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.Our topic is about “thin film interference”
and film already means “thin” so thin film
means really really thin layer of a medium.
.When it rains outside there will be puddles
of water and because there is oil left over
on the road, sometime some small thickness
of oil will float on top of the water. we call
this thickness ’t’ as you see on the
figure.We know there is oil because when
you look down you see a colourful pattern of
red, green,yellow, orange and etc. formed in
the puddle. and this incident is due to “thin
=========> HOW Does it happen….???!!
Just a simple example…
light (purple line) comes in (this light can be from any source) when the light ray hits the oil part of will reflect
from the surface and we call it light ray #1. ( the ray is going to reflect back on top of itself but here i drew it
beside it to prevent messiness. but in real life it should reflect back on top of itself if it was coming straight in.)
The other part of the ray will pass through the oil ( so the medium should be translucent) so the light ray in ray
again meets a new interference and ** each time a light ray meets a new interference part of it reflects back
and part of it passes through the medium. The reflected ray we call it light ray #2.
Now these two ray #1 and 2 will overlap and now our eye will experience interference and they might be
destructive or constructive and we might see different colours depending on the length of the wavelength ….
SO THE QUESTION IS HOW DOES THE THICKNESS OF THIS OIL AND WAVELENGTH OF THE
LIGHT DETERMINE IF THE REFLECTED RAYS ARE GING TO BE
CONSTRUCTIVE, DESTRUCTIVE ??
1. we know that the difference of the path way length is m
2. we know that the difference of the pathway length is (m+1/2)λ
**** BUT these two are flipped if one of these two is pi shifted and
the other is not.
**** IF they are both pi shifted the condition stays the same.
3. every time there is a reflection, there might be a pi shift and it
depends on the speed of the wave in these materials.
4. reflected light will experience a 180 degree phase change when it
reflects from a higher index of refraction and NO phase change
when it reflects from a medium of lower index.
5. delta X= 2t (* so we can write in the form in second picture)
6. wave have different λ in air and oil; but we always use the λ that
the light had IN THE THIN FILM or in this case in the oil.
7. frequency does not change when the wave enters a different
medium but the speed does change.
* so as you see in this picture the first light ray experiences a pi shift because the INDEX(n) of the
oil is more than air, but for the second light it won’t experiences a pi shift because the INDEX(n) of
water is less than oil.
So based on the things we’ve learnt we can say that:
. the wavelength of the wave in a medium with an index of refraction, it can be
written in this form:
λn = λ / n
. as we said the length travelled is 2t so we can say that:
2t = λn / 2 or t = (2m + 1) λn / 4
Let’s combine our knowledge and solve this question…
Q: when a narrow beam of white light shines almost perpendicular to the
surface of oil, the colour appears tO be blue (480nm in air). the index
refraction of oil is approximately n=1.4 so what is one possible thickness
for the oil layer?