Lecture notes La Rosa
Portland State University
PH-213
Interference from Thin Films

Reflection and transmission at an airglass interface
The effects of interference can be best illustrated by observing what happens when a beam of light shines on an air-glass interface.
Consider the incidence of a harmonic EM-wave:
Calculation of the reflection E r
and transmission E t amplitudes
E r
= - 0.2E
i
Calculation of the reflection I r
and transmission I t intensities

Incidence from AIR into GLASS
Likewise, for the case of Incidence from GLASS into AIR, one obtains,

Out of phase

In phase

Key reasoning for analyzing interference in a thin film:
Waves undergo phase shift due to
i) reflections at a interface, and
ii) while travelling through the film
CASE-1: The film has a higher index of refraction than
the surrounding other two media
How to attain maximum reflection?

Reflection from the left-side interface:
Incident wave n
2
Reflected wave from the left-side
interface
Reflection from the left-side interface L
Reflection from the right-side interface:
At the interface:
Electric fields out of phase by 180 o , due to reflection

Wave reflected from the right-side
interface
Incident wave
L
Transmission through the leftside interface
Transmission through the rightside interface
Reflection from the right-side interface
Question: How do the wave profiles look like after 1/4 period of time?
Thus, we have found a condition for maximum reflection

L= 3
λ
2
4

N
N
N

CASE-1: The film has a higher index of refraction than
the surrounding other two media
How to attain maximum transmission?

M
M M

Summary CASE-1:
Analysis of the reflected wave
Interference at P (from the reflected waves)
Therefore the above expression be- comes a condition for destructive interference on reflection.

2
2

Β
Β

CASE-3: n
1
< n
2
< n
3
How to attain minimum reflection?

which causes destructive interference (minimum reflection)

If you already developed enough skills to solve film interference problems, you may want to skip the following pages. Below we have just an alternative way of reasoning to figure out the constructive and destructive interference in thin-films