Geometrical Optics Questions and Answers

Question 14 The refractive index of space changes with y whose f unction is given as 1 if y 0 u y ky if 0 sy s2yo if 2yo sys4yo w 14 The refractive index of space changes with y whose function is given as 1 y ky l if if if y 0 0 y 2yo 2y0 y 4yo where k and are positive constant A light ray is incident at point A as shown in figure When the ray reaches to point B it becomes parallel to xz plane Choose the wrong statement YA B 200 T Yo A a is independent of k C a is independent of both k and l B a is independent of D a is 90 14 The refractive index of space changes with y

In prism theory in general any given value of angle of deviation except i e there corresponds to two values of Zi and Ze i e deviation angle remains same if Zi and Ze are interchanged This statement is 1 True NCERT Pg 331 2 Folos

33 A compound microscope has an eyepiece of focal length 10 cm and an objective of focal length 5 cm If an object is kept at a distance of 6 cm from the objective then magnification of the microscope for the final image at least distance of distinct vision of 25 cm is 1 15 3 22 5 2 17 5 4 25 40 A W re 1 3

22 At what temperature RMS velocity of O molecule will be one third of H molecule at 3 C 1 90 K 2 3 C 4 207 C 3 1167 C 23 A body is projected from surface of earth with a velocity 2V where V is the escape velocity The velocity of object when it escapes from gravitational field of earth is 1 2V 2 3V 3 7V 4 11V 24 If a planet is revolving around the sun in circular orbit with force Fay 5 2 where y is radius then square of period is propotional to 1 7 4 3 72 25 If weight of container along with water is W then reading of weighing machine will be 2 h d 2 7 2 4 2 W Weighing Machine 1 W W 3 W W 26 A cubical container is completely filled with water with its top face open to atmosphere If container is accelerated horizontally with 5 m s2 then find the volume of water spills out edge length of container is 5 m 1 125 m 2 100 m 4 31 25 m 3 10 m 27 A plane mirror is fixed at a heighth above the bottom of a beaker containing water refractive index u upto a height d Find the position of the image of the bottom formed by the mirror 2 W W 4 W W 1 h d behind the mirror d behind the mirror 3 d 4 4 d d h 2 28 There is a small air bubble inside a glass sphere u 1 5 of radius 10 cm The bubble is 4 0 cm below the surface and is viewed normally from outside Find the apparent depth of the bubble 1 3 1 cm from the surface Medica IIT 2 2 cm from the surface 3 4 cm from the surface 4 1 cm from the surface 29 What is the value of X for which image of point object O coincides with itself 1 d 1 behind the mirror 1 3 cm 2 4 cm 4 6 cm 3 5 cm 30 A thin lens is made with a material having refractive index u 1 5 Both the sides are convex It is dipped in water u 1 33 It will behave like 1 A convergent lens 2 A divergent lens 3 A rectangular slab 4 A prism 31 The magnetic field at the origin due to a current element Id placed at a position 7 is 3 15 cm Hol dixr 43 behind the mirror undation Holrxdi 4 mg nil f 2mg nil 2 3 32 A square coil of edge length I having n turns carries a current I It is kept on a smooth horizontal plane A uniform magnetic field Bexists in a direction parallel to an edge The total mass of coil is m What should be the minimum value of B for which the coil will start toppling f 12 cm 2 4 Holrxdi 4x H l dixr 4 3 mg 2nll 4mg nll

A plano convex lens made of transparent material having refractive index has a maximum thickness of 1 mm If the 3 diameter of its aperture is 4 cm Its focal length in air in cm is Guadaich and urgeff ug I Affa ys aodada da ufuga da 1 mm 3 Such cm R 2 cm 1 mm AM G GA G

9 During rainy season secondary rainbow is formed when light rays coming from the sun undergo the following through spherical water droplets 1 Refraction internal reflection refraction 2 Refraction internal reflection internal reflection and refraction 3 Three refractions only 4 Refraction internal reflection reflection

2 14 When bichromatic light is incident on a parallel glass slab at some angle both light will come out of slab 1 From one point and parallel to incident ray 2 From two different points and parallel to incident ray 3 From one point and not parallel to incident ray 4 From two points and not parallel to incident ray

In the following questions a statement of Assertion A is followed by a statement of Reason R 1 Both A and R are true and R is the correct explanation of A 2 Both A and R are true but R is not the correct explanation of A 3 A is true but R is false 4 A is false but R is true A The sky appears dark instead of blue from the moon R The size of air molecules on the moon is so small so scattering of sunlight does not take place

an object is placed at a distance of 36c m in front of a concave mirror of focal l ength 12cm At what distance from th e mirror should a screen be placed in o rder to obtain a sharp image What is t he nature if the image

A point object O is placed in a medium of refractive index 1 4 S and S are two concentric spherical surfaces of radii 1m and 2m To the right of O contains a medium of refractive index 1 5 between the interfaces S and S Find the object distance of O form S in meter so that an image of O as seen by observer from air coincides with O 0 14 a S air H P

There are two mediums 1 and 2 with refractive index and A light ray is entering from medium 1 to medium 2 Thickness of medium 2 is t Two light rays A and B are forming interference pattern as shown in figure Then minimum thickness of medium 2 so that rays A and B are forming Then value of B 2 maxima is of the form B cosr will be Where r is angle of refraction for and where is wavelength of light in air 2 14 H B

4 1 cm from the surface 29 What is the value of X for which image of point object O coincides with itself 15 cm 1 3 cm 3 5 cm X f 12 cm 2 4 cm 4 6 cm

22 A hollow double concave lens is made of very thin transparent material It can be filled with air or either of two liquids L and L having refractive indices and respectively 1 The lens will diverge a parallel beam of light if it is filled with a air and placed in air b air and immersed in L c L and immersed in L d L and immersed in L IIT 20001

i guess this solution is wrong because we c an use this formula which is used in the foll owing solution of shift only when object an d observer are in same medium and in this question we are given that only observer an d slab are dipped in water that means objec t is in air only am i right An object is seen through a glass slab of thickness 35 cm and refractive index 3 2 The observer and the slab are dipped in water 4 3 The shift produced in the position of the object is OPTIONS O O A B 12 cm 4 cm Solution Here the observer is not in air the surroundings for slab is water Thus shift produced for object position 14 S S 36 1 or S 36 3 S 36 3 28 36 cm 100 36 4 cm

7 In the adjoining figure the object O is viewe from the top of the hemisphere If the observe 10 vertical shift is then the refractive index of th 3 glass is 1 1 2 3 1 5 10 cm 3 2 1 3 4 2 0

Two equi convex lenses of focal lengths 20 cm and 30 cm respectively are placed at a separation d with their principal axes coinciding An object placed at a distance u from the first lens forms an image at a distance v from the second lens Find the ratio V if it is observed that u and v have U r the same set of values for d 30 cm 60 cm 120 cm and 150 cm 1 2 B 2 3 Your Answer 2

1 4s 2 65 4 38 The distance traveled by a ray of light in two media in the same time are in the ratio 2 3 Refractive index of first medium with respect second medium is 1 3 2 2 2 3 3 4 9 4 9 8 A ray of light is incident on the surface of a medium at an angle 450 and is

A ray of light is incident on the surface of a medium at an angle 450 and is refracted in the medium at an angle 30 What is the velocity of light in the medium 1 1 96x10 ms 2 2 12X10 ms 1 3 3 18X10 ms 4 3 33X10 ms 1 The speed of light in glass of refractive index 1 5 is 2X105 ms In a certain liquid the speed of light is 2 5 X10 ms 1 The refractive index of the liquid is

View in English A prism of a certain angle deviates the red and blue rays by 8 and 12 respectively Another prism of the same angle deviates the red and blue rays by 10 and 14 respective prisms are small angled and made of different materials The dispersive powers of the materials of the prisms are in the ratio 1 4 Correct Answer 3 Status unattempted 5 6 9 11 6 5 11 9

5 31 A ray of light travels in the way as shown in th figure After passing through water the ray graze along the water air interface The value of g terms of i is 1 2 3 sini Glass H 3 water 3 2 4sini 4 Medt

For an equilateral triangular prism ABC placed in air the minimum possible angle of incidence on the face AB such that light ray is refracted from the face AC is 30 Then My yh Agalg Ayuick MH ABC Bad A 49 39a0c uchu a da aa B The refractive index of prism is 7 12 aich The refractive index of prism is 3 aich 7 3 2 Correct Answer Your Answer C The angle of maximum deviation by the prism is 30 30 D The angle of maximum deviation by the prism is 60

The convex surface of a thin concavo convex lens of glass of refractive index 1 5 has a radius of curvature 20 cm and the concave surface has radius of curvature 60 cm The lens is placed on the plane mirror as shown An object O is placed on the principal axis at distance x from the lens such that object O and image coincide After that water is filled in the lens such that the top surface becomes flat I O Then the object is again shifted by Ax such the object and image coincide again If then refractive index of water is 3 1 5 ci ad gada 3d da H 3AA AAG A 20 Ads Scal A60 cm Tefy uzaz anda 749 92 zu ga 1 yc de 2 SA UHR ZU GA fu such as da ga c 38 UHR HR Ga f eff zag anda s ud 1 A c r faz fa sa fc azg ay ufafara ya arudi s i uft va mi 4 3 B C 1 0 D l X x 30 cm nc Ax 10 cm x 60 cm Correct Answer Ax 15 cm Correct Answer

A glass paper weight 1 5 has a small air bubble at O such that CO 6 cm this is seen by an observer at 1 The distance of image from C is H 1 5 O C 9 2 cm 10 cm 13 0 cm 6 9 cm R 10 cm

A prism has the same refractive index as that of a liquid The prism is kept in this liquid The deviation produced by the prism in the liquid is equal to zero The prism will not appear in the liquid The prism will show dispersion O Both 1 2

When a point source of light is placed at a depth h inside a liquid of refractive index then the light rays come out of the surface of the liquid through a circular area only The radius of the circular area depends on Depth h OR I of the liquid Colour of the light All of these

24 The angle of a prism is A One of its refracting surfaces is silvered Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface The refractive index u of the prism is S 1 2sinA 2 2cos A 3 1 2 COSA 4 tanA

3 180 2A 4 180 3A Two identical thin plano convex glass lenses refractive index 1 5 each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre The intervening space is filled with oil of refractive index 1 7 The focal length of the combination is 1 25 cm 2 50 cm 3 50 cm 4 20 cm

A ray of light is incident on a 60 prism at the minimum deviation position The angle of refraction at the first face i e incident face of the prism is 1 30 2 45 3 60 4 Zero

An equiconvex lens is silvered at one of the faces The R I of the material of the lens is 1 5 and its radius of curvature is 8 cm An object O is placed at a distance 10 c from the lens Find the position of the image formed At a distance 2 5 cm from the lens At a distance 0 15 cm from the lens At infinity At a distance 8 cm from the lens

1 A plano convex lens fits exactly into a plano concave lens Their plane surfaces are parallel to each other If lenses are made of different materials of refractive indices P1 and H and R is the radius of curvature of the curved surface of the lenses then the focal length of combination is 1 3 2R H H R 2 11 11 2 4 R 2 R

If the focal length of objective lens is increased then magnifying power of 1 microscope will increase but that of telescope decrease 2 microscope and telescope both will increase 3 microscope and telescope both will decrease 4 microscope will decrease but that of telescope increase

4 The figure shows the modified Fresnel biprism experiment with monochromatic source of wavelength 500 nm The refractive angle of the glass prism is 2 Find the number of bright fringes formed F 32 Water

A sphere of glass is placed symmetrically on x axis A ray parallel to x axis is incident on the sphere at point P and emerges on x axis If angle of refraction at P is 30 for the refractive index of the glass is x Then find x P x axis

A point source is kept on the principle axis of a convex lens of focal length f at a distance 4f from it Behind the lens there is a concave mirror of focal length f There are two positions of mirror such that final image coincides with the point source If the ratio of the distance between lens and mirror for the two cases is n then find the 1 value of n

A monochromatic beam of light is incident at 60 on one face of the normal see the figure for n 3 the value of is 60 and an equilateral prism of refractive index n and emerges from the opposite face making an angle n with de m The value of m is 989 90 dn 60

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60 see figure If the refractive index of the material of the prism is 3 which of the following is are correct chauffa che fu OP ABCD TABR 60u 43 214 B Acht 34faa aa fa t uk fu4 f 3 au had as 3 A B B 60 90 135 75 A The ray gets totally internally reflected at face CD D CD 2 yufa 31 dkg uzaffa s mat 3 Correct Answer Your Answer fach AD The ray comes out through face AD Correct Answer Your Answer C The angle between the incident ray and the emergent ray is 90 ufa fazu a Ara fzu 90 Correct Answer D The angle between the incident ray and the emergent ray is 120

A thin glass slab of thickness t and refractive index is inserted between an object O and an observer both of which are in a medium of refractive index Calculate the shift for the given object H 00 1 4 1 t 3 t 1U H eye 2 1 1 1 2 4 t 1U

A shape of ngled triar and is place of a concave mirror of focal length f as shown in the figure Which of the figures shown in the four options qualitatively represent s the shape of the image of the bent wire These figures are not to scale A B C A 45 A 8 a 45 Apraco 0 a 45

10 The outer surface of a transparent glass slab of refractive index g 1 5 is coated by a thin layer of transparent medium of refractive index c 1 6 Orange light of wavelength 6400 falls normally on the coating The reflected light at the upper surface and at the lower surface of the coat interfere destructively If thickness of the coat is 5K x 10 8 m calculate the minimum value of K ismer

d 14 In young s double slit experiment d distance between slits D distance of screen from the slits At a point P on the screen resulting intensity is equal to the intensity due to individual slit lo Then the distance of point P from the central maximum is 6000 1 2 mm 3 0 5 mm 2 1 mm 4 4 mm 10 4

A ray of light passing through prism having refractive index 2 minimum deviation It is found that angle of incidence is double the angle of refraction within prism Then angle of prism is 60 90 O 120 O 45

A plane mirror is placed at origin parallel to y z plane facing positive x axis An object starts from 2 m 0 0 with a velocity of 21 31 m s The relative velocity of image is O 21 3 ms O 21 3j ms O 41 ms

Fig 10 3 CONCE Box Fig 10 4 7 A beam of light is incident through the holes on side A and emerges out of the holes on the other face of the box as shown in the Figure 10 4 Which of the following could be inside the box a Concave lens b Rectangular glass slab c Prism d Convex lens

A cylindrical rod made of some unknown glass is placed on a ruled white paper of a common exercise book If axis of the rod makes an angle with the ruled lines the lines will appear broken and tilted at some angle a as shown in the figure a Explain this appearance of the ruled lines shown b Find refractive index of the glass assuming the rod not to be thick and lines are being observed from a height vertically above the rod a

Radius of curvature of the concave mirror is 60 cm In front of this a glass slab is situated very close to the mirror as show the figure A point object O lie at a distance of 100 cm from the pole then the position of the image from the pole is 20 cm O 45 cm O 55 cm O 40 cm 60 cm

The students were asked to find the refractive index of the material of the prism if the angle of minimum deviation from prism is 60 and the angle of prism is 30 What will be the refractive index of the material A B 1 78 skipped 7 3 C 2 73

Please solve this une plane mirror and then at the concave mirror Ans 1 125 m M 15 A very thin plane glass plate is put in front of a convex mirror of focal length 0 15 m A point ob is so placed on the principal axis of the mirror that its image formed by reflection at the front surface the plate coincides with that formed by the convex mirror If the distance between the plate and the min be 0 10 m find the distance between the object and the plate 16 A convex mirror of radius of curvature 0 0 Ans 0 20

One thin bi convex lens 2 and on thin bi concave lens u 1 5 are joined to form an optical system a shown in the figure Let the radii of curvature of each surface is R 30 cm D fi A 15 2 If object distance is equal to the image distance then find object distance O 16 cm O 60 cm 40 cm Onone of these

A ray of light of frequency 5 10 4 Hz is passing through a liquid The wavelength of light measured inside liquid is found to be 450 x 10 9 m The refractive index of the liquid is 1 33 O 1 5 O 1 72 O 1 2

In the arrangement shown in figure image of light source O is to be obtained at the bottom of beaker containing water upto height 20 cm Find H f 30 cm 36 cm O 80 cm 85 cm O 75 cm 90 cm H 1m 20 cm