Interference in Thin Interference in Thin FilmsFilms

Interference effects are Interference effects are commonly observed in thin filmscommonly observed in thin films Examples are soap bubbles and oil Examples are soap bubbles and oil

on wateron water Assume the light rays are Assume the light rays are

traveling in air nearly normal to traveling in air nearly normal to the two surfaces of the filmthe two surfaces of the film

Interference in Thin Films, Interference in Thin Films, 22

Rules to rememberRules to remember An electromagnetic wave traveling from a An electromagnetic wave traveling from a

medium of index of refraction medium of index of refraction nn11 toward a toward a medium of index of refraction medium of index of refraction nn22 undergoes a undergoes a 180° phase change180° phase change on reflection when on reflection when nn22 > > nn11

There is There is no phase changeno phase change in the reflected in the reflected wave if wave if nn22 < < nn11

The wavelength of light The wavelength of light λλnn in a medium with in a medium with index of refraction index of refraction nn is is λλnn = = λλ//nn, where , where λλ is the is the wavelength of light in vacuumwavelength of light in vacuum

Phase Changes Due To Phase Changes Due To ReflectionReflection

An electromagnetic An electromagnetic wave undergoes a wave undergoes a phase change of phase change of 180° upon reflection 180° upon reflection from a medium of from a medium of higher index of higher index of refractionrefraction than the than the one in which it was one in which it was travelingtraveling Analogous to a Analogous to a

reflected pulse on a reflected pulse on a stringstring

Phase Changes Due To Phase Changes Due To Reflection, cont.Reflection, cont.

There is no phase There is no phase change when the change when the wave is reflected wave is reflected from a boundary from a boundary leading to a leading to a medium of lower medium of lower index of refractionindex of refraction Analogous to a Analogous to a

pulse in a string pulse in a string reflecting from a reflecting from a free supportfree support

Interference in Thin Films, Interference in Thin Films, 33

Ray 1 undergoes a Ray 1 undergoes a phase change of phase change of 180° with respect 180° with respect to the incident rayto the incident ray

Ray 2, which is Ray 2, which is reflected from the reflected from the lower surface, lower surface, undergoes no undergoes no phase change with phase change with respect to the respect to the incident waveincident wave

180 phase change

iiii

Interference in Thin Films, Interference in Thin Films, 44

Very Thin Films: Destructive Very Thin Films: Destructive interference (t<<interference (t<<λλ)) Since the top reflected wave is inverted and the Since the top reflected wave is inverted and the

bottom one is not, the result is out of phase by bottom one is not, the result is out of phase by 1/21/2λλ

Thin Films: Constructive Interference Thin Films: Constructive Interference (t=(t=λλ/4)/4) Path difference is Path difference is λλ/2/2

Since the top reflected wave is inverted and Since the top reflected wave is inverted and the bottom one is not, the result is now in the bottom one is not, the result is now in phasephase

Interference in Thin Films, 5Interference in Thin Films, 5

Thin Films: Destructive interference Thin Films: Destructive interference (t=(t=λλ/2)/2) Path difference is Path difference is λλ

Since the top reflected wave is inverted Since the top reflected wave is inverted and the bottom one is not, the result is in and the bottom one is not, the result is in now one half wavelength out of phasenow one half wavelength out of phase

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

Interference in Thin Films - Interference in Thin Films - CoatingsCoatings To form a nonreflecting coating a thin-To form a nonreflecting coating a thin-

film on glass with a minimum film film on glass with a minimum film thickness of thickness of λλ /(4/(4nn11) is required.) is required.

Destructive Destructive interference interference when: 2when: 2tt==λλ/(2/(2nn11))

Minimum Minimum thickness for thickness for nonreflecting nonreflecting surfaces: surfaces: tt==λλ/(4/(4nn11))

Newton’s RingsNewton’s Rings Another method for viewing interference is to Another method for viewing interference is to

place a planoconvex lens on top of a flat glass place a planoconvex lens on top of a flat glass surfacesurface

The air film between the glass surfaces varies The air film between the glass surfaces varies in thickness from zero at the point of contact to in thickness from zero at the point of contact to some thickness some thickness tt

A pattern of light and dark rings is observedA pattern of light and dark rings is observed This rings are called This rings are called Newton’s RingsNewton’s Rings The particle model of light could not explain the The particle model of light could not explain the

origin of the ringsorigin of the rings Newton’s Rings can be used to test optical Newton’s Rings can be used to test optical

lenseslenses

Newton’s rings, cont. Newton’s rings, cont.

Newton’s rings, cont. Newton’s rings, cont.

Ray 1 undergoes Ray 1 undergoes a phase change of a phase change of 180180 on reflection, on reflection, whereas ray 2 whereas ray 2 undergoes no undergoes no phase changephase change

Problem Solving Strategy Problem Solving Strategy with Thin Films, 1with Thin Films, 1

Identify the thin film causing the Identify the thin film causing the interferenceinterference

The type of interference – The type of interference – constructive or destructive – that constructive or destructive – that occurs is determined by the phase occurs is determined by the phase relationship between the upper relationship between the upper and lower surfacesand lower surfaces

Problem Solving with Thin Problem Solving with Thin Films, 2Films, 2

Phase differences have two causesPhase differences have two causes differences in the distances traveleddifferences in the distances traveled phase changes occurring on reflectionphase changes occurring on reflection BothBoth must be considered when determining must be considered when determining

constructive or destructive interferenceconstructive or destructive interference The interference is The interference is constructiveconstructive if the if the path path

difference is an integral multiple of difference is an integral multiple of λλ and and destructive if the path difference is an odd destructive if the path difference is an odd half multiple of half multiple of λλ The conditions are reversed if one of the waves The conditions are reversed if one of the waves

undergoes a phase change on reflectionundergoes a phase change on reflection