Transcript Document
by Bhaskar Department of Physics K L University Lecture 4&5 (06,07 & 13 Aug) Interference in Thin Films Interference in thin films Types 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 Interference produced by the division of amplitude But interference pattern can also be produced by division of amplitude of a single wave. But the positions of the dark and bright fringes are reversed here when compared to the patterns of Young’s double slit experiment. Interference in thin films 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: Wave exerts upward force on support => downward force on rope => inversion of original wave Interference in thin films Reflection of a Transverse Wave from a Free End: If end is free to move wave is not inverted No force on free end So wave is just reflected Interference in thin films Reflection by denser medium Reflection by less dense medium Interference in thin films 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. A rarer medium A B a ar B ar2 rarer medium O ar O denser medium at art denser medium at D C A C | att B ar2 rarer medium ar O art D atr| denser medium at C M VENKAT 10 Interference in thin films 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 travelled by light ǂ Actual path Interference in thin films Thin 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 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. 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. Interference in thin films Interference 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 films Interference in plane parallel films due to reflection of light: T N S Q i i air i C r A µ r t M E B t r P Interference in thin films Interference 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 films Interference 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 thin films Interference in wedge-shaped films: Interference in thin films Interference in wedge-shaped 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 … Interference in thin films 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: Thickness of paper: Interference in thin films • 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: 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 films NON-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. Interference in thin films NEWTON'S RINGS: