engineering physics

Engineering Physics

by

BhaskarDepartment of Physics

K L University

Lecture 4&5 (06,07 & 13 Aug)

Interference in Thin Films

Interference in thin filmsTypes of Interference: The phenomenon is divided into two

classes based on the mode of production of interference. These are

Interference produced by the division of wave front

Young’s double slit experiment.

Interference produced by the division of amplitudeBut interference pattern can also be produced by division of amplitude

of a single wave.

Lloyd’s mirror. But the positions of the dark and bright fringes are reversed here when

compared to the patterns of Young’s double slit experiment.

Stocks Principle: According to stocks principle an wave undergoes a phase change of 180 degrees on reflection from a medium of higher index of refraction than the one in which it is travelling.

Interference in thin films

Reflection of a Transverse Wave from a Fixed End:

Interference in thin films

Wave exerts upward force on support=> downward force on rope=> inversion of original wave

Reflection of a Transverse Wave from a Free End:

Interference in thin films

If end is free to move wave is not inverted No force on free endSo wave is just reflected

Interference in thin films

Reflection by denser mediumReflection by less dense medium

This reflection produces a phase difference of ½λ from the original wave and is called a fixed-end reflection.

Interference in thin films

The reflection produces no phase difference with the original wave, this is called a free-end reflection.

Interference in thin films

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Optical Path:

•The optical path travelled by a light ray in a medium of refractive index 'μ' is not equal to actual path travel led by the light ray.

Optical path travelled by light beam ǂ Actual path travelled by light

Interference in thin films

Interference in thin filmsThin film planes can be parallel to each other or

inclined. That is why, the concept of interference in thin films can be studied under two categories, namely,

1. Interference in parallel plate film and 2. Interference in wedge-shaped films.

Soap Film – Why Color?

Interference in thin films• We observes colors in such thin films as soap bubbles, coatings on

camera lenses and in a butterfly's wings or peacock's feathers. 

When ray 4 strikes the top interface from underneath, some is reflected (not shown) and some is refracted, ray 5.  It is the interference between rays 2 and 5 that produces a thin film's color when the film is viewed from above.

When ray 1 strikes the top interface, some of the light is partially reflected, ray 2, and the rest is refracted, ray 3.  When ray 3 strikes the bottom interface, some of it is reflected, ray 4, and the remainder is refracted, ray 6.

Interference in thin filmsInterference in plane parallel films due to reflection

of light:

• Ray 2 undergoes a phase change of 180° with respect to the incident ray

• Ray 1, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave

Interference in thin filmsInterference in plane parallel films due to reflection

of light: S

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Interference in thin filmsInterference in plane parallel films due to reflection

of light:

• For constructive interference 2 μ t cos r =(2n±1) λ/2 n = 0, 1, 2 …• For normal incidence r=00

2 μ t = (2n±1) λ/2 n = 0, 1, 2 …

• For destruction interference 2 μ t cos r = n λ n = 0, 1, 2 … • For normal incidence r=0° 2 μ t = n λ n = 0, 1, 2 …

Interference in thin films• Two factors influence interference

– Possible phase reversals on reflection– Differences in travel distance

• The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface

• If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed

Interference in thin filmsInterference in plane parallel films due to

transmitted of light:

The conditions for bright is 2 μ d cos r = n λ n = 0, 1, 2 … The conditions for dark is 2 μ d cos r =(2n±1) λ/2

n = 0, 1, 2 … We can say the interference pattern due to reflected and transmitted rays are complementary each other.

Interference in wedge-shaped films:

Interference in thin films

Interference in wedge-shaped films:

Interference in thin films

• For constructive interference 2 μ t cos (r + α) =(2n±1) λ/2 n = 0, 1, 2 …• For normal incidence r=00

2 μ t cos α = (2n±1) λ/2 n = 0, 1, 2 …

• For destruction interference 2 μ t cos (r + α) = n λ n = 0, 1, 2 … • For normal incidence r=00 2 μ t cos α = n λ n = 0, 1, 2 …

Applications of Wedge method:

1) Determination of thickness of a paper or diameter of a wire/hair.

2) Verification of flatness of the given transparent surface.

Interference in thin films

Determination of thickness of paper or thin film:

Interference in thin films

Determination of thickness of paper or thin film:

Interference in thin films

Thickness of paper:

• Ray 2: No phase change from internal reflection BUT wave travels extra distance 2 t during which wavelength is

number of “extra”

wavelengths from travel through the film is

• Ray 1: 180° (i.e. π) phase

change from external reflection equivalent to a path

difference of

Interference in thin films

NON-REFLECTIVE COATINGS:

Interference in thin films

If film is between layers with higher and lower refractive index, conditions reverse constructive interference for 2 μ t = n λ n = 0, 1, 2 … Get 180° phase change at both reflections

Interference in thin filmsNON-REFLECTIVE COATINGS:

Non-reflecting medium can prepared by coating the thin films on to the mediums. These films were useful to prevent the reflection of light(still some light can reflects but reflected ratio decreases). Here the condition for reflection minimum requires a path difference is λ/2.

NEWTON'S RINGS:

Interference in thin films