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Monochromatic light of wavelength 589 nmis incident from air on a water surface. Whatare the wavelength, frequency and speed ofreflected, and (b) refracted light ?
Refractive index of water is 1'33.
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What is the shape of the wavefront in eachof the following cases :
(a) Light diverging from a point source.
(b) Light emerging out of a convex lens whena point source is placed at its focus.
(c) The portion of the wavefront of light froma distant star intercepted by the Earth.
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(a) The refractive
index of glass is 1.5. Whatis the speed of light in glass ? (Speed oflight in
vacuum is
)
(b) Is the speed of
light in glass independent of the colour of light ? If not, which of the two colours
red and violet travels slower ina glass prism ?
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In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is place 1.4 m away. The distancebetween the central bright fringe and thefourth bright fringe is measured to be 1.2cm. Determine the wavelength of light usedin the experiment.
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In Young's double
slit experiment using monochromatic light of wavelength
the intensity
of light at a point on the screen where path difference is
is K
units. What is the intensity of light at a point where path difference is
?
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A beam of light consisting of two wavelengths650 nm and 520 urn is used to obtaininterference fringes in a Young's doubleslit experiment.
(a) Find the distance of the third brightfringe on the screen from the centralmaximum for wavelength 650 nm.
(b) What is the least distance from thecentral maximum where the brightfringes due to both the wavelengthscoincide ?
The distance between two slits is 2 mm anddistance between the plane of the slits and the screen is 1.2 m.
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In a double-slit
experiment, the angular widthof a fringe is found to be 0.2° on a screenplaced
1 m away. The wavelength of light usedis 600 nm. What will be the angular width
ofthe fringe if the entire experiment apparatusis immersed in water ? Take
refractive indexof water to be
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What is the Brewster angle for air to glasstransition ? (Refractive index of glass = 1.5.)
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Light of wavelength 5000 Å falls on a planereflecting surface. What are the wavelengthand frequency of the reflected light ? Forwhat angle of incidence is the reflected raynormal to the incident ray ?
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Estimate the distance for which ray opticsis good approximation for an aperture of 4mm and wavelength 400 nm.
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The
line
emitted by hydrogen ina star is found to be red-shifted by
Estimate
the speed with which the star isreceding from the Earth.
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Explain how Corpuscular theory predictsthe speed of light in a medium, say, water, tobe grater than the speed of light in vacuum.
Is the prediction confirmed by experimentaldetermination of the speed of light in water? If not, which alternative picture of light isconsistent with experiment ?
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You have learnt in the text how Huygens'principle leads to the laws of reflection andrefraction. Use the same principle to deducedirectly that a point object placed in front ofa plane mirror produces a virtual imagewhose distance from the mirror is equal tothe object distance from the mirror.
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Let us list some of the factors, which couldpossibly influence the speed of wavepropagation:
(i) nature of the source, (ii) direction ofpropagation, (iii) motion of the source and/or observer.
(iv)wavelength, (v) intensity of the wave.
On which of these factors, if any, doesthe speed of light in vacuum, (b) the speedof light in a medium (say, glass or water),depend ?
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For sound waves, the Doppler formula forfrequency shift differs slightly between thetwo situations :(i) source at rest; observermoving, and (ii) source moving; observer atrest. The exact Doppler formulae for the caseof light waves in vacuum are, however, strictlyidentical for these situations. Explain why thisshould be so. Would you expect the formulaeto be strictly identical for the two situationsin case of light travelling in a medium ?
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In double slit experiment using light ofwavelength 600 nm, the angular width of afringe formed on a distant screen D 0.1°.
What is the spacing between two slits ?
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Answer the following questions :
(a) In a single-slit diffraction experiment,the width of the slit is made double the originalwidth. How does this affect the size andintensity of the central diffraction band ?
(b) In what way is diffraction from each slitrelated to the interference pattern in adouble-slit experiment ?
(c) When a tiny circular obstacle is placedin the path of light from a distant source, abright spot is seen at the centre of the shadowof the obstacle. Explain why ?
(d) Two students are separated by a 7 mpartition wall in a room 10 m high. If bothlight and sound waves can bend aroundobstacles, how is it that the students areunable to see each other even though theycan converse easily ?
(e) Ray optics is based on the assumptionthat light travels in a straight line.
Diffraction effects (observed when lightpropagates through small apertures/slitsor around small obstacles) disprove thisassumption. Yet the ray optics assumptionis so commonly used in understandinglocation and several other properties ofimages in optical instruments. What is the justification?
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TWO towers on top of two hills are 40 kmapart. The line joining them passes50 m above a hill halfway between the towers.
What is the longest wavelength of radiowaves, which can be sent between the towerswithout appreciable diffraction effects ?
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A parallel beam of light of wavelength 500nm falls on a narrow slit and the resultingdiffraction pattern is observed on a screen1 m away. It is observed that the first minimum is at a distance of 2.5 mm fromthe centre of the screen. Find the width ofthe slit.
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Answer the following questions :
(a)When a low flying aircraft passesoverhead, we sometimes notice a slightshaking of the picture on our TV screen.
Suggest a possible explanation.
(b)As you have learnt in the text, theprinciple of linear superposition of wavedisplacement is basic to understandingdistributions in diffraction and interferencepatterns. What is the justification of thisprinciple ?
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