Today5/1

Questions? Waves (review)

phase shifts interference reftaction lenses/mirrors etc..

Interference in 2-DSources “in phase”

Crest meets crest and trough meets trough, constructive, loud sound or bright light

Crest meets trough and trough meets crest, destructive, no sound or dark

Crest

Trough

Interference in 2-DSources “in phase”

Constructive at a point if it is the same distance from each source

Destructive at a point if it is 1/2 farther away from one source

Crest

Trough

Interference in 2DSources “out of phase”

Crest meets trough and trough meets crest, destructive, no sound or dark

Crest meets crest and trough meets trough, constructive, loud sound or bright

Crest

Trough

Interference in 2-DSources “out of phase”

Destructive at a point if the point is the same distance from each source

Constructive at a point if the point is 1/2 farther away from one source

Crest

Trough

Reflections at Boundaries Four situations

Fixed end

Free end

Light to heavy

Heavy to light

Fixed End Reflections

Fixed end

Crest turns into trough

Leading edge is the same

See “Wave Interference” handout for how the string looks during the reflection.

Same velocity, length, and amplitude

Free End Reflections

Free end

Crest stays a crest

Leading edge is the same

See “Wave Interference” handout for how the string looks during the reflection.

Same velocity, length, and amplitude

Light to HeavyBoth transmission and reflection

Boundary feels like a fixed end to the light string

Reflection just like fixed end, inverted

Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave.

Slower, so not as far from boundary

Shorter, “bunched up” Inverted wave

Heavy to LightBoth transmission and reflection

Boundary feels like a free end to the heavy string

Reflection just like free end, not inverted

Faster, farther from boundary

Longer, “spread out” Wave not inverted

Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.

Slower, so not as far from boundary

Shorter, “bunched up” Inverted wave

Faster, farther from boundary

Longer, “spread out” Same as incoming wave

Light: Glass to Air

Light: Air to Glass

Two slit geometry (screen far away)

Screen

PLD = d sin (d = slit separation)

d

PLD

d

(close enough)

Two slit geometry

Screen

PDL = d sin (d = slit separation)

d sin = m constructive interference

d sin = (m+ 1/2) destructive interference

When the sources (slits) are “in phase”

d

A simpler picture

Screen very far away (L)

Two slits very close together (d)

d sin = m constructive interference

d sin = (m+ 1/2) destructive interference

When the sources (slits) and “in phase”

The m’s

m = 0

m = 1

m = 2

m = 1

m = 2m = 1

m = 0

m = 0

m = 1d sin = md sin = (m+ 1/2)

0 “zeroth order” fringe1 “first order” fringe2 “second order” fringe

Thin Films

Eyeball

The wavelength is different in the film.

Wavelength ()Film thickness (PLD)Index of refraction (n)Phase shifts

film = vacuum /nfilm

Thin Film Problems

Draw picture Consider reflected wave phase shifts

none, one, or both can be shifted

Find in the film Chose m or (m + 1/2) (use in the film)

Constructive or destructive? Phase shifts?

PLD = 2t for thin films

Total internal reflection

Water - index of refraction nW = 1.33

nAsin A = nWsin W Air - index of refraction nA = 1.0

A

W

As W increases, so does A

until A becomes 90°. C is called the “critical angle”. If W is greater that C no light will escape the water and all will be “internally reflected.”

Total internal reflection only happens when light goes from high n to low n and it depends on both n’s!

nAsin 90 = nWsin C ornA = nWsin C

C

Example:What is the critical angle for light traveling from water into air?

n2 = n1sin C

n1 = 1.33

C

n2 = 1.0sin C = n2/n1 = 0.752C = 48.8°

Note that there is no critical angle for light from low index to higher index.

Example:What happens if the angle of incidence is greater than 48.8°?

n2 = n1sin C

n1 = 1.33

1 = 50°

n2 = 1.0

50°

Example:What happens if I place a sheet of glass on the water, ng = 1.5?

n2sin 2 = n1sin 1

n1 = 1.33

1 = 50

n2 = 1.0

ng = 1.5

No internal reflection possible-low to high n!

n2 = n1sin C

1.5sin g = 1.33sin50° g = 42.8°

Now what happens? C = Arcsin1/1.5 = 41.8°

The light reflected back into the glass.

g = 42.8

Diverging Lens-Ray Diagrams

ff

Bend the ray at the middle of the lensIn parallel-out as if from left focus

Also straight through the center of the lens

For lenses (both types) di is positive on the right.Here di will be a negative number. f is negative for diverging lenses.

di

In as if toward right focus-out parallel

Diverging Lens-Ray Diagrams and Math

ff

di

d0 = +12 cm, f = -4 cm find di, m, hi

fdd i

111

0

00 d

d

h

hm ii

Virtual and Real Images

Real: Virtual:

A screen placed at the image will produce an image.

A screen placed at the image will not produce an image.

All image forming rays actually pass through the image.

At most only one image forming ray will pass through the image.

do

MathFirst lens do = 9, f = 6 di = ? di = 18

Second lens do = -9, f = -18 di = ?

do

di = 18

di

di

First image m1 = -18/9 = -2

Second image m2 = -18/-9 = +2 Total m = -2(2) = -4

Inverted and real

Example: f = + 6 cm and - 18 cm lenses are 1 cm apart do = + 12 cm

minus sign because “virtual object”