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

AIR (less dense)

AIR (less dense)

GLASS (more dense)

“ZAP!”

“LASER…”

“Costingone MILLION

dollars…”

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

vc

n

rrii sin n sin n

f1

q1

p1

pq-

hh'

M

i

r1-c n

n sin

h

h