Two small boats are 10m apart on a lake....

Two small boats are `10m` apart on a lake. Each pops up and down with a period of 4.0 seconds due to wave motion on the surface of water. When one boat is at its highest point, the other boat is its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is:

2.5 m/s

5.0 m/s

14 m/s

40 m/s

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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. 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?

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?

When a particle is undergoing motion, the diplacement of the particle has a magnitude that is equal to or smaller than the total distance travelled by the particle. In many cases the displacement of the particle may actually be zero, while the distance travelled by it is non-zero. Both these quantities, however depend on the frame of reference in which motion of the particle is being observed. Consider a particle which is projected in the earth's gravitational field, close to its surface, with a speed of 100sqrt(2) m//s , at an angle of 45^(@) with the horizontal in the eastward direction. Ignore air resistance and assume that the acceleration due to gravity is 10 m//s^(2) . The motion of the particle is observed in two different frames: one in the ground frame (A) and another frame (B), in which the horizontal component of the displacement is always zero. Two observers locates in these frames ill agree on :-

A metallic rod of length 1m is rigidly clamped at its mid point. Longirudinal stationary wave are setup in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is 2 xx 10^(-6) m . Write the equation of motion of a point 2 cm from the midpoint and those of the constituent waves in the rod, (Young,s modulus of the material of the rod = 2 xx 10^(11) Nm^(-2) , density = 8000 kg-m^(-3) ). Both ends are free.

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?

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?

ALLEN -RACE-Basic Maths (Wave Motion & Dopplers Effect) (Fundamental)

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