TEST-05(Solution) TOPIC: OPTICS COMPLETE

Transcription

1 Q. boy is walking uner an incline mirror at a constant velocity V m/s along the x-axis as shown in figure. If the mirror is incline at an angle with the horizontal then what is the velocity of the image? Y () V sin i + V cos j () V cos i + V sin j V () V sin i + V cos j V cos i + V sin j [D] Q. telescope has focal length of objective an eyepiece as 00 cm an 5 cm respectively. What is the value of magnifying power? () 40 () 80 () 50.0 f0 00 [] MP 40 f 5 e Q.3 plane mirror is Incline at an angle 30 with the horizontal surface. particle P is projecte with velocity V 0 m/s as shown in figure. Time when the image will come momentarily at rest w.r.t. to the particle TEST-05(Solution) TPI: PTIS MPLETE X length of telescope is.m. The magnification when image is forme at least istance of istinct vision (D 5 cm) is - () 4 () 6 () 6 8 f 0 [] 0 f f 0 + f e e. f 0 m 00 cm & f e 0. m 0 cm Now; When final image is at D MP f 0 D f e Q.5 telescope of objective lens iameter m uses light of wavelength 5000 Å for viewing stars. The imum angular separation between two stars whose image is just resolve by telescope- () ra () ra () ra ra [] a ra ra. Q.6 n astronomical telescope has a converging eyepiece of focal lengths 5 cm an objective of focal lengths 80 cm. When the final image is forme at the least istance of istinct vision (5 cm), the separation between the two lenses is- () 75.0 cm () 80.0 cm () 8.. cm 85.0 cm fed 5 5 [] l f o t S o t f D 5 5 e P V () 3 () () 3 [D] Q.4 The magnification prouce by an astronomical telescope for normal ajustment is 0 an the 5 S o t cm 30 Q.7 The magnification prouce by an astronomical telescope for normal ajustment is 0 an the length of telescope is.m. The magnification when image is forme at least istance of istinct vision is - () 4 () 6 () 6 8 [] 0 f o / f e L f o + f e 0 cm f o 00 cm & f e 0 cm Page of 9

2 MP f o D MP 4 f e Q.8 In a microscope the focal lengths of two lenses are.5 cm an 6.5 cm. If an object is place at cm from objective an final image is forme at 5 cm from eye lens, the istance between two lenses is - () 6 cm () 7.75 cm () 9.5 cm cm [D] For objective lens v 0 6cm.5 v0 For eye lens : u e u e 5cm L v 0 + u e cm Q.9 Magnification of a compoun microscope is 30. Focal length of eye - piece is 5 cm an image is forme at a istance of 5 cm from eye - piece. The magnification of objective lens is - () 6 () 5 () [] MP m o m e D m e f e 30 m o 6 m o 5 Q.0 The mirror of length makes 0 revolutions per ute about the axis crossing its mi point an perpenicular to the plane of the figure There is a light source in point an an observer at point of the circle of raius rawn aroun centre ( 90º) What is the proportion if the observer first sees the light source when the angle of mirror 5º? () () [] I 30º 5º 45º Sine rule sin 45º 5 0º sin 30º 30 () 30º sin 45º ; sin 30º Q. Two plane mirror which are perpenicular are forg two sies of a vessel fille with liqui of refractive inex.5. fter all possible refraction an reflection, fin the eviation () in ray () 0º () 80º () 90º 30º.5 90º we can't fin out eviation as other two angles an in figure is not given [] Page of 9

3 S 3 45º 3 90º º 35º º 80º 3 45º º 45º º 4 45º + 90º º 80º 45º º 80º 5 80º 6 (y snell law) Q. If an object moves towars a plane mirror with a spee v at an angle to the perpenicular to the plane of the mirror, fin the relative velocity between the object an the image - y I [] () () () So rea S ( ) 3 [ 3 ] 3 Q.4 boy of mass 00g is tie to one en of spring of constant 0 N/m. The istance between pole of mirror an mean position of the boy is 0cm. The focal length of convex mirror is 0cm. ne of the amplitues of vibration of the image is - v 0 v () v () v () v cos v sin [] nly normal component of plane mirror will be change, it becomes reverse so, relative velocity of image w.r.t. object v cos Q.3 n opaque sphere of raius lies on a horizontal plane. n the perpenicular through the point of contact there is a point source of light at a istance above the sphere. The area of the shaow on the plane is x () 0 cm 0cm f 0cm () 50 cm () 0.67 cm 0.33 cm [] Kx mg mg 0.0 x 5 cm, K 0 0 pply v u f Q.5 concave mirror is place on a horizontal table with its axis irecte vertically upwars. Let be the pole of the mirror an its centre of Page 3 of 9

4 curvature. point object is place at. It has a real image, also locate at. If the mirror is now fille with water, the image will be- () eal an will remain at () eal an locate at a point between an () Virtual an locate at a point between an eal an locate at a point between an [D] Part PQ transverse magnification f length of image L L 0 f u 5 L L ( 0) 3 For part Q : longituinal magnification f L length of image L L 0 0 f u 9 L 3 So L Q.7 real inverte image in a concave mirror is represente by: (u, v, f are coorinates) v/f () + + u/f () + Initially Final () v/f + u/f v/f + u/f From the above figure it is clear that real image (I) will be forme between an. Q.6 small piece of wire bent into an L shape with upright an horizontal portions of equal lengths, is place with the horizontal portion along the axis of the concave mirror whose raius of curvature is 0 cm. If the ben is 0 cm from the pole of the mirror, then the ratio of the lengths of the images of the upright an horizontal portions of the wire is - () : () 3 : () : 3 : 0 [] Focal length of mirror f 5 cm Q P 0 cm 0 cm [] Q.8 n object is place infront of a convex mirror at a istance of 50 cm. plane mirror is introuce covering the lower half of the convex mirror. If the istance between the object an plane mirror is 30 cm, it is foun that there is no parallax between the images forme by two mirrors. aius of curvature of mirror will be - 50 ().5 cm() 5 cm () cm 8 cm 3 [] ccoring to property of plane mirror it will form image at a istance of 30 cm behin it bject 30 cm 0 cm 50 cm 0 cm Hence for convex mirror u 50 cm v + 0 cm f v u f f cm f 5 cm Page 4 of 9

5 Q.9 slab of glass, of thickness 6 cm an refractive inex.5, is place in front of a concave mirror, the faces of the slab being perpenicular to the principal axis of the mirror. If the raius of curvature of the mirror is 40 cm an the reflecte image coincies with the object, then the istance of the object from the mirror is - () 30 cm () 4 cm [] x () cm 8 cm t 6 cm, Distance. 5 of object from concave mirror cm x 40cm Q.0 glass ro of rectangular cross-section is bent into the shape shows in the Fig. (a). parallel beam of light falls perpenicularly on the flat surface. Detere the imum value of the ratio / for which all light entering the glass through surface will emerge from the glass through surface. The inex of refraction of the glass is.5. Fig. (a) () () 4 () 5 7 [] onsier the representative rays shown in Fig. (b). ray entering the glass through surface an passing along the inner sie of the ro will be reflecte by the outer sie with the smallest angle, at which the reflecte ray is tangent to the inner sie. We have to consier the conitions uner which the ray will unergo total internal reflection before reaching. Fig. (b) If > c, the critical angle, at which total internal reflection occurs, all the incient beam will emerge through the surface. Hence we require sin > n. The geometry gives sin. ( ) Therefore or, n n.5. Q. Two transparent slabs are of equal length. ne is mae of a material of.i..5 an the other of materials an, the ratio of thickness being :. The.I. of is.6. When light passes through them, the two slabs have the same number of waves. The.I. of is ().4 ().3 ()..05 [] Q. ray of light travels from a meium of refractive inex to air. Its angle of incience in the meium is i, measure from the normal to the bounary, an its angle of eviation is. is plotte against i which of the following best represents the resulting curve - () / i () / i Page 5 of 9

6 [] () / i / i Q.3 ritical angle for light going from meium (i) to (ii) is. The spee of light in meium (i) is v, then spee in meium (ii) is - () v ( cos ) () v / sin () v / cos v ( sin ) [] v v sin v v v sin v sin Q. 4 prism of refractive inex an angle is place in the imum eviation position. If the angle of imum eviation is, then the value of in terms of is - () sin () cos () sin cos sin m [] sin, m sin sin sin / cos / cos (/) Q.5 Light is incient normally on face of a prism as shown in figure. liqui of refractive inex is place on face of the prism. The prism is mae of glass of refractive inex 3/. The limits of for which total internal reflection takes place on face is : Liqui 30º 30º 90º () > 3 () < () > 3 < 3 [] Q.6 prism having an apex angle 4º an refractive inex.5 is locate in front of a vertical plane mirror as shown in figure. Through what total angle is the ray eviate after reflection from mirror [] 4º () 76º () 4 () 78º º º º º prism ( ) (.5 ) 4 tatal prism + mirror º + (80 i) º + (80 ) 78º Q.7 given ray of light suffers imum eviation in an equilateral prism P. itional prisms Q an of ientical shape an material are now ae to P, as shown in the figure. The ray will suffer - P Q () greater eviation () same eviation (3) no eviation (4) total internal reflection [] Q.8 spherical surface of raius separates two meium of refractive inices an, as shown in Fig. Where an object shoul be place in the meium so that a real image is forme in meium at the same istance? Page 6 of 9

7 /////////////// /// () () P I x x () [] Q.9 convex lens of focal length 0 cm is cut into two equal parts so as to obtain two plano-convex lenses as shown in fig. (). The two parts are then put in contact as shown in fig.(). What is the focal length of combination () () () () zero () 5 cm () 0 cm 0 cm [D] Q.30 Focal length of the shown plano-convex lens is 5 cm. Plane surface of the lens is silvere. n object is kept on the principal axis of the lens at a istance 0 cm. Image of the object will form at. [IIT-JEE 006] bject 0cm () 60 cm, left () 60 cm, right () cm, left 30 cm, right [] Q.3 The relation between n an n if the behaviour of light ray is as shown in the fig. is - Q.3 iverging lens, focal length f 0 cm is separate by 5 cm from a converging mirror, focal length f 0 cm. Where shoul an object be place from the lens so that a real image is forme at the object itself? () 30 cm () 60 cm () 0 cm 40 cm [] I f 0 f 0 5 f 0 For lens f 0, u?, v (0 5) u u 0 5 u 60 Q.33 The iagram shows a concavo-convex lens. What is the conition on the refractive inices so that the lens is iverging. 3 I of lens is () 3 < + () 3 > + () 3 > ( ) None of these [] Q.34 convex lens is mae up of three ifferent materials as shown in the figure. For a point object place on its axis, the number of images forme are - n n Lens () n > n () n >> n () n > n n n [] Page 7 of 9

8 () () 3 (3) 4 (4) 5 Q.35 Interference fringes were prouce in Young's ouble slit experiment using light of wavelength 5000 Å. When film of thickness cm was place over one slit, the fringe pattern shifts by a istance equal to 0 fringe with. The refractive inex of film material is - ().5 ().33 ().4.5 [] D ( ) t 0D t Q.36 In YDSE if a slab whose refractive inex can be varie is place in front of one of the slits. Then the variation of resultant intensity at mi point of screen with will be best represente by ( is greater than or equal to ) () () I 0 I 0 () I 0 I 0 [] Q.37 n unpolarise beam of intensity I 0 is incient on a pair of nicol prisms making an angle of 60º with each other. The intensity of light emerging from the pair is - I () I 0 () 0 I () 0 I [D] Intensity of light emerging from I st prism I 0 / an intensity of light emerging from secon prism is I 0 I cos 60º 0. 8 Q.38 Two sources give interference pattern which is observe on a screen, D istance apart from the sources. The fringe with is. If the istance D is now ouble, then the fringe with will become - Sol () () 4 D [] Fringe with fringe with D. () remains same If D is now ouble ; then fringe with also oubles. Q.39 In an interference experiment, thir bright fringe is obtaine on the screen with a light of 700 nm. What shoul be the wavelength of light source in orer to obtain 5 th bright fringe at the same point - () 40 nm () 500 nm () 750 nm 630 nm Sol [] 3D 5D' 3 5' ' nm 40 nm 5 5 Q.40 In young's ouble slit experiment, a coherent parallel stream of electrons, accelerate by a potential ifference V 45.5 volt is use to obtain interference pattern. If slits are separate by a istance 66.3 m an istance of screen is D 09. cm from plane of slits, calculate istance between two consecutive maxima on the screen : [mass of electron kg Plank constant h J-s] () 6 m () m () 9 m 3 m [D] mv ev v ev m h h mv mev D hd m 3 m mev Page 8 of 9

9 Q.4 Fringe with observe in the Young's ouble slit Sol experiment is. If the frequency of the source is ouble, the fringe with will () remain () become / () become remain 3/ [] With of fringe if frequency is ouble then, wavelength becomes halve, because velocity of light in air remain same / Q.4 In Young's experiment, the ratio of maximum an imum intensities in the fringe system is 9 :. The ratio of amplitues of coherent sources is () 9 : () 3 : () : : [] Imax 9 (a a ) a a 3 I (a a ) a a a 3 a 3 Q.43 When unpolarise light beam is incient from air onto glass at polarising angle - () eflecte light is polarise 00 percent () eflecte & refracte beams are partially polarize () eflecte & refracte beams are completely I 0 I I Q.45 The maximum number of possible interference Sol maxima for slit-separation equal to twice the wavelength in Young's ouble-slit experiment is () three () five () infinite zero [] Path ifference sin sin Maximum path ifference max So path ifference for maxima,,0,, polarise efracte light is polarise 00 percent Sol [] Q.44 If the intensities of the two interfering beams in Young's ouble slit experiment be I an I, then the contrast between the maximum an imum intensity is goo when () I is much greater than I () I is much smaller than I () Either I or I is zero I I For goo visibility conition is [D] Page 9 of 9