobjects
converging lens diverging lens
Total Internal Reflection
Light traveling through water (n = 1.333) is incidenton the water/air boundary at 48.606626o. Find angleof refraction.
sin n sin n rrii
ir
ir sin
nn
sin
i
r
i1-r sin
nn
sin
626)sin(48.606 1.0001.333
sin 1-
= 90.0o
The Critical Angle, c the i for which r = 90o
refracted rays normal
reflected ray
boundary
(MOREdense
medium)
(LESSdense
medium)
c
total internal reflection
-- no light escapes from MORE dense medium
-- light is incident from MORE dense medium to a LESS dense medium at i > c
e.g., T.I.R. in fiber optic cables
light entering light exiting
= 53.23o
Equation for the Critical Angle
Find critical angle for light traveling fromflint glass (n = 1.900) to crown glass (n = 1.522).
i
r1-c n
n sin
i
r1-c n
n sin
1.9001.522
sin 1-
crownglass
flintglass
Dispersion when polychromatic light is separated into its component s
--
--
-- By convention, the accepted index of refraction for a material is for = 589 nm.
occurs because different s interactdifferently w/matter
n differs for different s
The various s traveling through a lensfocus at slightly different points;
resulting blurring =
-- reduced by...
chromatic aberration
F F
WHITE
R
V 589 nm
combining converging and
diverging lenses made from
different types of glass