Geometrical Optics Questions and Answers

A transparent plastic bag filled with air forms a concave lens Now if this bag is completely immersed in water then it behaves as a divergent lens c equilateral prism b convergent lens d rectangular slab

Figure 9 34 shows an equiconvex lens of refractive index 1 50 in contact with a liquid layer on top of a plane mirror A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle The distance of the needle from the lens is measured to be 45 0 cm The liquid is removed and the experiment is repeated The new distance is measured to be 30 0 cm What is the refractive index of the liquid 9 P P to be FIGURE 9 34 9

A cylindrical bucket of depth 60 cm is partly filled with a liquid of refractive index 1 5 and with oil on top of liquid of refractive index 2 It appears that the volume of air volume of liquid and volume of oil are equal to an observer who views from top of the bucket The apparent depth of the bucket as seen by the observer is given as a cm Fill 5 in OMR sheet

Two concave mirror of focal length f and f are placed facing each other and d distance apart Find the value of dmin If object is placed between the mirrors that object and image will coincide 1 f f 2 2f 2f 3 f 2f 4 2f f

26 A plano convex lens of focal length 10 cm is silvered at its plane face The distance d at which an object must be placed in order to get it image on itself is in cm n 3 2 d

A convergent beam incident on a concave lens as shown in figure Which of the following statements is not correct The image formed is real The image formed is virtual The image formed is erect The image formed is magnified

The refractive index of a slab of length 2 changes X MO T Mo as x 1 Mo 0 x 1 x 21 where x is measured from left and the equivalen refractive index of the slab would be Borista 1 15 o 7 06749 01 mon de 200 l 2 17 Mo 12

A biconvex thin lens of radius of curvature R is made up of variable refractive index 21 Assume d very small aperture 2d R A point object O is placed at a distance R 7 5 m on the principal axis from the lens as shown Due to variable refractive index of lens there are infinite numbers of image on the principal axis These image are spreaded over the length 1 Find the value of 1 in m R A P RR

The circular boundary of the concave mirror subtends a cone of half angle at its centre of curvature The minimum value of for which any ray incident on this mirror parallel to the principal axis suffers reflection more than once is A

An equilateral triangular prism is made of glas u 1 5 A ray of light is incident normally on on of the faces The angle between the incident ar emergent ray is clos telolv er 1011 1 60 Teoloo ben 2 90 3 120 en 4 180

Two convex lens each of focal length 50 cm and a concave lens of focal length 20 cm are placed in closed contact The power of combination is 50 cm a dd di 20 cm ichu ych wada s Age 44YTH ZUI a A B C 1 D 9 D 1 D

Monochromatic light of wavelength falls normally on a single slit of width b Show that intensities of the first and second secondary maxima are approximately 4 5 of I and 1 62 of Io respectively where Io is initial intensity 3

1 Observe the following diagram carefully and identify the statement that is correct as per this diagram 1 Medium A Medium B i Speed of light in medium A is less than the speed of light in medium B ii The optical density of medium A is more than the optical density of medium B iii The absolute refractive index of medium B is less than the absolute refractive index of medium A iv The absolute refractive index of medium B is higher than the absolute nofrootivo ind

In a plane transmission grating the angle of diffraction for the second order principal maximum for the wavelength 500 nm is 30 The number of lines in two centimeter of the grating surface will be 1000 lines 5000 lines 10 000 lines 500 lines

Two parallel plane mirrors M and M have a length of 20 m each and are 10 cm apart A ray of light is incident on one end of mirror M at an angle of 53 Calculate the number of times the ray undergoes reflections After light emerges out of the system Given tan 53 x d tan53 10 x ution Let it cover a distance x along the mirror after each reflection it emeges out 20 40 3 4 40 3 3 cm 3 x 100 1 150 1 151 530 53 20 m O d 10 cm am M 180 2 1906 iM

A ray is incident at a height h 1 cm on an infinite stack of very thin convex lenses each having thickness 1 cm and focal length 100 cm as shown in figure As a result of this the ray follows a curved path Then which of the options is are correct Assuming ray to be paraxial always h for Rough work focco A The ray will again be parallel to x axis after travelling a distance of 10 1 10 B Whenever it cuts the x axis it makes an angle of magnitude tan C The deviation in the ray after crossing the very first lens is nearly 0 01 m D Whenever it cuts the x axis it makes an angle of magnitude tan 1 metres is x directin with x axis with x axis

There is an equiconvex glass lens with radius of each face as R and alg 3 2 and alw 4 5 If there is water in object space and air in image space then the focal length is 1 2R 2 R 3 3 R 2 4 R

2 Two spherical mirrors one convex and other concave cach of same radius of curvature R are arranged coaxially at a distance of 2R from each other A small circle of radius a is drawn on the convex mirror near the pole as shown in the igure Find the radii of the first three images of the circle 2R le

An object is 17 cm in front of a diverging lens that has a focal length of 13 cm How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of 2 3 Number 16 9 Units cm

1 A plane mirror is moving with velocity 4 5j 8k A point object in front of the mirror moves with a velocity 31 4j 5k Here is along the normal to the plane mirror and facing towards the object The velocity of the image is 1 51 4j 5k 3 31 41 5k 2 5 4j 8k 4 6i 4j 5k

parallel plate condenser with a dielectric constant K between the plates has a capacity C and is charged to a potential V volt The dielectric slab is slowly removed from between the plates and then reinserted The net work done by the system in this process is a zero c CV K 1 K b K 1 CV 2 d K 1 CV

A linear object AB is placed along the axis of a concave mirror The object is moving towards the mirror with speed V The speed of the image of the point A is 4 V and the speed of the image of B is also 4V If centre of the line AB is at a distance L from the mirror then length of the object AB will be 5L 3L A 3 14 B C L A D AL B

3 Two plane mirrors A and B are aligned parallel to each other as shown in the figure A light ray is incident at an angle 30 at a point just inside one end of A The plane of incidence coincides with the plane of the figure The maximum number of times the ray undergoes reflections including the first one before it emerges out is 2002 2M 2 3 m T 0 2 m a 28 c 32 B A b 30 d 34 30

For the same angle of incidence angle of refraction of 2 media A and B are 25 and 35 respectively In which one of the two media is the speed of light lesser 2 For noroviol cove show that the focal length o sphorical mirror is 14

i Name the phenomenon on which the working of an optical fibre based ii What are the prerequisites for this phenomenon to occur iii Draw a ray diagram of an optical fibre and show how light propagates through the optical fibre using this phenomenon

A beam of width t is incident at 45 on an air water boundary The width of the beam in water is Air Water u 45

A point source of light O is at a distance 2 m from a vertical screen AB An opaque object of height 0 5 m moves translationally at a constant speed of 10 cm s starting at t 0 from 0 towards the screen along the line OA The speed in cm s of the upper edge Pof the shadow of the object at t 5 s will be 10 cm s 2 m Answer 8 A

20 A thin equiconvex lens has focal length and refractive index 1 5 One of its faces is now silvered and for an object placed at a distance u in front of it the image coincides with the object The value of u is 1 10 cm 2 5 cm 3 20 cm 4 15 cm Cu il A 1 27 R

AT Q 1 i Monochromatic light of wavelength 589 nm is incident from air on a water surface If u for water is 1 33 find the wavelength frequency and speed of the refracted light ii A double convex lens is made of a glass of refractive index 1 55 with both faces of the same radius of curvature Find the radius of curvature required if the focal length is 20 cm

Find the position of final image from O for the arrangement shown Object 20cm 1 24 cm 3 40 cm 20cm f 40cm YA f 40cm 2 120 cm 4 20 cm

A ray of light after successive reflections from two plane mirrors deviates totally through an angle 2000 What is the angle between the mirrors A 70 B 80 C 90 D 120

A diverging lens with magnitude of focal 12 length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm A beam of parallel light falls on the diverging lens The final image formed is 1 real and at a distance of 40 cm from the divergent lens 2 real and at a distance of 6 cm from the convergent lens 3 real and at a distance of 40 cm from convergent lens 4 virtual and at a distance of 40 cm from convergent lens

What is the focus distance of a combined lens made by combining concave lens of 20 cm focus distance placed in contact with a convex lens of 30 cm focus distance Whether this combination is convergent lens or divergent

A cylindrical tube filled with water 4 3 is closed at its both ends by two silvered plano convex lenses as shown in the figure Refractive index of lenses L and L are 2 0 and 1 5 while their radii of curvature are 5 cm and 9 cm respectively A point object is placed some where at a point O on the axis of cylindrical tube It is found that the object and image coincides each other 10 11 The position of object w r t lens L is A 8 cm B 10 cm The position of object w r t lens L is B 10 cm A 8 cm O 12 L C 12 cm C 12 cm D 14 cm D 14 cm

To a fish in water a bird in air appears to be 4 at 30 cm from the surface If then the 3 true distance of the bird from the surface is 1 40 cm 3 80 cm W 2 22 5 cm 4 None of the above

As shown in the figure a monochromatic ray of light tavelling in air is incident perpendicular to side a of an equilateral triangle prism with 1 5 Which side will the light ray emerge and what is the angle 0 between incident ray and emergent ray 36 b 60T 60 C 1 Side b 0 60 3 Side c 0 30 2 Side c 0 60 4 Side b 0 120

Statement 1 When two plane mirrors are kept perpendicular to each other as shown O is the point object 3 images will be formed O Statement 2 In case of multiple reflection image of one surface can act as an object for the next surface A Statement 1 is true statement 2 is true and statement 2 is correct explanation for statement 1 B Statement 1 is true statement 2 is true and statement 2 is NOT the correct explanation for statement 1 C Statement 1 is true statement 2 is false D Statement 1 is false statement 2 is true

3 A converging mirror M a point source S and a diverging mirror M are arranged as shown in figure 18 E4 The source is placed at a distance of 30 cm from M The focal length of each of the mirrors is 20 cm Consider only the images formed by a maximum of two reflections It is found that one image is formed on the source itself a Find the distance between the two mirrors b Find the location of the image formed by the single reflection from M M S Figure 18 E4 M

By what angle should M be rotated so that the light ray after reflection from both the mirrors become horizontal 40 25 M

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it It is found that an object and its image coincide if the object is placed at a distance of 20 cm from the lens The focal length of the convex mirror is a 27 5 cm c 25 0cm b 20 0 cm d 30 5 cm

Which one of the following instruments is used to study dispersion of light O Microscope O Telescope Spectrometer

A concave mirror of radius R is kept on a horizontal table figure 18 E2 Water refractive index u is poured into it up to a height h Where should an object be placed so that its image is formed on itself To C R Figure 18 52 T h

A ray of light passes through a medium whose refractive index varies with distance x as X Ho 2 Calculate the time taken by a ray to a move from x 0 to x a 0 X 0 3 2c 5a o 2c a o 2c 7a o 2c X a

A point object O is placed at distance of 15cm from concave morror between a concave and a plane mirror separated by 25cm Considering 1st reflection from concave mirror position of image after 3rd reflection will be Radius of curvature of concave mirror is 20cm P 000 15om O 100m

19 A bird is flying up at angle sin 1 3 5 with the horizontal A fish in a pond looks at that bird When it is vertically above the fish the angle at which the bird appears to fly to the fish is nwater 4 3 A sin 1 3 5 B sin 1 4 5 C 45 D sin 1 9 16 protes two

11 The observer O sees the distance AB as infinitely large If refractive index of liquid is and that of glass is then is A 2 B 1 2 1 C 4 D None of these Glass Liqui

A ray of light undergoes deviation of 30 when incident on an equilateral prism of refractive index 2 The angle made by ray inside the prism with the base of the prism is a Zero b 30 d 60 atorial of the two c 45

8 In the figure ABC is the cross section of a right angled prism and ACDE is the cross section of a glass slab The value of q so that light incident normally on the face AB does not cross the face AC is given sin 1 3 5 37 A 0 37 B 0 37 C 0 53 D 0 53 n 3 2 Wr n 6 5

10 For a prism kept in air it is found that for an angle of incidence 60 the angle of refraction A angle of deviation and angle of emergence e become equal Then the refractive index of the prism is A 1 73 B 1 15 C 1 5 D 1 33

A sin 3 5 B sin 20 In the figure shown a point object O is placed in air A spherical boundary separates two media AB is principal axis The refractive index above AB is 1 6 and below AB is 2 0 The separation between the images formed due to refraction at spherical surface is A 12 m C 14 m B 20 m D 10 m 2m 1 6 B 2 0 Ankur Sir Geometrical Optics 2