A stone thrown into still water creates a circular wave pattern moving radially outwards. If r is the distance measured from the centre of the pattern, the amplitude of the wave varies as .....
A stone thrown into still water creates a circular wave pattern moving radially outwards. If r is the distance measured from the centre of the pattern, the amplitude of the wave varies as .....
A
`r^((-1)/(2))`
B
`r^(-1)`
C
`r^(-2)`
D
`r^(-(3)/(2))`
Text Solution
Verified by Experts
The correct Answer is:
B
Intenstiy `I prop ("pressure")/("Area" 4pir^(2))`
`E^(2) prop (P)/(4pi r^(2)) [ :. I prop E^(2)]`
where E is amplitude
`E^(2) prop (I1)/(r^(2)) " "` [ all terms are constant ]
`:.E prop (1)/(r)`
`E^(2) prop (P)/(4pi r^(2)) [ :. I prop E^(2)]`
where E is amplitude
`E^(2) prop (I1)/(r^(2)) " "` [ all terms are constant ]
`:.E prop (1)/(r)`
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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?
A horizontal cylinderical tank (6)/(pi)m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam towards the centre of the water surface. When the laser has moved a distance s=1m or more (measured from curved face) from the lowest point in water, no light enters the gas. The refractive index of gas is (mu_("water") = 4//3)
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?
Statement-1: In Young's double slit experiment the two slits are at distance d apart. Interference pattern is observed on a screen at distance D from the slits. At a poit on the screen when it is directly opposite to one of the slits, a dard fringe is observed then the wavelength of wave is proportional of square of distance of two slits. Statement-2: In Young's double slit experiment, for identical slits, the intensity of a dark fringe is zero.
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 soap film of thickness t is surrounded by air and is illuminated at near normal incidence by monochromatic light wavelength lambda in the film. With respect to the wavelength of the monochromatic ligth in the film, what film thickness will produce maximum consturctive interference
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?
KUMAR PRAKASHAN-WAVE OPTICS-SECTION-D (MULTIPLCE CHOICE QUESTIONS (MCQS)) (MCQS FROM DARPAN BASED ON TEXTBOOK)
- A double slit experiment is performed with light of wavelength 500 nm....
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- In case of linearly polarised light, the magnitude of the electric fie...
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- A stone thrown into still water creates a circular wave pattern moving...
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- When exposed to sunlight, thin films of oil on water often exhibit bri...
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- Which properties are independent of each other for waves propagating i...
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- In Young's double slit experiment, the distance between two slits is m...
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- Light is incident normally on a diffracting grating through which the ...
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- Which out of following cannot produce two coherent sources ?
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- In Young's double slit experiment, the two slits act as coherent sourc...
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- In an interference the intensity of two interfering waves are I and 4I...
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- In a single slit diffraction with lambda = 500 nm and a lens of diamet...
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- A: Particle theory fails to explain the velocity of light in air and w...
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- A: It is not possible to have an interference between sound waves prod...
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- A: The obstacle must be in the order of 10^(-7)m to see the differatio...
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- A: To increase resolving power of a telescope, the diameter of objecti...
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- What changes during the polarisation of light?
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- If light of intensity lo is incident at an angle 45^(@) with optical a...
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- What should be wavelength of light to get 5^(th) bright fringe at a po...
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- The polarisation of light proved that light is composed of ......
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- The limit of resolution of an optical instrument arises an account of ...
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