Objectice-Physics Part I

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    Geometrical Optics

    1. A lens is a piece of __________ material that can focus a transmitted beam of

    light.

    2. A lens is a piece of transparent material that can focus a __________ beam oflight.

    3. A lens is usually bounded by two __________ surfaces.

    4. Lenses fall into __________ categories.

    . A con!e" lens is thic#er in the middle and __________ on the edges.

    $. A con!e" lens is __________ in the middle and thinner on the edges.

    %. A con!e" lens __________ the light rays towards its optical a"is.

    &. A con!e" lens con!erges the light rays towards its __________.

    '. A con!e" lens is thinner in the middle and __________ on the edges.

    1(. A di!erging lens is __________ in the middle and thic#er on the edges.11. A conca!e lens __________ the light rays from its optical a"is.

    12. A di!erging lens bends light rays from its __________.

    13. )he point to which the light rays are brought to focus is called __________.

    14. )he point to which the light rays are brought to __________ is called principal

    focus.

    1. )he distancebetween the optical centre of the lens and its principle focus is

    called __________.

    1$. )he distance between the __________ of the lens and its principle focus is

    called its focal length.

    1%. )he point is the lens through which the light rays will pass without any de!iation

    is called its __________.

    1&. )he point is the lens through which the light rays will pass without any de!iation

    is called its __________.

    1'. *n +on!e" lens, when the ob-ect is placed in between and 2 then its image will

    form __________ on the other side of the lens.

    2(. +on!entionally the focal length of the di!erging lens is ta#en as __________.

    21. /hen the two lenses are combined to form a single lens, then this lens is called__________ lens.

    22. )he defect in the lens is due to the fact that the focal points of the light rays

    far from the optical a"is of a spherical lens are different from those rays passing

    through the centre is called __________.

    23. +hromatic aberration can be reduced to a greater e"tent by the combination of

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    __________ lenses.

    24. )he angle subtended by the ob-ect at the eye is called __________.

    2. )he least distance up to which a normal person could see the ob-ect without

    ta#ing any strain on his eyes is called least distance of __________.

    2$. +ompoundmicroscopeis an optical de!ice, which is used to see the __________ob-ect with !ery high magnification.

    2%. *n compound microscope an eyepiece of __________ focal length is used.

    2&. *n compound microscope to obtain the large magnification lenses of __________

    focal length are used.

    2'. *n compound microscope the eyepieces will be used as a __________.

    3(. )elescopeis used to see __________ ob-ect.

    31. )he focal length of the ob-ecti!e in astronomical telescope is __________ than

    the focal length of eyepiece.

    32. Galilean telescope is used to see the ob-ect on __________.

    33. *n Galilean telescope the con!e" lens will be used as an __________.

    34. )errestrial telescope consists of __________ lenses.

    3. *n spectromter, collimeter produces a __________ beam of light.

    3$. )he spectrum of light in which the images o!erlap each other is called

    __________ spectrum.

    3%. )he front of eye is co!ered by a transparent membrane called __________.

    3&. )he abnormality in which the image of the distant ob-ect is focused in from of

    retina is called __________.

    3'. *n the case of the abnormality named as 0yopia the person is said to

    __________.

    4(. hort ightedness can be corrected by using a __________ a lens.

    )he cope of hysics

    1. hysical sciences and biological sciences are the two branches of

    __________.

    2. )he branch of physics, which dealswith the interaction of matter andenergy, is called __________.

    3. *bneina was famous in the field of __________.

    4. 0edical te"t boo#Alannunil)ib was written by __________.

    . *n +.G. system the unit of force is __________.

    $. 5nit of luminous intensity is __________.

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    %. 6imension of !olume is __________.

    &. 6imension of linear momentum is __________.

    '. 1$.% contain __________ significant figures.

    1(. Logarithm was in!ented by __________.

    11. )he biological science deals with __________.

    12. )he classof science, which deals with the properties and beha!iour of

    nonli!ing matter is called __________ science.

    13. +hinese for the first time manufactured __________.

    14. 7gyptian used to measure the flood le!el in the ri!er __________.

    1. )he people of 7uphrate and )igris !alleys were aware of calendar and had

    the #nowledge of __________.

    1$. )he people of indus !alley were pioneers of __________ system.

    1%. )here are two main branches of physics, namely classical physics and

    __________ physics.

    1&. )he founder of analytical algebra was __________.

    1'. )he author of Alshhifa was __________.

    2(. A high precision de!ice for measuring the time with tremendously large

    accuracyis the __________.

    21. __________ is the unit of thermodynamic temperature.

    22. Ampere is the unit of __________.

    23. __________ is the amount of substance of a system which contain as

    many elementary entities as there are atom in (.(12#g of carbon 12.

    24. )he word dimension is used to denote the __________ of a physical

    8uantity.

    2. )he dimension of area is __________.

    2$. )he dimension of linear !elocity is __________.

    2%. )he dimension of acceleration is __________.

    2&. )he dimension of tor8ue is __________.

    2'. 6imension of uni!ersal gra!itational constant 9G: is __________.

    3(. A number 4.%1 contained __________ significant figures.

    31. ome concepts of static electricity were introduced by __________.

    32. 7lectromagnetic wa!e theory was proposed by __________.

    33. )he name of a#istani physicist renowned all o!er the world for his

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    nuclear research is __________.

    34. )he dimension of force is __________.

    3. ;el!in the unit of thermodynamic temperature is 1ectors

    1. A physical 8uantity, which can be completely specified by its magnitude only, is

    called __________.

    2. A physical 8uantity, which can be completely described by its magnitude and

    direction, is called __________.

    3. 6isplacement is a __________ 8uantity.

    4. ower is a __________ 8uantity.. )wo !ectors are __________ when they ha!e same magnitude and same direction.

    $. )he magnitude of !ector will always be __________.

    %. *n parallelogram law of !ector additionthe resultant of two !ectors is represented

    by __________ of the parallelogram.

    &. ?ormally law of cosine is used to determine the __________ of the resultant

    !ector.

    '. Law of __________ is normally used to determine the direction of resultant

    !ector.

    1(. )he magnitude of __________ will always be e8ual to unity.

    11. )he rectangular unit !ectors are mutually __________ to each other.

    12. )he dot product of two !ectors is a __________.

    13. )he __________ product of two !ectors is a !ector.

    14. )he scalar product can be defined as that it is the product of magnitude of two

    !ectors and __________ of the angle between them.

    1. )he !ector product can be defined as that it is the product of the magnitude of

    two !ectors and __________ of the angle between them.

    1$. )he dot product will not obey the __________ law for !ector multiplication.1%. )he crossproduct will not obey the __________ law for the !ector

    multiplication.

    1&. A !ector, which can be displaced parallel to itself and applied at any point, is

    called __________ !ector.

    1'. ?ull !ector can be obtained by __________ a !ector with its negati!e !ector.

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    2(. @ero !ectors ha!e __________ particular direction.

    21. *f two !ectors are __________ to each other then their dot product is =ero.

    22. *f two !ectors are parallel to each other then their __________ product is

    =ero.

    23. *f , then the magnitude of either of the two !ector is __________.24. )he direction of resultant !ector in a !ector product can be determined by the

    __________ rule.

    2. )he magnitude of the resultant of two !ectors can be __________ than the sum

    of the magnitudes of indi!idual !ectors.

    2$. )he magnitude of __________ !ector will always be =ero.

    2%. __________.

    2&. __________.

    2'. )or8ue is the __________ product of force and force arm.

    3(. __________ is the dot product of force and !elocity.

    31. A !ector, in any gi!en direction whose magnitude is one is called __________.

    32. )he set of unit !ectors along ", y and = a"es are called __________ unit

    !ectors.

    33. *f the magnitude of the resultant of two !ectors e8ual in magnitude is the same,

    then the angle between the two !ectors is __________.

    34. *f __________.

    3. )wo forces, one of $? and the other of &?, act on a point at angle '( with

    each other, the magnitude of resultant force is __________.

    +hapter 3 0otion

    1. )he change of position of a body in a particular direction is called its__________.2. )he change of displacement of a body with respect to time is called its

    __________.3. )he rate of change of position in a particular direction is called the

    __________ of the body.4. )he total change in displacement di!ided by the total change in time of abody is called its __________.. )he acceleration of a body is uniform when a!erage and instantaneous!alues of the acceleration are __________.$. *f the body mo!es towards earth, neglecting air resistance and smallchanges in acceleration with altitude. )his body is referred to as free falling

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    body and its motion is called __________.%. __________ is an agent which changes or tends to change the state of thebody.&. __________ is the property of the matter due to which it will try to

    remain in the same state.'. /hen a constant force is applied on a body then it will start to mo!e withconstant __________.1(. 0ass of the body is the measure of __________.11. )ension in string is a __________which will be produced in it whene!er itis sub-ected to pull.12. )he 8uantity of motion produced in a body is called its __________.13. )he momentum of a body is defined as the product of mass and

    __________ of the body.

    14. A system in which the particles of the system may e"ert some force oneupon the other because of their collision but no e"ternal force can be appliedon them is called __________ system of interacting bodies.1. )he collision between the two bodies is the __________ if totalmomentum as well as the #inetic energy of the system remain the same.1$. *n inelastic collision the #inetic energy of the system will __________conser!ed.1%. *f a massi!e body will collide elastically with a lighter body at rest thenthe lighter body will start to mo!e with a !elocity e8ual to __________ firstbody.1&. )he force, which opposes the motion of body on a surface, is called

    __________.1'. )he friction is due to the __________ of the material of the surfaces incontract.2(. )he force of friction always acts __________ to the surfaces in contact.

    21. )he direction of the friction will always be __________ to the directionof motion.22. )he friction within a fluid is called its __________.

    23. )he friction is said to be __________ when the body slides o!er theother.24. liding friction is __________ than the rolling friction.2. )he ratio of limiting friction to the normal reaction acting between twosurfaces in contact is called __________.2$. *n bicycles the sliding friction is replaced by __________.

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    2%. On frictionless inclined plane the acceleration of the body is __________of its mass.2&. On frictionless inclined plane where a B gsin8 if 8 B '( then a B

    __________.

    2'. On an inclined plane the Cwcos8D will always be e8ual to __________.3(. According to the second law of motion a!erage force applied on the bodyis e8ual to its rate of change of __________.31. __________ friction arises when one solid ob-ect is set into motion acrossthe surface of another solid body.32. __________ friction results when a solid ob-ect mo!es through fluid.33. 1 newton B __________ dynes.34. )he acceleration produced in the body if the applied force is e8ual to theweight of the body is __________.

    3. )he law of conser!ation of momentum is e8ui!alent to the ?ewtonDs__________ law of motion.3$. )he motion of -et plane and roc#et are based on conser!ation of

    __________.3%. /hen the friction between the surface of an inclined plane and a body onit is e8ual to the component of the weight of the body __________ to theplane, then the body remains at rest on the inclined plane.3&. )he acceleration of body on a smooth inclined plane is ma"imum when theplane is ma#ing an angle of __________ with the hori=ontal.3'. )he terminal !elocity of a spherical body in fluid is in!ersely proportionalto the __________ of the body.4(. *n fluid the acceleration of spherical body becomes =ero when the forceof gra!ity is e8ual to the __________ force offered by the fluid

    +hapter 4 0otion in )wo 6imensions

    1. )he motion of the ob-ect along a straight line is called __________.

    2. )he motion of the ob-ect along a cur!ed path is called __________.

    3. ro-ectile motion is the e"ample of the motion of the body in __________dimension.

    4. *n pro-ectile motion the ob-ect is purely under the influence of __________.

    . *n pro-ectile motion the acceleration due to gra!ity 9g: will always be ta#en as

    __________.

    $. 6uring the pro-ectile motion the hori=ontal component of its !elocity will

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    __________.

    %. 6uring the pro-ectile motion the !ertical component of its !elocity is always

    __________.

    &. )he path of the pro-ectile is a __________ path.

    '. 6uring pro-ectile motion the acceleration along hori=ontal direction is __________.

    1(. *n pro-ectile the acceleration along !ertical is always __________

    11. *n pro-ectile the acceleration along !ertical direction is e8ual to the

    __________.

    12. )he e"pression for the time to reach the ma"imum height of the pro-ectile is

    __________.

    13. )he e"pression for the __________ is 2>osin8

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    from one point to another on its circumference is called angular __________.

    2'. )he unit of angular shift is __________.

    3(. )he angular shift per unit time of the particle is called its angular __________.

    31. )he direction of angular !elocity can be determined by __________ rule.

    32. )he unit of angular !elocity is __________.33. *f a particle co!ers e8ual angular displacement in e8ual inter!als of time then its

    angular !elocity is __________.

    34. )he rate of change of __________ is called angular acceleration.

    3. )he !elocity of the particle tangent to its circular path is called __________.

    3$. *n circular motion the time period and angular !elocity of a particle are

    __________ proportional to each other.

    3%. *f a particle is mo!ing with constant speed along the circumference of a circle

    then the acceleration produced in it is called __________.

    3&. )he direction of centripetal acceleration will always be towards the __________

    of the circle.

    3'. +entripetal force is also called __________ force.

    4(. )he tangential component of acceleration arises when the speed of the particle is

    __________.

    41. *n circular motion the centripetal component of acceleration arises when the

    __________ is changed.

    42. +entripetal and tangential acceleration are always __________ to each other.

    43. /hen an ob-ect mo!es around the circular trac#, the centripetal force is

    pro!ided by __________ force.

    +hapter )or8ue, Angular 0omentum and 78uilibrium

    1. A body is said to be in e8uilibrium if it is at rest or is mo!ing with __________

    !elocity.

    2. *f a body is mo!ing with uniform !elocity then the body is said to be in

    __________ e8uilibrium.

    3. or the transnational e8uilibrium the net force acting on the body must be

    __________.

    4. or the rotational e8uilibrium, the net tor8ue acting on the body must be

    __________.

    . )he body is said to be in complete e8uilibrium if __________ acceleration as well

    as angular __________ is =ero.

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    $. According to the first condition of e8uilibrium the algebraic sum of all the forces

    acting on a body must be e8ual to __________.

    %. *f the algebraic sum of all tor8ue acting on a body is e8ual to =ero then the body

    will be in __________ e8uilibrium.

    &. )he magnitude of tor8ue is e8ual to the product of magnitude of force and its__________.

    '. )he unit of tor8ue is * system is __________.

    1(. )he !ector product of force and displacement is #nown as __________.

    11. )he cloc#wise tor8ue is ta#en as __________ tor8ue.

    12. *f the lines of action of the two forces acting on the body are not same then

    the body will be in __________ e8uilibrium.

    13. )he physical 8uantity, which tends to rotate a body, is called __________.

    14. )he angular momentum of a body is conser!ed if the net __________ on it is

    =ero.

    1. )he force which cannot be replaced by a single e8ui!alent force are said to form

    a __________.

    1$. __________ is defined as the time rate of change of angular momentum.

    1%. *n the system international the units of angular momentum are __________.

    1&. )he angular momentum of an isolated system is __________.

    1'. A body is said to be in __________ e8uilibrium, if the net force on it is =ero.

    2(. *f the net tor8ue on a body is =ero then the body is said to be __________

    e8uilibrium.

    21. A __________ body is that in which different particles always maintain the same

    position relati!e to each other, whether the body is at rest or in motion.

    22. *n rotational motion, different particles of the body perform circular motion and

    the centers of all these circular orbits lie along a straight line called the

    __________.

    23. *f a rigid body rotates with a constant angular !elocity w, then different

    particles of the body perform uniform circular motion with the __________ angular

    !elocity but __________ linear !elocities.

    24. )he moment of inertia of a rigid body about a gi!en a"is of rotation is e8ual tothe sum of the products of the mass of each particle of the body and the s8uare of

    its __________ from the gi!en a"is.

    2. )he __________ of a rigid body about a gi!en a"is of rotation is gi!en by * B

    mr2 where CmD is the mass of any particle of the body situated at a distance CrD

    from the a"is.

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    2$. )he angular momentum of a particle is defined as the __________ product of

    the position !ector and the linear momentum of the particle.

    2%. )he angular momentum L of a particle is gi!en in terms of m, !, r and 8 as L B

    __________.

    2&. )he direction of the angular momentum of a particle lies along the __________to the plane formed by the !ectors and .

    2'. )he angular momentum of a particle can be e"pressed in the determinant form as

    B __________.

    3(. )he direction of the angular momentum of a particle mo!ing with !elocity ! in a

    circular orbit of radius r is __________ to the direction of the angular !elocity w

    which lies along the a"is of rotation.

    31. )he centre of gra!ity of uniform circular hoop is at the __________ of the

    hoop.

    32. )he angular momentum is associated with __________ motion.

    33. )he total angular momentum is associated with __________ motion.

    34. )he total angular momentum of a system of particles is __________ if the net

    e"ternal tor8ue acting on the system is =ero..

    3. )he time rate of charge of angular momentum of a body is e8ual to the

    __________.

    +hapter $ Gra!itation

    1. According to the law of gra!itation, e!ery body in the uni!erse attractse!ery other body with a force that is directly proportional to the

    __________ and in!ersely proportional to the s8uare of the distance betweentheir centres.2. *f the distance between two bodies is doubled, the gra!itational forcebetween them decreases to __________ of its former !alue.3. *f the distance between two bodies is hal!ed, the force of attractionbetween them increases to __________ its former !alue.4. )he acceleration due to gra!ity is in!ersely proportional to the

    __________ of the distance from centre of earth.. )he force of attraction, which the earth e"erts on a body, is called

    __________.$. pring balance is used to determine __________ of a body.%. )he point of body at which whole weight of the body seems to act is called

    __________.&. *f the force acting on a body is e8ual to its weight then the acceleration

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    produced in the body is e8ual to __________.'. )he centre of gra!ity of a body of rectangular shape is the point where its

    __________ intersect each other.1(. __________ is the centre of solar system.

    11. )he distance from the centre of the earth to the centre of the moon iscalled __________.12. )he time ta#en by the earth to complete one re!olution around the sun is

    __________.13. )he direction of weight is always toward the centre of the __________.14. ?ewton made the hypothesis that e!ery body in the uni!erse __________the other body.1. )he moon is freely falling to __________.1$. )he time ta#en by the moon to complete one re!olution around the earth

    is __________.1%. )he acceleration of the moon is __________.1&. )he moonDs orbit is about __________.1'. Acceleration due to gra!ity decreases at __________ rate for a pointabo!e the surface of earth then for the same point below the surface of theearth.2(. /eight of a body is a __________ 8uantity.21. )he __________ is responsible for the motion of the planets around thesun.22. Artificial gra!ity is produced in a satellite by spinning its own

    __________.23. )he !alue of CgD is in!ersely proportional to the __________ of the radiusof the earth.24. *f the mass of earth becomes four times then the !alue of CgD will be

    __________.2. )he acceleration due to gra!ity on moon is __________ the accelerationdue to gra!ity on the surface of the earth.2$. Acceleration due to gra!ity at the centre of the earth is __________.2%. )he weight of a body at the pole is __________ than at e8uator.2&. )he gra!itational pull at e8uator is __________ than at poles.2'. )he force re8uired to pre!ent a body from falling or accelerating in aframe of reference is called the __________ of the body.3(. An astronaut in a satellite orbiting around the earth e"periences a stateof __________ because the satellite orbiting with a centripetal acceleratione8ual to CgD.

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    31. Artificial gra!ity is produced in the satellite to o!ercome the __________in the satellite.32. Artificial gra!ity is produced in the satellite by __________ it about itsown a"is.

    33. )he !alue of the a!erage density of the earth is __________ #g

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    13. )he unit of energy of elementary particles and atoms is __________.

    14. )he energy possessed by a body by the !irtue of its motion is called the

    __________ energy.

    1. )he potential energy of a body is due to its change of __________.

    1$. )he wor# done against the gra!itation field is always __________.

    1%. )he law of conser!ation of energy states that __________ can neither be

    created nor destroyed but it can changed its form.

    1&. )he rate of change of momentum multiplied by displacement is called

    __________.

    1'. /or# done in the gra!itation field is __________ of the path followed.

    2(. /or# done in the gra!itation field along a closed path is e8ual to __________.

    21. )he source of tidal energy is the rotation of the earth around the __________.

    22. )he source of geothermal energy is the __________ in the earthDs interior.

    23. )he source of nuclear energy is __________ in hea!y nucleus.

    24. 7instein mass energy e8uation is 7 B __________.

    2. )he unit of energy is the same as the unit of __________.

    2$. )he dimensions of wor# are __________.

    2%. 0L2)3 are the dimensions of __________.

    2&. )he rate of e"penditure of energy is called __________.

    2'. )he amount of wor# done in lifting a body from the surface of the earth to the

    =ero point is called __________ energy.

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    3(. One horsepower is e8ual to __________ watt.

    31. One horsepower is e8ual to __________ ft.lb

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    temperature.

    24. )he particleDs !elocity at antinodes in standing wa!e is __________.

    2. )he pitche of a sound note depends upon its __________ of !ibration.

    2$. H B Aosin #" 9coswt: represents the e8uation of a __________ wa!e.

    2%. Another term used for 8uality of sound is __________.

    2&. )he characteristic by which one sound can be distinguished from other is

    #nown as __________.

    2'. )he sound absorbing soft porous materials are used in big hall is order to

    ha!e good __________.

    3(. Iadar is an abbre!iation of __________.

    31. *n standing wa!es the distance between two __________ nodes or

    antinodes is e8ual to one wa!elength.

    32. *n standing wa!es the distance between one node and nearest antinode ise8ual to __________ wa!elength.

    33. *n standing wa!es the particles !elocity at the nodal point is __________.

    34. )he !elocity of sound wa!es in !acuum is __________.

    3. /hen sound wa!es tra!el through any gas the phenomena is __________.

    +hapter ' /a!e Aspect of Light

    1. ?ewton supported __________ theory of light.

    2. __________ suggested wa!e theory of light.

    3. __________ formulated electromagnetic theory.

    4. hoton is a __________ of light.

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    . /a!e theory predicts __________ !elocity of light in material medium then

    !acuum.

    $. )he first clear demonstration that light is a wa!e phenomenon was made by

    __________.

    %. )he electromagnetic radiation ha!ing wa!elength between 4(((A and %(((A arecalled __________.

    &. )he electromagnetic radiation of wa!elength more than %(((A are #nown as

    __________.

    '. hotoelectric effect and +ompton effect supported the __________ theory of

    light.

    1(. *nterference of light can be e"plained on the basis of __________ theory of

    light.

    11. )he locus of all points, which are in same state of !ibration, is called

    __________.

    12. )he points of constructi!e interference are always of __________ intensity.

    13. )he points of destructi!e interference are of __________ intensity.

    14. A small portion of a spherical wa!e front, at a large distance from the source

    becomes almost.

    1. )he shape of wa!e front at a !ery small distance from the source of light is

    __________.

    1$. or points of constructi!e interference the path difference between two

    interfering wa!e is =ero of __________ of the wa!elength.

    1%. or the points of __________ interference the path difference between two

    interfering wa!es is odd multiple of half wa!elength.

    1&. *f we decrease the distance between slits and screen, in HoungDs 7"periment,

    fringe spacing will __________.

    1'. *f we decrease the separation between the slits in HoungDs 7"periment the fringe

    will __________.

    2(. *n HoungDs 7"periment the fringes are e8ually __________.

    21. *n HoungDs e"periment the __________ fringe is always bright.

    22. A glass plate on which e8ually spaced lines are ruled is #nown as __________.23. )he distance between two consecuti!e slits of diffraction during grating is #nown

    as __________.

    24. )o obtain ?ewtonDs Iings a __________ lens of __________ focal length is

    re8uired.

    2. ?ewtonDs rings are formed due to the phenomena of __________ interference.

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    2$. *n __________ the central ring may be bright or dar#.

    2%. *n thin film interference for destructi!e interference between two interfering

    wa!es be __________ or __________ of wa!elength.

    2&. *n HoungDs 7"periment two narrow sites are used to obtain __________.

    2'. *n 0ichlsonDs interferometer the purpose of beam splitter is to obtain__________.

    3(. *n thin film interference phase coherence is obtained by reflecting the light from

    __________ and __________ surface of the air film.

    31. ?ewtonDs rings are formed due to __________ film formed between con!e"

    surface and plane glass sheet.

    32. )he speed of Jrays is __________ to the speed of light.

    33. __________ is a special type of interference.

    34. )he phenomenon of polari=ation confirms the __________ of light.

    3. Jray diffraction can be obser!ed when they are made incident on __________.

    3$. *n case of HoungDs 7"periment the distance between two consecuti!e bright or

    dar# fringes is #nown as __________.

    3%. )he bending of light around an obstacle or sharp edge is called __________.

    3&. )he phenomenon of polari=ation can be used to chec# __________ of optically

    acti!e substances in a solution.

    3'. )he points at which two sources cancel each other effects are #nown as points

    __________ interference.

    4(. *f l is the wa!elength of light in a medium of refracti!e inde" n then wa!elength

    of light in air l is e8ual to __________