Lecture 33Reflection and refraction.

Introduction to geometric optics

Select an object of your choice (table, book, coin, neighbor’s head). Think about and discuss:

• what it means to “see it”

• how you perceive the position of that object

EM waves (light) from lamps hit surface and are reflected.

Waves propagate spherically in all directions from object.

Your eye is sensitive to light

brain “traces back” to where the light comes from.

3D perception comes from brain comparing images from each eye.

Light rays

= Geometrical abstraction that allows us to work with the direction that an E/B wave travels

Instead of drawing E/Bfields, we draw a “ray”

Ray : a line in the directionalong which light energy is traveling

Ray Model of Light

• Light travels through a transparent medium in straight lines at a speed v =c /n (n = index of refraction)

• Light rays do not interact with each other• A light ray continues forever unless it interacts with matter

medium 1 medium 2

reflection refraction

scattering absorption

Interactions light/matter:• at an interface between two media reflected and refracted• within a medium, light can be scattered or absorbed

ACT: Vertical slit

You have a point source of light behind a wall with a 5 cm tall vertical slit aperture. A screen is placed 2 m in front of the wall. How tall is the slit you see on the screen?

Light source

1m 2m

screen

5cm

A. 5 cm

B. 10 cm

C. 15 cm

15 cmx 5 cm1 m 3 m

x

Image of point A

Image of point B

A

B

x

Two types of reflection

specular reflectionsmooth surfacee.g. mirrors

diffuse reflectionrough surfacee.g. screens

Mirror reflection

• Incident angle = reflected angle• Always draw line that is “normal” (90°) to mirror

– calculate angles with respect to this normal

mirror

i r

DEMO: Mirrors

Image reflected on a plane mirror

A book is in front of a plane mirror. If you see it through the mirror, where does it appear to be?

All the reflected rays seem to be coming from here!

No rays really pass behind the mirror. This is a virtual image.

How to find the image

• Draw two rays (one of them the normal to the surface, it’s a trivial one)

• Draw reflected rays.

• Extrapolate rays until they intersect.

ss’

s : location of the object

s’: location of the image

Positive in front of mirror

Negative behind mirror

Plane mirror:

s = -s’

EM waves not in vacuum

Phys 221:

E field inside a material is characterized by dielectric constant or the dielectric permittivity 0

Similarly:

B field inside a material is characterized by relative permeability m or the permeability

0 (of ten 1)m m

cn

m

c

EM wave speed in a dielectric:

1v

1 alwaysmn

Refraction index

Refraction

Reason: Speed of light is different in both media

– At boundary, part of wavefront is in slower media– Travels shorter distance in t

Fact: Light changes direction when it crosses a boundary

slower

Snell’s law

Angles defined with respect to normal

sin sina a b bn n

ACT: Angle of refraction I

n1

n2A

B C

If n1 > n2 , which direction does the ray go?

1 1 2 2sin sinn n

12 1 1

2

2 1

sin sin sin

n

n

Remember: angles defined with respect to normal!

DEMO: Refraction air/plastic

ACT: Angle of refraction II

n2

When it re-emerges into medium 1, the direction of the ray is:

n1

n1

A

BC

1 1 2 2sin sinn n

2

2

1

1 1sinn

1 1

It comes out exactly parallel to the original ray.

DEMO: Refraction

air/plastic/air

1

In-class example: Refraction

A ray of light strikes the interface between air and an unknown substance at an angle θ1 = 75° from the normal to the surface. The refracted beam makes an angle θ2 = 30° from the normal. What is the index of refraction of this substance?A. 2.5

B. 1.9

C. 1.3

D. 1.0

E. 0.50

Impossible, n 1

75° 75°

30°

air

X

air Xsin75 sin30n n

X

sin751.9

sin30n

= 1.0

Total internal reflection

As light goes to a medium with lower n, the angle from the normal increases (θ1 < θ2):

n1

n2 < n1

If θ1 is large enough, θ2 = 90° !!

1

2

1

2

1c

2

Beyond this angle, there is no more refraction, only reflection.

1

DEMO: Total internal

reflection

Critical angle

n1

n2 < n1

1c

2 90

1 1c 2sin sin90n n

1 21c

1

sinn

n

= 1

Fiber optics

Light internally reflects within the inner glass fiber– no refracted ray going outside– minimal light loss

cladding

core

Both cladding and core are glass such that ncore > ncladding

DEMO: Water tank. Fiber optics

Road mirages

Hot air lower density lower n

Hot road

Low n

High n

Image of sky on the road (that brain interprets as water to explain “reflection”)

Total internal reflection

Light through matter: a simple model

What does really happen when light travels through matter?

v = c

v = c

absorb & re-emit with some phase delay

atom

It depends on how you want to think about it.

You can say that the photons occasionally interact with atoms in a dielectric, being absorbed and re-emitted, and that this only appears to slow them down. Here, the photons travel at “c”.

Or you can say that the wave that propagates through the solid is a combination of a photon and virtual excitations of the atoms of the solid. This wave travels with v < c.

What defines a color?

So the atom oscillates with the frequency of the radiation and then re-emits.

Frequency remains the same

Wavelength changes

n1

n2 < n1

11

1

v cf nf

22 1

2

v cf nf

“Color” correspond to a fixed frequency. The wavelength depends on the medium.