Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected ligth waves. If two waves are in phase, their crests and troughs will coincide. The interference will be cosntructive and the amlitude of resultant wave will be greater then either of constituentwaves. If the two wave are not of phase by half a wavelength (180^(@)), the crests of one wave will coincide width the troughs of the other wave. The interference will be destructive and the ampliutde of the resultant wave will be less than that of either consituent wave. 1. When incident light I, reaches the surface at point a, some of the ligth is reflected as ray R_(a) and some is refracted following the path ab to the back of the film. 2. At point b, some of the light is refracted out of the film and part is reflected back through the film along path bc. At point c, some of the light is reflected back into the film and part is reflected out of the film as ray R_(c). R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film fo abc. If the angle of incidence is small, then abc is approxmately twice the film's thickness . If R_(a) and R_(c) are in phase, they will undergo constructive interference and the region ac will be bright. If R_(a) and R_(c) are out of phase, they will undergo destructive interference and the region ac will be dark. I. Refraction at an interface never changes the phase of the wave. II. For reflection at the interfere between two media 1 and 2, if n_(1) gt n_(2), the reflected wave will change phase. If n_(1) lt n_(2), the reflected wave will not undergo a phase change. For reference, n_(air) = 1.00. III. If the waves are in phase after reflection at all intensities, then the effects of path length in the film are: Constrictive interference occurs when 2 t = m lambda // n, m = 0, 1,2,3,... Destrcutive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3,... If the waves are 180^(@) out of the phase after reflection at all interference, then the effects of path length in the film ara: Constructive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3,... Destructive interference occurs when 2 t = (m lambda)/(n) , m = 0, 1, 2, 3,... A thin of liquid polymer, n = 1.25, coats a slab of pyrex, n = 1.50. White light is incident perpendicularly on the film. In the reflection, full destructive interference occurs for lambda = 600 nm and full constructive interference occurs for lambda = 700 nm What is the thickness of the polymer film?

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Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected ligth waves. If two waves are in phase, their crests and troughs will coincide. The interference will be cosntructive and the amlitude of resultant wave will be greater then either of constituentwaves. If the two wave are not of phase by half a wavelength (180^(@)), the crests of one wave will coincide width the troughs of the other wave. The interference will be destructive and the ampliutde of the resultant wave will be less than that of either consituent wave.  1. When incident light I, reaches the surface at point a, some of the ligth is reflected as ray R_(a) and some is refracted following the path ab to the back of the film.  2. At point b, some of the light is refracted out of the film and part is reflected back through the film along path bc. At point c, some of the light is reflected back into the film and part is reflected out of the film as ray R_(c).    R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film fo abc. If the angle of incidence is small, then abc is approxmately twice the film's thickness .  If R_(a) and R_(c) are in phase, they will undergo constructive interference and the region ac will be bright. If R_(a) and R_(c) are out of phase, they will undergo destructive interference and the region ac will be dark.  I. Refraction at an interface never changes the phase of the wave.  II. For reflection at the interfere between two media 1 and 2, if n_(1) gt n_(2), the reflected wave will change phase. If n_(1) lt n_(2), the reflected wave will not undergo a phase change. For reference, n_(air) = 1.00.    III. If the waves are in phase after reflection at all intensities, then the effects of path length in the film are:  Constrictive interference occurs when 2 t = m lambda // n, m = 0, 1,2,3,...  Destrcutive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n),  m = 0, 1, 2, 3,...  If the waves are 180^(@) out of the phase after reflection at all interference, then the effects of path length in the film ara:  Constructive interference occurs when  2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3,...  Destructive interference occurs when  2 t = (m lambda)/(n) , m = 0, 1, 2, 3,...  A thin of liquid polymer, n = 1.25, coats a slab of pyrex, n = 1.50. White light is incident perpendicularly on the film. In the reflection, full destructive interference occurs for lambda = 600 nm and full constructive interference occurs for lambda = 700 nm What is the thickness of the polymer film?

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1.	Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected ligth waves. If two waves are in phase, their crests and troughs will coincide. The interference will be cosntructive and the amlitude of resultant wave will be greater then either of constituentwaves. If the two wave are not of phase by half a wavelength (180^(@)), the crests of one wave will coincide width the troughs of the other wave. The interference will be destructive and the ampliutde of the resultant wave will be less than that of either consituent wave. 1. When incident light I, reaches the surface at point a, some of the ligth is reflected as ray R_(a) and some is refracted following the path ab to the back of the film. 2. At point b, some of the light is refracted out of the film and part is reflected back through the film along path bc. At point c, some of the light is reflected back into the film and part is reflected out of the film as ray R_(c). R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film fo abc. If the angle of incidence is small, then abc is approxmately twice the film's thickness . If R_(a) and R_(c) are in phase, they will undergo constructive interference and the region ac will be bright. If R_(a) and R_(c) are out of phase, they will undergo destructive interference and the region ac will be dark. I. Refraction at an interface never changes the phase of the wave. II. For reflection at the interfere between two media 1 and 2, if n_(1) gt n_(2), the reflected wave will change phase. If n_(1) lt n_(2), the reflected wave will not undergo a phase change. For reference, n_(air) = 1.00. III. If the waves are in phase after reflection at all intensities, then the effects of path length in the film are: Constrictive interference occurs when 2 t = m lambda // n, m = 0, 1,2,3,... Destrcutive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3,... If the waves are 180^(@) out of the phase after reflection at all interference, then the effects of path length in the film ara: Constructive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3,... Destructive interference occurs when 2 t = (m lambda)/(n) , m = 0, 1, 2, 3,... A thin of liquid polymer, n = 1.25, coats a slab of pyrex, n = 1.50. White light is incident perpendicularly on the film. In the reflection, full destructive interference occurs for lambda = 600 nm and full constructive interference occurs for lambda = 700 nm What is the thickness of the polymer film?
Answer» 120 nm 280 nm 460 nm 840 nm Solution :Both rays `R_(a)` and `R_(b)` are reflected with a CHANGE of phase Therefore, the net change of phase with reflection is zero. For constructive interference , `2t = (m + 1//2) lambda//n` `t = (m + 1//52) (600nm)//2 (1.25) = m xx 700 // 2(1.25)` `600 m + 300 = 700 m implies 300 = 100 m implies m = 3` SOLVING EITHER equation for t, we have `t = 3(700 nm)// 2 (1.25)` `= 840 nm`