Interference Applications

Physics 202Professor Lee

CarknerLecture 25

PAL #23 Interference

Light with = 400 nm passing through n=1.6 and n=1.5 material N = (L/)(n) L = N/n = (5.75)(400)/(0.1) = 23000

nm Compare to L = 2.6X10-5 m

N = (2.6X10-5)(0.1)/(400X10-9) = 6.5 6.5 is total destructive interference and

so the above situation is brighter (5.75 )

What directions will the beam be bent towards as it enters A, B and C?

a) Up, up, upb) Down, down, downc) Up, down, upd) Up, up, downe) Down, up, down

A B C

n=1

n=1.4

n=1.3

n=1.5

Rank the 3 materials by the speed of light in them, greatest first.

a) A, B, Cb) B, C, Ac) C, A, Bd) A, C, Be) Speed is the same in all

A B C

n=1

n=1.4

n=1.3

n=1.5

What happens to the distance between the fringes if the distance between the slits increases?

a) Increasesb) Decreasesc) Stays the same

What happens to the distance between the fringes if the light is switched from red to green?

a) Increasesb) Decreasesc) Stays the same

What happens to the distance between the fringes if the entire apparatus in submerged in a clear liquid?

a) Increasesb) Decreasesc) Stays the same

Orders

At the center is the 0th order maxima, flanked by the 0th order minima, next is the 1st order maxima etc.

The orders are symmetric e.g. the 5th order maxima is located both to the left and the right of the center at the same distance

The intensity varies sinusoidally between minima and maxima

Intensity of Interference Patterns How bright are the fringes?

The phase difference is related to the path length difference and the wavelength and is given by:

= (2d sin ) / Where d is the distance between the slits, and is the

angle to the point in question is in radians

Intensity The intensity can be found from the electric

field vector E:I E2

I = 4 I0 cos2 (½ )

For any given point on the screen we can find the intensity if we know ,d, and I0 The average intensity is 2I0 with a maximum and

minimum of 4I0 and 0

Intensity Variation

Thin Film Interference

Camera lenses often look bluish

Light that is reflected from both the front and the back of the film has a path length difference and thus may also have a phase difference and show interference

Reflection Phase Shifts

The phase shift depends on the relative indices of refraction

If light is incident on a material with lower n, the phase shift is 0 wavelength Example:

If light is incident on a material with higher n, the phase shift is 0.5 wavelength Example:

The total phase shift is the sum of reflection and path length shifts

Reflection and Thin Films

Since nfilm > nair and nglass > nfilm

Example: optical antireflection coatings

Since nfilm > nair and nair < nfilm

Have to add 0.5 wavelength shift to effects of path length difference Example: soap bubble

Path Length and Thin Films

For light incident on a thin film, the light is reflected once off of the top and once off of the bottom

If the light is incident nearly straight on (perpendicular to the surface) the path length difference is 2 times the thickness or 2L Don’t forget to include reflection

shifts

Reflection and Interference What kind of interference will we get for a particular

thickness?

The wavelength of light in the film is equal to:2 = /n2

For an anti-reflective coating (no net reflection shift), the two reflected rays are in phase and they will produce destructive interference if 2L is equal to 1/2 a wavelength

2L = (m + ½) (/n2) -- dark film

2L = m (/n2) -- bright film

Interference Dependencies

For a film in air (soap bubble) the equations are reversed

Soap film can appear bright or dark depending on the thickness

Since the interference depends also on soap films of a particular thickness can produce strong constructive interference at a particular This is why films show colors

Color of Film What color does a soap film (n=1.33) appear to be

if it is 500 nm thick? We need to find the wavelength of the maxima:

2L = (m + ½) (/n)

= [(2) (500nm) (1.33)] / (m + ½)

= 2660 nm, 887 nm, 532 nm, 380 nm … Only 532 nm is in the visible region and is green

Next Time

Read: 36.1-36.6 Homework: Ch 35, P: 40, 53, Ch

36, P: 2, 17

Interference: Summary Interference occurs when light beams

that are out of phase combine The interference can be constructive or

destructive, producing bright or dark regions

The type of interference can depend on the wavelength, the path length difference, or the index of refraction What types of interference are there?

Reflection

Depends on: n Example: thin films Equations:

• n1 > n2 -- phase shift = 0• antireflective coating

• n1 < n2 -- phase shift = 0.5• soap bubble

Path Length Difference

Depends on: L and Example: double slit interference Equations:

d sin = m -- maxima d sin = (m + ½) -- minima

Different Index of Refraction

Depends on: L, , n Example: combine beams from two

media Equations:

N2 - N1 = (L/)(n2 -n1)