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Calculate the angle at which (a) first o...

Calculate the angle at which (a) first order reflection and (b) second order reflection will occur in an X-ray spectrometer when X-ray of wavelength `1.54A^@` are diffracted by the atoms of a crystal, given that the interplanar distance is `4.04A^@`.

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`10^@59. , 22^@24`
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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 constituent waves. 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 film with index of refraction 1.33 coats a glass lens with index of refraction 1.50. Which of the following choices is the smallest film thickness that will not reflect light with wavelength 640 nm?

Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected light waves. If two waves are in phase, their crests and troughs will coincide. The interference will be constructive and the amplitude of resultant wave will be greater then either of constituent waves. 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 amplitude of the resultant wave will be less than that of either constiuent wave. 1. When incident light I, reaches the surface at point a, some of the light 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 traveled the extra distance within the film of abc. If the angle of incidence is small, then abc is approximately 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 ,... Destructive 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 area: 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 ,... 72. A film with index of refraction 1.50 coats a glass lens with index of refraction 1.80. What is the minimum thickness of the thin film that will strongly reflect light with wavelength 600 nm?

A prism of refractive index n_(1) & another prism of reactive index n_(2) are stuck together without a gap as shown in the figure.The angle of the prisms are as shown. n_(1)&n_(2) depend on lambda ,the wavelength of light according to n_(1)=1.20+(10.8xx10^(4))/(lambda^(2)) & n_(2)=1.45+(1.80xx10^(4))/(lambda^(2)) where lambda is in nm. (i)Calculate the wavelength lambda_(0) for which rays incident at any angle on the interface BC pass through without bending at that interface. (ii) for light of wavelength lambda_(0) ,find the angle of incidencei on face AC such that the deviation produced by the combination of prism is minimum.

Thin films, including soap bubbles and oil slicks, show patterns of alternating dark and bright regions resulting from interference among the reflected light waves. If two waves are in phase their crest and troughs will coincide. The interference will be constructive and the aplitude of the resultant wave will be greater than the amplitude of either constituent wave. if the two waves are out of phase, the crests of one wave will coincide with the troughs of the other wave. The interference will be destructive and the amplitude of the resultant wave will be less than that of either constituent wave. at the interface between two transparent media some light is reflected and some light is refracted. * When incident light, reaches the surface at point a, some of the light is reflected as ray R_(a) and and some is refracted following the path ab to the back of the film. *At point b some of the light is refracted out of the film and part is reflected back refracted out of the fiml as ray R_(c) . R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film of abc. if the angle of incidence is small then abc is approximately 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. * Refraction at an interface never changes the phase of the wave. * For reflection at the interface between two media 1 and 2, if n_(1)ltn_(2) the reflected wave will change phase by pi . if n_(1)gtn_(2) the reflected wave will not undergo a phase change. for reference n_(air)=1.00 * if the waves are in phase after refection at all interfaces, then the effects of path length in the film are Constructive interference occur when (n= refractive index) 2t=mlamda//n" "m=0,1,2,3... .. Destructive interference occurs when 2t=(m+1//2)lamda//n" "m=0,1,2,3... Q. The average human eye sees colors with wavelengths between 430 nm to 680 nm. For what visible wavelength will a 350 nm thick n=1.35 soap film produce maximum destructive interference?

Thin films, including soap bubbles and oil slicks, show patterns of alternating dark and bright regions resulting from interference among the reflected light waves. If two waves are in phase their crest and troughs will coincide. The interference will be constructive and the aplitude of the resultant wave will be greater than the amplitude of either constituent wave. if the two waves are out of phase, the crests of one wave will coincide with the troughs of the other wave. The interference will be destructive and the amplitude of the resultant wave will be less than that of either constituent wave. at the interface between two transparent media some light is reflected and some light is refracted. * When incident light, reaches the surface at point a, some of the light is reflected as ray R_(a) and and some is refracted following the path ab to the back of the film. *At point b some of the light is refracted out of the film and part is reflected back refracted out of the fiml as ray R_(c) . R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film of abc. if the angle of incidence is small then abc is approximately 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. * Refraction at an interface never changes the phase of the wave. * For reflection at the interface between two media 1 and 2, if n_(1)ltn_(2) the reflected wave will change phase by pi . if n_(1)gtn_(2) the reflected wave will not undergo a phase change. for reference n_(air)=1.00 * if the waves are in phase after refection at all interfaces, then the effects of path length in the film are Constructive interference occur when (n= refractive index) 2t=mlamda//n" "m=0,1,2,3... .. Destructive interference occurs when 2t=(m+1//2)lamda//n" "m=0,1,2,3... Q. A 600 nm light is perpendicularly incident on a soap film suspended in air. The film is 1.00 mum thick with n=1.35. Which statement most accurately describes the interference of the light reflected by the two surfaces of the film?