SME
University Physics III: Waves, Optics & Modern · Problem type
Thin-film interference
Use this for “A soap film (n = 1.33) is 250 nm thick. Which visible wavelength does it reflect most strongly?”
Diagram
Bright:
2nt
=
(m
+
1
2
)λ,
λ
=
2
×
1.33
×
100
nm
0.5
=
532
nm
(green)
One reflection flips by half a wave (the top, into the denser film), so the extra path must be a whole number of waves plus a half.
This is an example. Type your own values to start a new problem.
2
×
n
×
t (nm)
=
(
m
+
½)
×
λ (nm)
2nt
Extra path
worked out (not typed) · nm
Formulas
2
nt
=
2
×
n
×
t
266 = 2 × 1.33 × 100
2
nt
=
(
m
+
1
2
)
×
λ
266
=
(0
+
1
2
)
×
532
Assumptions
•
Light falls nearly square on a film in air, so the ray reflected at the bottom goes an extra path of 2nt.
•
Only the top reflection (air into film) flips by half a wave, so the reflection is bright when 2nt = (m + ½)λ, m = 0, 1, 2, …
•
If both reflections flip, or neither (a coating on glass), bright is 2nt = mλ instead.
•
λ is the wavelength in air (λ ÷ n inside the film). Visible light runs from about 380 to 750 nm: try m = 0, 1, 2, … until λ falls in it.
Step-by-step
WE KNOW
n = 1.33, t = 100 nm, m = 0
FIND
extra path (2nt), reflected bright wavelength (λ)
Step 1 · Find extra path (2nt)
Use 2nt = 2 × n × t
Down
and
back
up
through
the
film:
twice
t
,
times
n
because
light
is
n
times
slower
there.
2
nt
=
2
×
1.33
×
100
2
nt
=
2.66
×
100
2
nt
=
266
nm
Step 2 · Find reflected bright wavelength (λ)
Use 2nt = (m + ½) × λ
One
flip
already
shifts
the
rays
half
a
wave,
so
the
path
holds
m
+
1
2
wavelengths.
λ
=
2
nt
m
+
1
2
λ
=
266
0 +
1
2
λ
=
532
nm
→
visible:
the
film
shows
this
color.
Check
Put the numbers back in. Both sides should match.
266 = 2 × 1.33 × 100 ✓
266
=
(0
+
1
2
)
×
532
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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