When light hits a thin film: - Part refracts into the film while part reflects off the film - If the index of refraction is lower before and higher after, the reflected wave is out of phase with the incident wave - The refracted wave then reflects again at the end of the thin film - For constructive or destructive interference to occur, the path difference of the two waves must satisfy the interference conditions.

1. Thin Film Interference

2. How does Film Interference Work?
● When light hits a thin-film:

3. How does Film Interference Work?
● When light hits a film:
● A part of it refracts into the
thin film while a part of it
reflect off the thin film.
● If nbefore < nafter , the reflected
wave becomes out of phase
compared to the incident
wave
● If nafter < nbefore, no phase
shift happens

4. How does Film Interference Work?
● When light hits a film:
● The refracted wave then
meets the end of the thin
film and again reflects.
● If nbefore < nafter ,out of phase
compared to the incident
wave
● If nafter < nbefore, no phase
shift happens In this case, the thin film is
surrounded with mediums that have
lesser indexes of refraction

5. How does Film Interference Work?
● When light hits a film:
● The refracted wave then
meets the end of the thin
film and again reflects.
● If nbefore < nafter ,out of phase
compared to the incident
wave
● If nafter < nbefore, no phase
shift happens In this case, the thin film is
surrounded with a medium with a
lesser n on top, while a higher n on
the bottom.

6. How does THIN Film Interference
Work?
● At near vertical angles:
● The distance travelled by the
light in the thin film approximates
to 2t, that is because of the
Pythagorean theorem:
h2 = x2 + t2
● As x goes to 0 (since near
vertical):
h2 ≈ t2 or h ≈ t

7. How does THIN Film Interference
Work?
● In this case, if we can see
that there is no phase
difference between these
two waves (each were hard
reflected exactly once), so,
if we want to achieve
destructive interference, our
path difference, 2t, must
meet the requirement of:
(m + 1/2)λ = 2t

8. How does THIN Film Interference
Work?
● In this case, if we can see
that there is a phase
difference of π between
these two waves so, if we
want to achieve destructive
interference, our path
difference, 2t, must meet
the requirement of:
mλ = 2t

9. NOTE!!!
● As we have made the assumption that:
1) the incident light is near vertical
2) it is a thin film
● If either of these are not true, the distance the light would
have travelled would have been described by the
Pythagorean theorem:
where 2h is the distance light travels
in the film
hcos(θ)=t

10. Check Your Understanding
1) Given a hypothetical film that is of thickness 0, would it
still be able to cause interference?
2) What then is the smallest m possible for both cases?
3) What would happen if we had the light come from a
medium of higher index of refraction to a lower one? How
would the shifts go?

11. Check Your Understanding
1) If such a material existed, it would essentially be a
mirror (without the glass in front). The light would never
had split and no interference would occur then.
2) m=0 for the low->high->higher n (since you 1/2λ is still a
viable distance)
m=1 for low->high->low as explained in #1
3) If would have a soft reflection first(with no phase shift
happening at first). A phase shift only occurs when it
travels from a lower inde of refraction to a higher n.

12. References
● Physics for Scientists and Engineers Revised Custom (Vol.
1, pp. 271-273). (2015). Toronto: Nelson Education.
● Made by Arnold Leigh Ryan Choa 32038144 as a
requirement for Phys 101