Optical Properties of Light: Mirror Reflections and Images in Plane and Spherical Mirrors, Slides of Physics

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Optical

properties

of

light

Mirror

reflections

Images

in

flat

and

spherical

mirrors

vt

x k v E t x B B

vt

x k E t x E E

z

z

y

y

cos

cos

max max

Plane

wave

solution

to

Maxwell’s

equations

in

dielectric

medium

with

v=c/n

Additional

comments:

For

this

solution,

the

y

direction

is

called

the

polarization

direction

(the

E

field

orientation)

This

is

a

periodic

wave,

where

k=

and

represents

the

wavelength

and

the

frequency

of

the

wave

is

kc/n=

f.

boundary

at

continuous

and

B

E

n

1

n

2

2

1

n

1 n

2

2

2

1

1

sin

sin

law

s

Snell'

n

n

1 

2

2

2

1

1

sin

sin

c

c n

n

ct

x c n c E t x B B

ct

x c n E t x E E

z

z

y

y





cos

cos

max max

General

case

reflection

and

refraction

2

1

n

1 n

2

1

1

2

1

2

1 0

1

2

1

(^20)

2

1

For

n

n

n

n

E E

n

n

n

E E

R

2

2

1

1

2

2

1

1

1 0

2

2

1

1

1

1

2 0

2

2

1

1

(^22)

2

2

1

1

(^22)

1 0

2

2 1

1

(^22)

1

2

1

2 0

cos

cos

cos

cos

cos

cos

cos

plane

scattering

of

out

polarized

For

cos

cos

cos

cos

cos

cos

cos

plane

scattering

in

polarized

For





























n

n

n

n

E E

n

n

n

E E

E

n n

n

n n

n

E E

n n

n

n n

E E

E

R R

and 0

then ,

If

0

0

1

0

0

2

2

E

E

E

E

E

E

n

R

Analysis

of

mirror

image

Using

geometry:

i^

=

p

h=h'

Mirror

symmetry:

i

Terminology:

Virtual

image

‐‐

perceived

image

but

no

light

can

be

detected

at

the

location

of

the

virtual

image

Real

image

‐ ‐

light

can

detected

at

the

location

of

the

real

image

Summary

of

geometric

optics

of

plane

mirror

“virtual” image

f

i

p

equation

Mirror

General

equation

describing

object

and

image

positions:

f

p

i

case

In this

Analysis

of

image

from

plane

mirror

Geometrical

relationships

|

i |

=

p

h=h’

Magnification

h^ h

M

height

Object

height

Image

(virtual)

Some

details:

By

convention,^ i

<

0

for

virtual

image

p

i

i

Why

does

this

satellite

dish

look

like

a

concave

mirror? A.

Because

it

is.

B.

It

doesn’t

not

shiny

enough.

Where

is

the

receive

placed

relative

to

the

radius

of

curvature

R?

A.

Placed

at

R.

B.

Placed

at

R/2.

Docsity.com

f

p

‐ i

“Proof”

of

mirror

equation:

h

’

h

Similar

triangles:

p

i

h h

Similar

triangles:

p

i

f

i

f

h h

h f

i

f

h

f

i

p

1

1

1





Image

formed

by

concave

mirror:

f

p

‐ i

General

result

for

virtual

image

formed

by

concave

mirror

p

<

f

image

is

upright

and

increased

in

size

Image

formed

by

concave

mirror:

f

i

p

1

1

1





p

i

h h

M

Example:

f

=

4

cm

p

=

10

cm

i^

=

cm

f

p

i

p

i

M