Download - Interference Applications
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)