Thin Films, Diffraction, and
Double slit interference
Young's Experiment
• Construction is reinforcement (adding)
• Suppose you have two waves with the
same phase at point P, and l1 and l2 are
the length the waves have traveled
• The waves differ by one wavelength
• So l1 = 2¼ l and l2 = 3¼ l
• So whenever l2-l1 = ml, where m =
1,2,3,…, there is constructive interference
Cont.
• Destruction is cancellation (subtraction)
• Suppose you have two waves that are out
of phase at point P, and l1 and l2 are the
length the waves have traveled
• The waves differ by one-half a wavelength
• So l1 = 2¾ l and l2 = 3¼ l
• So whenever l2-l1 = (m + ½)l, where m =
0,1,2,3…, there is destructive interference
Coherent Sources
• Two sources are coherent if the waves
they emit maintain a constant phase
relation.
• This means the wave do not shift relative
to one another
• Lasers are coherent, incandescent bulbs
are non coherent
Young
• In 1801, Thomas Young demonstrated the
wave nature of light by overlapping light
waves and showing interference
• He was also able to determine the
wavelength of light
• When the path difference is = l, a bright
fringe is made
• When the path difference an odd multiple
of ½ l, a dark fringe is made
Cont
• For Bright Fringes, sin 
• For Dark Fringes, sin 
m
l
d
 (m  )
1
2
l
d
Thin film interference
• Young double slit experiment is one form
of interference
• Light is reflected off of both boundaries,
but one ray travels further than the other
• This causes the waves to “construct,” 0o,
or 360o phase difference or “ destruct,”
180o phase difference.
• The determining factor is the number of
whole wavelengths
Cont.
• Using index of refraction n=c/v
• Stating c = fl and vfilm = fl
flvacuum
lvacuum
c
n 

v
fl film
l film
• When light travels to a more refractive
material (e.g. air to gasoline), relection at
the boundary occurs along with a phase
change that is ½ of a wavelength in the
film
Cont.
• When light travels to a less refractive
material, there is no phase change
• Example 3 pg 827
• Let “t” represent the thickness of the film
• Since light goes from air to gasoline there
is a 1/2l phase shift, so:
• 2t + 1/2l = 1/2l,3/2l,5/2l,...subtracting ½
• 2t = 1l,2l,3l...so t = ml/2, m = 1,2,3
Cont.
• Multicolored films
• If the thickness is different at different
parts of the film then different colors
subtract, green subtraction would look
magenta, red subtraction would look cyan
Diffraction
• The bending of light around obstacles
• Christian Huygens (1629-1695) describes that
Every point on a wave front acts as a source
of tine wavelet that move forward with the
same speed as the wave.
• The wave front at a later instant is the surface
that is tangent to the wavelets.
• The amount of bending is determined by l/ W,
where W is the width of the opening
• For dark fringes sin = ml/W
Diffraction Grating