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Reflection, Snell's law

1.
Today’s agenda:

Introduction to Light.

You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).

You must be able to determine the path of light rays using the laws of reflection

and refraction.

Total Internal Reflection and Fiber Optics.

You must be able to determine the conditions under which total internal

reflection occurs, and apply total internal reflection to fiber optic and similar

materials.

Dispersion.

You must understand that the index of refraction of a material is wavelength-

dependent.

Introduction to Light.

You must develop a general understanding of what light is and how it behaves.

Reflection and Refraction (Snell’s Law).

You must be able to determine the path of light rays using the laws of reflection

and refraction.

Total Internal Reflection and Fiber Optics.

You must be able to determine the conditions under which total internal

reflection occurs, and apply total internal reflection to fiber optic and similar

materials.

Dispersion.

You must understand that the index of refraction of a material is wavelength-

dependent.

2.
Light striking a surface may be reflected, transmitted,

or absorbed. Reflected light leaves the surface at the

same angle it was incident on the surface:

i = r

i r

Real Important Note: the angles are measured relative to the

surface normal.

Possible homework hint: the sum of the angles in a 4-sided polygon

is 360.

or absorbed. Reflected light leaves the surface at the

same angle it was incident on the surface:

i = r

i r

Real Important Note: the angles are measured relative to the

surface normal.

Possible homework hint: the sum of the angles in a 4-sided polygon

is 360.

3.
Reflection from

a smooth

surface is

(mirror- like).

Reflection from

a rough surface

is diffuse (not

a smooth

surface is

(mirror- like).

Reflection from

a rough surface

is diffuse (not

4.
Light travels in a straight

line except when it is

reflected or when it

moves from one medium

to another.

Refraction—the “bending,” or change of direction of

light rays when light moves from one medium to a

different one—takes place because light travels with

different speeds in different media.

line except when it is

reflected or when it

moves from one medium

to another.

Refraction—the “bending,” or change of direction of

light rays when light moves from one medium to a

different one—takes place because light travels with

different speeds in different media.

5.
The speed of light in a vacuum is c = 3x108 m/s. The

index of refraction of a material is defined by

c

n= , If you study light in advanced

classes, you’ll find it is more complex

v than this.

where c is the speed of light in a vacuum and v is the

speed of light in the material.

The speed and wavelength of light change when it

passes from one medium to another, but not the

frequency, so c

v= and n = .

n n

index of refraction of a material is defined by

c

n= , If you study light in advanced

classes, you’ll find it is more complex

v than this.

where c is the speed of light in a vacuum and v is the

speed of light in the material.

The speed and wavelength of light change when it

passes from one medium to another, but not the

frequency, so c

v= and n = .

n n

6.
Because light never travels faster than c, n 1.* For

water, n = 1.33 and for glass, n 1.5. Indices of

refraction for several materials are listed in your text.

Example: calculate the speed of light in diamond (n =

c

v =

n

3×108 m/s

v =

2.42

v = 1.24×108 m/s

*Actually, not true but don’t worry about it unless you take advanced courses in optics.

water, n = 1.33 and for glass, n 1.5. Indices of

refraction for several materials are listed in your text.

Example: calculate the speed of light in diamond (n =

c

v =

n

3×108 m/s

v =

2.42

v = 1.24×108 m/s

*Actually, not true but don’t worry about it unless you take advanced courses in optics.

7.
Because n 1, If n < 1, we

we see this: would see this:

Thanks to Dr. Xiaodong Yang for the

images.

we see this: would see this:

Thanks to Dr. Xiaodong Yang for the

images.

8.
Snell’s Law

When light moves from one medium into another, some

is reflected at the boundary, and some is transmitted.

The transmitted light is refracted (“bent”).

a is the angle of incidence, and b is the angle of

in re

ci fr

de ac

nt te

ra d

y a ra b

air (na) y air (nb)

water (nb) water (na)

b a

inc

ref

ide

ra

nt

cte

ray

d

nb>na na>nb

ray

na sin θa = nb sin θb

When light moves from one medium into another, some

is reflected at the boundary, and some is transmitted.

The transmitted light is refracted (“bent”).

a is the angle of incidence, and b is the angle of

in re

ci fr

de ac

nt te

ra d

y a ra b

air (na) y air (nb)

water (nb) water (na)

b a

inc

ref

ide

ra

nt

cte

ray

d

nb>na na>nb

ray

na sin θa = nb sin θb

9.
Light passing from air (n 1) into water (n 1.33).

Light “bends” towards the normal to the surface as

it slows down in water.

in

ci

de

nt

ra

y a

air (na)

(1) sin θa = (1.33) sin θb

water (nb)

θa > θb

b

ref

ra

cte

d

nb>na

ray

na sin θa = nb sin θb

Light “bends” towards the normal to the surface as

it slows down in water.

in

ci

de

nt

ra

y a

air (na)

(1) sin θa = (1.33) sin θb

water (nb)

θa > θb

b

ref

ra

cte

d

nb>na

ray

na sin θa = nb sin θb

10.
Light passing from water (n 1.33) into air (n 1).

Light “bends” away from the normal to the surface

as it speeds up in air.

re

fr

ac

te

(1.33) sin θa = (1) sin θb d

ra

y

b

air (nb)

water (na)

θa < θb

a

inc

ide

nt

ray

na>nb

na sin θa = nb sin θb

Light “bends” away from the normal to the surface

as it speeds up in air.

re

fr

ac

te

(1.33) sin θa = (1) sin θb d

ra

y

b

air (nb)

water (na)

θa < θb

a

inc

ide

nt

ray

na>nb

na sin θa = nb sin θb

11.
Snell’s law, also called the law of refraction, gives the

relationship between angles and indices of refraction:

na sin θa = nb sin θb .

air (na) air (na)

a a

b b

water (nb) water (nb)

You are free to choose which is “a” and which is “b.”

is the angle the ray makes with the normal!

relationship between angles and indices of refraction:

na sin θa = nb sin θb .

air (na) air (na)

a a

b b

water (nb) water (nb)

You are free to choose which is “a” and which is “b.”

is the angle the ray makes with the normal!