JEE Main & Advanced Physics Ray Optics Question Bank

done Self Evaluation Test - Ray Optics and Optical Instruments Total Questions - 100

• question_answer1)
  A person walks at a velocity v in a straight line forming an angle a with the plane of a plane mirror. Determine the velocity \[{{v}_{rel}}\] at which he approaches his image, assuming that the object and its image are symmetric relative to the plane of the mirror.     
  A)
  \[2v\,\text{sin}\,\alpha \] done clear
  B)
  \[2v\cos \alpha \] done clear
  C)
  \[v\sin \alpha \] done clear
  D)
  \[v\cos \alpha \] done clear
  View Solution play_arrow

• question_answer2)
  A point object is located at a distance 15cm. from the pole of a concave mirror of focal length 10cm on its principal axis is moving with a velocity \[(8\hat{i}+11\hat{j})\]cm/s and velocity of mirror is \[(4\hat{i}+2\hat{j})\] cm/s as shown. If \[\vec{v}\] is the velocity of image. Then find the value of \[\left| {\vec{v}} \right|\] in (cm/s).
  A)
  20 done clear
  B)
  30     done clear
  C)
  10 done clear
  D)
  40 done clear
  View Solution play_arrow

• question_answer3)
  Two mirrors, one concave and the other convex, are placed 60 cm apart with their reflecting surfaces facing each other. An object is placed 30 cm from the pole of either of them on their axis. If the focal lengths of both the mirrors are 15 cm, the position of the image formed by reflection, first at the convex and then at the concave mirror, is:
  A)
  19.09 cm from the pole of the concave mirror done clear
  B)
  19.09 cm from the pole of the convex mirror done clear
  C)
  11.09 cm from the pole of the concave mirror done clear
  D)
  11.09 cm from the pole of the convex mirror done clear
  View Solution play_arrow

• question_answer4)
  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 \[30{}^\circ \] at a point just side 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      
  A)
  28 done clear
  B)
  30     done clear
  C)
  32  done clear
  D)
  34 done clear
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• question_answer5)
  The inner surface of a cone coated by a reflecting layer forms a conical mirror. A thin incandescent filament is stretched in the cone along its axis. Determine the minimum angle a of the cone for which the rays emitted by the filament will be reflected from the conical surface not more than once
  A)
  \[120{}^\circ \] done clear
  B)
  \[90{}^\circ ~~\] done clear
  C)
  \[150{}^\circ \] done clear
  D)
  \[135{}^\circ \] done clear
  View Solution play_arrow

• question_answer6)
  I is the image of a point object 0 formed by spherical mirror, then which of the following statement is incorrect? (Take real or virtual objects at finite distances from pole)
  A)
  If O and/are on the same side of the principal axis, then they have to be on opposite sides of the mirror done clear
  B)
  If O and / are on opposite sides of the principal axis, then they have to be on same side of the mirror done clear
  C)
  If O and / are on opposite sides of the principal axis, then they have to be on opposite sides of the mirror as well done clear
  D)
  If O is on principal axis, then / has to lie on principal axis only done clear
  View Solution play_arrow

• question_answer7)
  When an object is placed at a distance of 25 cm from a mirror, the magnification is\[{{m}_{1}}\]. The object is moved 15cm further away with respect to the earlier position, and the magnification becomes  If \[{{m}_{1}}/{{m}_{2}}=4,\] the focal length of the mirror is:
  A)
  10 cm done clear
  B)
  30 cm done clear
  C)
  15 cm done clear
  D)
  20 cm done clear
  View Solution play_arrow

• question_answer8)
  In an experiment to determine the focal length (f) of a concave mirror by the u - v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,
  A)
  \[x<f\] done clear
  B)
  \[f<x<2f\] done clear
  C)
  \[x=-2f\] done clear
  D)
  \[x>2f\] done clear
  View Solution play_arrow

• question_answer9)
  A plane mirror is kept parallel to y-axis. A point object is approaching the mirror with velocity \[\vec{u}=(10\hat{i}+10\hat{j})m/s.\] The magnitude of relative velocity of objective w.r.t image is equal to
  A)
  \[20\sqrt{2}m/s\]   done clear
  B)
  \[20m/s\] done clear
  C)
  \[10\sqrt{2}m/s\] done clear
  D)
  \[10m/s\] done clear
  View Solution play_arrow

• question_answer10)
  The width of man's face is 10cm. The distance between the eyes of the man is 4cm. Then the minimum width of plane mirror to see his fall face, is
  A)
  5cm done clear
  B)
  4cm done clear
  C)
  3cm done clear
  D)
  10cm done clear
  View Solution play_arrow

• question_answer11)
  A point source has been placed as shown in the figure. What is the length on the screen that will receive reflected light from the mirror?
  A)
  2H done clear
  B)
  3H        done clear
  C)
  H done clear
  D)
  None of these   done clear
  View Solution play_arrow

• question_answer12)
  A point object is kept in front of a plane mirror. The plane mirror is doing SHM of amplitude 2 cm. The plane mirror moves along the x - axis which is normal to the mirror. The amplitude of the mirror is such that the object is always in front of the mirror. The amplitude of SHM of the image is
  A)
  0 done clear
  B)
  2 cm done clear
  C)
  4 cm done clear
  D)
  1 cm done clear
  View Solution play_arrow

• question_answer13)
  An object is moving with speed \[{{v}_{0}}\] towards a spherical mirror with radius of curvature R, along the central axis of the mirror. The speed of the image with respect to the mirror is (U is the distance of the object from mirror at any given time  
  A)
  \[+\left( \frac{R}{U-2R} \right)v_{0}^{2}\] done clear
  B)
  \[-{{\left( \frac{R}{R-2U} \right)}^{2}}v_{0}^{{}}\] done clear
  C)
  \[-{{\left( \frac{R}{2U-2R} \right)}^{2}}v_{0}^{{}}\] done clear
  D)
  \[+\left( \frac{R}{2U-2} \right)v_{0}^{2}\] done clear
  View Solution play_arrow

• question_answer14)
  A point object is moving with velocity \[u=2\hat{i}+\hat{j}-\hat{k}m/s\] in front of a stationary plane mirror. The magnitude of relative velocity of the image with respect to object is maximum if the normal of the plane mirror will be along
  A)
  \[2\hat{i}+\hat{j}+\hat{k}\] done clear
  B)
  \[-\,2\hat{i}+\hat{j}-\hat{k}\] done clear
  C)
  \[2\hat{i}+\hat{j}-\hat{k}\] done clear
  D)
  \[2\hat{i}-\hat{j}-\hat{k}\] done clear
  View Solution play_arrow

• question_answer15)
  A ray of light is incident at \[50{}^\circ \] on the middle of one of the two plane mirrors arranged at an angle of \[60{}^\circ \]between them. The ray then touches the second mirror, get reflected back to the first mirror, making an angle of incidence of
  A)
  \[50{}^\circ \] done clear
  B)
  \[60{}^\circ \]    done clear
  C)
  \[70{}^\circ \]  done clear
  D)
  \[80{}^\circ \] done clear
  View Solution play_arrow

• question_answer16)
  A ray parallel to principal axis is incident at \[30{}^\circ \]from normal on concave mirror having radius of curvature R. The point on principal axis where rays are focused is Q such that PQ is
  A)
  \[\frac{R}{2}\] done clear
  B)
  \[\frac{R}{\sqrt{3}}\] done clear
  C)
  \[\frac{2\sqrt{R}-\sqrt{R}}{\sqrt{2}}\] done clear
  D)
  \[R\left( 1-\frac{1}{\sqrt{3}} \right)\] done clear
  View Solution play_arrow

• question_answer17)
  A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the pole of the mirror and C its center of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be.
  A)
  real, and will remain at C. done clear
  B)
  real, and located at a point between C and O. done clear
  C)
  virtual, and located at a point between C and O done clear
  D)
  real, and located at a point between C and O done clear
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• question_answer18)
  A point object P moves towards a stationary convex mirror with a constant speed v, along the optical axis. The speed of the image
  A)
  is always less than v maybe greater than, equal done clear
  B)
  to or less than v, depending upon the position of P done clear
  C)
  is always greater than v done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer19)
  A short linear object of length i lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is approximately equal to
  A)
  \[\ell {{\left( \frac{u-f}{f} \right)}^{1/2}}\] done clear
  B)
  \[\ell {{\left( \frac{u-f}{f} \right)}^{2}}\] done clear
  C)
  \[\ell {{\left( \frac{\,f}{u-f} \right)}^{1/2}}\] done clear
  D)
  \[\ell {{\left( \frac{\,f}{u-f} \right)}^{2}}\] done clear
  View Solution play_arrow

• question_answer20)
  A point object ?O? is at the center of curvature of a concave mirror. The mirror starts to move at a speed u, in a direction perpendicular to the principal axis. Then, the initial velocity of the image is
  A)
  2u, in the direction opposite to that of mirror's velocity done clear
  B)
  2u, in the direction same as that of mirror's velocity done clear
  C)
  zero done clear
  D)
  u, in the direction same as that of mirror's velocity done clear
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• question_answer21)
  You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be:
  A)
  60 cm done clear
  B)
  - 24 cm done clear
  C)
  - 60 cm done clear
  D)
  24 cm done clear
  View Solution play_arrow

• question_answer22)
  Two rays are incident on a spherical mirror of radius R = 5 cm. parallel to its optical axis at distances \[{{h}_{1}}=0.5\text{ }cm\]. and \[{{h}_{2}}=3\text{ }cm\]. Determine the distance Ax (approximately) between the points at which these rays intersect the optical axis after being reflected at the mirror.
  A)
  0.2cm. done clear
  B)
    1.5cm. done clear
  C)
  0:6 cm. done clear
  D)
  1.0cm. done clear
  View Solution play_arrow

• question_answer23)
  A cube of side 2 misplaced in front of a concave mirror of focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the image efface P and Q is
  A)
  1m   done clear
  B)
  0.5m done clear
  C)
  0.5m done clear
  D)
  025m done clear
  View Solution play_arrow

• question_answer24)
  In figure find the total magnification after two successive reflections first on \[{{M}_{1}}\] and then on \[{{M}_{2}}.\]
  A)
  +1   done clear
  B)
  -2         done clear
  C)
  +2   done clear
  D)
  -1         done clear
  View Solution play_arrow

• question_answer25)
    A boy of height h is walking away from a street lamp with a constant speed v. The height of the street lamp is 3 h. The rate at which the length of the boy's shadow is increasing when he is at a distance of 10 h from the base of the street lamp is:                        
  A)
  2v done clear
  B)
  v      done clear
  C)
  v/2   done clear
  D)
  v/3 done clear
  View Solution play_arrow

• question_answer26)
  A point source of light B is placed at a distance L in front of the center of a mirror of width 'd' hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1L from it as shown in fig. The greatest distance over which he can see the image of the light source in the mirror is
  A)
  d/2 done clear
  B)
  d done clear
  C)
  2d done clear
  D)
  3d done clear
  View Solution play_arrow

• question_answer27)
  An object kept on the principle axis is moving in the same directions as that of mirror as shown in figure. Speed of object and mirror is 10m/s and 40/ 12 m/s. Radius of the curvature of the mirror is 20 cm. What should be the distance of object from the mirror at this instant so that the image is stationary?
  A)
  25 cm done clear
  B)
  45 cm        done clear
  C)
  37.5 cm done clear
  D)
  15 cm                       done clear
  View Solution play_arrow

• question_answer28)
  A ray of light is incident at Air the glass-water interface at an angle i, it emerges finally parallel to the surface of water, then the value of would be
  A)
  \[\left( 4/3 \right)sini\] done clear
  B)
  \[1/sini\] done clear
  C)
   4/3 done clear
  D)
  \[1\] done clear
  View Solution play_arrow

• question_answer29)
  A point light source S is outside a cylinder on its axis near the end face (base). Determine the minimum refractive index n of the cylinder material for which none of the rays entering the base will emerge from the lateral surface.
  A)
  \[1/\sqrt{2}~\] done clear
  B)
  \[\sqrt{2}\]   done clear
  C)
  \[1/2~~\] done clear
  D)
  \[~1\] done clear
  View Solution play_arrow

• question_answer30)
  A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:
  A)
  14 cm below flat surface done clear
  B)
  20 cm below flat surface done clear
  C)
  16 cm below flat surface done clear
  D)
  30 cm below flat surface done clear
  View Solution play_arrow

• question_answer31)
  A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. The distance of virtual image from the surface is
  A)
  6 cm done clear
  B)
  4 cm done clear
  C)
  12 cm done clear
  D)
  9 cm done clear
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• question_answer32)
  A plane mirror is held at a height h above the bottom of an empty beaker. The beaker is now filled with water up to depth d. The general expression for the distance from a scratch at the bottom of the beaker to its image in terms of h and the depth d of water in the beaker is\
  A)
  \[2h-d\left( \frac{\mu }{\mu -1} \right)\] done clear
  B)
  \[2h-\frac{d}{2}\left( \frac{\mu -1}{\mu } \right)\] done clear
  C)
  \[2h-d\left( \frac{\mu -1}{\mu } \right)\] done clear
  D)
  \[2h-d\left( \frac{2\mu -1}{\mu } \right)\] done clear
  View Solution play_arrow

• question_answer33)
  A diver looking up through the water sees the outside world contained in a circular horizon, the refractive index of water is \[\frac{4}{3}\], and the diver's eyes are 15 cm below the surface of water. Then the radius of the circle is:
  A)
  \[15\times 3\times \sqrt{5}cm\] done clear
  B)
  \[15\times 3\sqrt{7}cm\] done clear
  C)
  \[\frac{15\times \sqrt{7}}{3}cm\] done clear
  D)
  \[\frac{15\times 3}{\sqrt{7}}cm\] done clear
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• question_answer34)
  A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4.3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as\[[Take\text{ }g=10m/{{s}^{2}}]\]
  A)
  9m/s done clear
  B)
  12m/s done clear
  C)
  16m/s done clear
  D)
  21.33 m/s done clear
  View Solution play_arrow

• question_answer35)
  A light beam is travelling from Region I to IV (figure). The refractive index in regionals I, II, III and IV are \[{{n}_{0}},\frac{{{n}_{0}}}{2},\frac{{{n}_{0}}}{6}\] and \[\frac{{{n}_{0}}}{8}\] respectively The angle of incidence 6 for which the beam just misses entering region IV is -
  A)
  \[si{{n}^{-1}}(3/4)\] done clear
  B)
  \[si{{n}^{-1}}(1/8)\] done clear
  C)
  \[si{{n}^{-1}}(1/4)~~\] done clear
  D)
  \[si{{n}^{-1}}(1/3)\] done clear
  View Solution play_arrow

• question_answer36)
  A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if
  A)
  \[\sin \theta \ge \frac{8}{9}\] done clear
  B)
  \[\frac{2}{3}<\sin \theta <\frac{8}{9}\] done clear
  C)
  \[\sin \theta \le \frac{2}{3}\] done clear
  D)
  \[\frac{1}{2}<\sin \theta <1\] done clear
  View Solution play_arrow

• question_answer37)
  A diverging beam of light from a point source S having divergence angle\[\alpha \], falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is
  A)
  zero done clear
  B)
  \[\alpha \] done clear
  C)
  \[{{\sin }^{-1}}\left( \frac{1}{n} \right)\]   done clear
  D)
  \[2{{\sin }^{-1}}\left( \frac{1}{n} \right)\] done clear
  View Solution play_arrow

• question_answer38)
  A mango tree is at the bank of river and one of the branch of tree extends over the river. A tortoise lives in river. A mango falls just above the tortoise. The acceleration of the mango falling from tree appearing to the tortoise is (Refractive index of water is 4/3 and the tortoise is stationary)
  A)
  g done clear
  B)
  3g/4   done clear
  C)
  4g/3      done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  A container is filled with water \[\left( \mu =1.33 \right)\] up to a height of 33.25 cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. Focal length of the mirror is
  A)
  15 cm done clear
  B)
  20cm done clear
  C)
  -18.31cm done clear
  D)
  10cm done clear
  View Solution play_arrow

• question_answer40)
  A ray of light passes through four transparent media with refractive indices \[{{\mu }_{1}},\,\,{{\mu }_{2}},\,\,{{\mu }_{3}}\] and \[{{\mu }_{4}}\] as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have
  A)
  \[{{\mu }_{1}}={{\mu }_{2}}\] done clear
  B)
  \[{{\mu }_{2}}={{\mu }_{3}}\] done clear
  C)
  \[{{\mu }_{3}}={{\mu }_{4}}\,\] done clear
  D)
  \[{{\mu }_{4}}={{\mu }_{1}}\,\] done clear
  View Solution play_arrow

• question_answer41)
  A point light source is moving with a constant velocity v inside a transparent thin spherical shell of radius R, which is filled with a transparent liquid. If at t=0 light source is at the center of the sphere, then at what time a thin dark ring will be visible for an observer outside the sphere. The refractive index of liquid with respect to that of shell is\[\sqrt{2}\].        
  A)
  \[\frac{R}{\sqrt{2}V}\] done clear
  B)
  \[\frac{R}{2V}\] done clear
  C)
  \[\frac{R}{3V}\] done clear
  D)
  \[\frac{R}{\sqrt{3}V}\] done clear
  View Solution play_arrow

• question_answer42)
  A ray of light is incident on a thick slab of glass (thickness t) as shown below. The emergent ray is parallel to the incident ray but displaced. Sideways by a distance d. If the angles are small then d is:    
  A)
  \[t\left( 1-i/r \right)\] done clear
  B)
  \[rt\left( 1-i/r \right)\] done clear
  C)
  \[rt\left( 1-\frac{r}{i} \right)\] done clear
  D)
  \[t\left( 1-\frac{r}{i} \right)\] done clear
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• question_answer43)
  Light is incident from a medium into air at two possible angles of incidence \[20{}^\circ \]and \[40{}^\circ .\]In the medium light travels 3.0 cm in 0.2 ns. The ray will:
  A)
  suffer total internal reflection in both cases and done clear
  B)
  suffer total internal reflection in case only done clear
  C)
  have partial reflection and partial transmission in case done clear
  D)
  have 100% transmission in case done clear
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• question_answer44)
  An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is a filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is                   
  A)
  \[\frac{5}{2}\] done clear
  B)
  \[\sqrt{\frac{5}{2}}\] done clear
  C)
  \[\sqrt{\frac{3}{2}}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer45)
  A point source of light is placed at a depth of h below the surface of water of refractive index \[\mu .\] A floating opaque disc is placed on the surface of water so that light from the sources is not visible from the surface. The minimum diameter of the disc is       
  A)
  \[2h{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\] done clear
  B)
  \[2h{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\] done clear
  C)
  \[h/\left[ 2{{\left( {{\mu }^{2}}-1 \right)}^{1/2}} \right]\] done clear
  D)
  \[h/{{\left( {{\mu }^{2}}-1 \right)}^{1/2}}\] done clear
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• question_answer46)
  A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is \[{{\theta }_{iC}}\] and Brewster's angle of incidence is \[{{\theta }_{iB}}\], such that \[\sin {{\theta }_{iC}}/\sin {{\theta }_{iB}}=\eta =1.28.\]The relative refractive index of the two media is:
  A)
   0.2 done clear
  B)
  0.4     done clear
  C)
   0.8 done clear
  D)
  0.9 done clear
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• question_answer47)
  Let the refractive index of a denser medium with respect to a rarer medium be \[{{n}_{12}}\] and its critical angle be \[{{\theta }_{C}}\]. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is \[90{}^\circ .\]Angle A is given by:
  A)
  \[\frac{1}{{{\cos }^{-1}}\left( \sin {{\theta }_{C}} \right)}\] done clear
  B)
  \[\frac{1}{{{\tan }^{-1}}\left( \sin {{\theta }_{C}} \right)}\] done clear
  C)
  \[{{\cos }^{-1}}\left( \sin {{\theta }_{C}} \right)\]            done clear
  D)
  \[{{\tan }^{-1}}\left( \sin {{\theta }_{C}} \right)\] done clear
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• question_answer48)
  In a thick glass slab of thickness i and refractive index \[{{n}_{1}}\]a cuboidal cavity of thickness m is carved as shown in the figure and is filled with liquid of RJ. \[~{{n}_{2}}({{n}_{1}}>\text{ }{{n}_{2}})\]. The ratio of \[\ell /m\], so that shift produced by this slab is zero when an observer A observes an object B with paraxial rays is     
  A)
  \[\frac{{{n}_{1}}-{{n}_{2}}}{{{n}_{2}}-1}\] done clear
  B)
  \[\frac{{{n}_{1}}-{{n}_{2}}}{{{n}_{2}}\left( {{n}_{1}}-1 \right)}\] done clear
  C)
  \[\frac{{{n}_{1}}-{{n}_{2}}}{{{n}_{1}}-1}\] done clear
  D)
  \[\frac{{{n}_{1}}-{{n}_{2}}}{{{n}_{1}}\left( {{n}_{2}}-1 \right)}\] done clear
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• question_answer49)
  A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively. If the thickness of the bottom of glass is 1 cm and depth of water is 5 cm, how much the page will appear to be shifted if viewed from the top?
  A)
  1.033 cm done clear
  B)
  3.581 cm done clear
  C)
  1.533 cm done clear
  D)
  1.90 cm done clear
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• question_answer50)
  A rectangular glass slab AB CD of refractive index  \[{{n}_{1}}\] is immersed in water of refractive index \[{{n}_{2}}({{n}_{1}}>{{n}_{2}}).\] A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence \[{{\alpha }_{\max }}\] such that the ray comes out only from the other surface CD is given by
  A)
  \[{{\sin }^{-1\grave{\ }}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right) \right) \right]\] done clear
  B)
  \[{{\sin }^{-1\grave{\ }}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\left( \frac{1}{{{n}_{2}}} \right) \right) \right]\] done clear
  C)
  \[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{n{{  }_{2}}} \right)\] done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{{{n}_{2}}}{n{{  }_{1}}} \right)\] done clear
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• question_answer51)
  Two point source \[{{S}_{1}}\] and \[{{S}_{2}}\] are 24 cm apart. Where a convex lens of focal length 9 cm should be placed in between them so that the images of both sources are formed at the same place?          
  A)
  6 cm from \[{{S}_{1}}\] done clear
  B)
  15 cm from \[{{S}_{1}}\] done clear
  C)
  10 cm from \[{{S}_{1}}\] done clear
  D)
  12 cm from \[{{S}_{1}}\] done clear
  View Solution play_arrow

• question_answer52)
  Two thin symmetrical lenses of different nature and of different material have equal radii of curvature R = 15 cm. The lenses are put close together and immersed in water \[(a=4/3).\] The focal length of the system in water is 30 cm. The difference between refractive indices of the two lenses is
  A)
  1/2  done clear
  B)
  1/4   done clear
  C)
  1/3 done clear
  D)
  3/4 done clear
  View Solution play_arrow

• question_answer53)
  A glass sphere, refractive index 1.5 and radius 10 cm, has a spherical cavity of radius 5 cm concentric with it. A narrow beam of parallel light is directed into the sphere. Find the final image and its nature.  
  A)
  25 cm left of \[{{S}_{4}},\]virtual   done clear
  B)
  25 cm right of \[{{S}_{4}},\]real done clear
  C)
  15 cm left of \[{{S}_{4}},\]virtual  done clear
  D)
  20 cm right of \[{{S}_{4}},\]virtual done clear
  View Solution play_arrow

• question_answer54)
  A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a
  A)
  convergent lens of focal length 3.5R done clear
  B)
  convergent lens of focal length 3.07R done clear
  C)
  divergent lens of focal length 3,5R done clear
  D)
  divergent lens of focal length 3.07R done clear
  View Solution play_arrow

• question_answer55)
  Choose the correct ray diagram of a thin equi-convex lens which is cut as shown in the figure.
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer56)
  A scuba diver in an empty swimming pool uses a magnifier (n = 1.25) to enlarge the print on a plastic instruction sheet. If the pool is filled with water (n = 1.33), what happens to the magnification of the print?   
  A)
  It increases and is greater than one. done clear
  B)
  It stays the same. done clear
  C)
  It decreases, but is still greater than one. done clear
  D)
  It decreases and is less than one done clear
  View Solution play_arrow

• question_answer57)
  A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination is a real image, at a distance of:        
  A)
  60 cm from the convex lens done clear
  B)
  60 cm from the concave lens done clear
  C)
  70 cm from the convex lens done clear
  D)
  70 cm from the concave lens done clear
  View Solution play_arrow

• question_answer58)
  The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is 40 cm. The area of the image is 9 times that of the square. The focal length of the lens is :
  A)
  36 cm done clear
  B)
  27 cm done clear
  C)
  60 cm done clear
  D)
  30 cm done clear
  View Solution play_arrow

• question_answer59)
  Convex surface of thin concavo-convex lens of refractive index 1.5 is silvered as shown. A small object is kept in air at 30 cm left of the lens on its principal axis. The distance of the final image is
  A)
  20cm done clear
  B)
  30cm done clear
  C)
  10cm done clear
  D)
  15cm done clear
  View Solution play_arrow

• question_answer60)
  Rays of light from Sun falls on a biconvex lens of focal length f and the circular image of Sun of radius r is formed on the focal plane of the lens. Then
  A)
  area of image is \[\pi {{r}^{2}}\] and area is directly proportional of done clear
  B)
  area of image is \[\pi {{r}^{2}}\] and area is directly proportional to \[{{f}^{2}}\] done clear
  C)
  intensity of image increases if f is increased done clear
  D)
  if lower half of the lens is covered with black paper area will become half done clear
  View Solution play_arrow

• question_answer61)
  A plastic hemisphere has a radius of curvature of 8 cm and an index of refraction of 1.6. On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object 0. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately
  A)
  1.0 cm done clear
  B)
  1.5 cm    done clear
  C)
  3.75 cm done clear
  D)
  2.5 cm     done clear
  View Solution play_arrow

• question_answer62)
    A small straight rod is placed at an inclination with the optical axis of a thin lens as shown in the figure. The base of the rod is on the optical axis and at a distance 2f(f= focal length of the lens) from the lens. The image of the rod would be  
  A)
  a straight line leaning towards the lens done clear
  B)
  a straight line leaning away from the lens done clear
  C)
  a curve leaning towards the lens done clear
  D)
  a curve leaning away from the lens done clear
  View Solution play_arrow

• question_answer63)
  A luminous object and a screen are at a fixed distance D apart. A converging lens of focal length l is placed between the object and screen. A real image of the object in formed on the screen for two lens positions of they are separated by a distance d equal to
  A)
  \[\sqrt{D\left( D+4f \right)}\]        done clear
  B)
  \[\sqrt{D\left( D-4f \right)}\] done clear
  C)
  \[\sqrt{2D\left( D-4f \right)}\] done clear
  D)
  \[\sqrt{{{D}^{2}}+4f}\] done clear
  View Solution play_arrow

• question_answer64)
  A thin convex lens of focal length 'f is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens-mirror combination, its image is formed at a distance \[\frac{a}{3}\]in front of the combination. The value of 'a' is:
  A)
  3f  done clear
  B)
  \[\frac{3}{2}\]f  done clear
  C)
  f   done clear
  D)
  2f done clear
  View Solution play_arrow

• question_answer65)
  A piano convex lens fits exactly into a piano concave lens. Their plane surface are parallel to each other. If the lenses are made of different materials of refractive indices \[{{\mu }_{1}}\] & \[{{\mu }_{2}}\] and R is the radius of curvature of the curved surface of the lenses, then focal length of combination is            
  A)
  \[\frac{R}{{{\mu }_{1}}-{{\mu }_{2}}}\] done clear
  B)
  \[\frac{2R}{{{\mu }_{1}}-{{\mu }_{2}}}\] done clear
  C)
  \[\,\frac{R}{2\left( {{\mu }_{1}}-{{\mu }_{2}} \right)}\] done clear
  D)
  \[\,\frac{R}{2-\left( {{\mu }_{1}}+{{\mu }_{2}} \right)}\] done clear
  View Solution play_arrow

• question_answer66)
  A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths?
  A)
  -15, 10              done clear
  B)
  -10, 15      done clear
  C)
  75, 50               done clear
  D)
  -75, 50      done clear
  View Solution play_arrow

• question_answer67)
  A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing
  A)
  a concave mirror of suitable focal length done clear
  B)
  a convex mirror of suitable focal length done clear
  C)
  a convex lens of focal length less than 0.25 m done clear
  D)
  a concave lens of suitable focal length done clear
  View Solution play_arrow

• question_answer68)
  Two lenses of focal length \[{{f}_{1}}=10cm\] and \[{{f}_{2}}=20cm\] are kept as shown. The resultant power of combination will  be
  A)
  -10 D                done clear
  B)
  5 D   done clear
  C)
  0                                  done clear
  D)
  10 D done clear
  View Solution play_arrow

• question_answer69)
  A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids \[{{L}_{1}}\] or \[{{L}_{2}}\] having refractive indices \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] respectively \[\left( {{\mu }_{2}}>{{\mu }_{1}}>1 \right)\]. The lens will diverge a parallel beam of light if it is filled with
  A)
  air and placed in air done clear
  B)
  air and immersed in \[{{L}_{1}}\] done clear
  C)
  \[{{L}_{1}}\] and immersed in \[{{L}_{2}}\] done clear
  D)
  \[{{L}_{2}}\] and immersed in \[{{L}_{1}}\] done clear
  View Solution play_arrow

• question_answer70)
  n silvering the convex side of a piano convex lens, focal length of the resulting mirror is: [where R = radius of convex lens, \[\mu \]= refractive index of glass]
  A)
  \[\frac{R}{2\mu }\]         done clear
  B)
  \[\frac{2R}{\mu }\] done clear
  C)
  \[\frac{R}{\mu }\] done clear
  D)
  \[\frac{3R}{2\mu }\] done clear
  View Solution play_arrow

• question_answer71)
  A thin convex lens of focal length 10 cm and refractive index 1.5 is cut vertically into two equal pieces. They are placed as shown with a liquid of refractive index 3 between them. What is the focal   length of the combination?
  A)
  -10cm. done clear
  B)
  -10/4 cm. done clear
  C)
  -10/3 cm. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer72)
  An eye specialist prescribes spectacles having combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm. The power of this lens combination in diopters is
  A)
  +1.5 done clear
  B)
  -1.5 done clear
  C)
  +6.67 done clear
  D)
  -6.67 done clear
  View Solution play_arrow

• question_answer73)
  Figure shows a concavo-convex lens \[{{\mu }_{2}}\] . What is the condition on the reflective indices so that the lens is diverging?     
  A)
  \[2{{\mu }_{3}}<{{\mu }_{1}}+{{\mu }_{2}}\] done clear
  B)
  \[2{{\mu }_{3}}>{{\mu }_{1}}+{{\mu }_{2}}\] done clear
  C)
  \[{{\mu }_{3}}>2\left( {{\mu }_{1}}-{{\mu }_{2}} \right)\] done clear
  D)
  None of these           done clear
  View Solution play_arrow

• question_answer74)
  Two identical thin Plano convex lenses of refractive index n are silvered, one on the plane side and the other on the convex side. The ratio of their focal lengths is
  A)
  \[\frac{n}{n-1}\] done clear
  B)
  \[\frac{n-1}{n}\] done clear
  C)
  \[\frac{n+1}{n}\] done clear
  D)
  \[n\] done clear
  View Solution play_arrow

• question_answer75)
  The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
  A)
  1.25cm done clear
  B)
  2.5 cm done clear
  C)
  1.05cm done clear
  D)
  2cm done clear
  View Solution play_arrow

• question_answer76)
  The given lens is broken into A four parts and rearranged as shown. If the initial focal length is/then after rearrangement the equivalent focal length is-
  A)
  f done clear
  B)
  f/2   done clear
  C)
  f/4 done clear
  D)
  4f done clear
  View Solution play_arrow

• question_answer77)
  A transparent sphere of radius R has a cavity of radius R/2 as shown in figure. Find the refractive index of the sphere if a parallel beam of light falling on left surface focuses at point P.        
  A)
  \[\mu =\frac{3+\sqrt{5}}{2}\]    done clear
  B)
  \[\mu =\frac{3-\sqrt{5}}{2}\] done clear
  C)
  \[\mu =3+\sqrt{5}\] done clear
  D)
  \[\mu =\frac{1+\sqrt{5}}{2}\] done clear
  View Solution play_arrow

• question_answer78)
  A triangular prism of glass is inside water. A ray, incident normally, on one of the faces, is totally reflected from face BC. Then the minimum refractive index of glass is -
  A)
  \[\frac{\sqrt{3}}{2}\]      done clear
  B)
  \[\frac{5}{3}\] done clear
  C)
  \[\frac{2\sqrt{2}}{5}\] done clear
  D)
  \[\frac{4\sqrt{2}}{3}\] done clear
  View Solution play_arrow

• question_answer79)
  ACB is right - angle prism with other angles as \[60{}^\circ \] and\[30{}^\circ \]. Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face AC. For total internal reflections, maximum refractive index of the liquid
  A)
  1.4        done clear
  B)
  1.3 done clear
  C)
  1.2        done clear
  D)
  1.6 done clear
  View Solution play_arrow

• question_answer80)
  A equilateral prism is made of a transparent material of refractive index\[\sqrt{2}\]. A ray of light AB is incident at \[45{}^\circ \]as shown. The net deviation in the path of ray when it comes out of prism is
  A)
  \[135{}^\circ \] done clear
  B)
  \[120{}^\circ \] done clear
  C)
  \[30{}^\circ \]   done clear
  D)
  \[150{}^\circ \] done clear
  View Solution play_arrow

• question_answer81)
  A thin prism \[{{P}_{1}}\] with angle \[4{}^\circ \] and made from glass of refractive index 1.54 is combined with another thin prism \[{{P}_{2}}\] made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism \[{{P}_{2}}\] is
  A)
  \[5.33{}^\circ \] done clear
  B)
  \[4{}^\circ ~\] done clear
  C)
   \[3{}^\circ \] done clear
  D)
  \[2.6{}^\circ \] done clear
  View Solution play_arrow

• question_answer82)
  A ray is incident normally on a right angle prism whose refractive index is \[\sqrt{3}\] and prism angle a \[\alpha =30{}^\circ ,\] after crossing prism ray passes through glass sphere. It strikes the glass sphere at \[\frac{R}{\sqrt{3}}\] distance from principal axis, as shown in figure sphere is half polished. Find the net angle of deviation of incident ray. 
  A)
  \[120{}^\circ ~\] done clear
  B)
  \[150{}^\circ ~\] done clear
  C)
  \[90{}^\circ ~\] done clear
  D)
  \[180{}^\circ \] done clear
  View Solution play_arrow

• question_answer83)
  A prism placed in air made up of flint glass is such that any incident ray on one surface does not emerge from the second surface. Critical angle for flint glass is \[36{}^\circ \] in air. Then, refracting angle A may be
  A)
  \[37{}^\circ ~\] done clear
  B)
  \[54{}^\circ \] done clear
  C)
  \[71{}^\circ \] done clear
  D)
  \[73{}^\circ \] done clear
  View Solution play_arrow

• question_answer84)

  The following data are given for a crown glass prism;

  refractive index for violet light \[{{n}_{v}}=1.521\]

  refractive index for red light \[{{n}_{r}}=1.510\]

  refractive index for yellow light \[{{n}_{y}}=1.515\]

  Then the dispersive power of a parallel glass slab made of the same material is

  A)
  0.01   done clear
  B)
  0.03   done clear
  C)
  0  done clear
  D)
  0.02 done clear
  View Solution play_arrow

• question_answer85)
  Two beams of red and violet colors are made to pass separately through a prism (angle of the prism is \[60{}^\circ \]). In the position of minimum deviation, the angle of refraction will be
  A)
  \[30{}^\circ \] for both the colors done clear
  B)
  greater for the violet color done clear
  C)
  greater for the red color done clear
  D)
  equal but not \[30{}^\circ \] for both the colors. done clear
  View Solution play_arrow

• question_answer86)
  r and r' denote the angles inside an equilateral prism, as usual, in degrees. Consider that during some time interval from \[t=0\] to\[t=t\], \[r'\] varies with time as \[r'=10+{{t}^{2}}\]. During this time r will vary as (assume that r and r' are in degree)
  A)
  \[50-{{t}^{2}}\] done clear
  B)
  \[50+{{t}^{2}}\] done clear
  C)
  \[60-{{t}^{2}}\] done clear
  D)
  \[60+{{t}^{2}}\] done clear
  View Solution play_arrow

• question_answer87)
  For an optical fiber consists of a core (refractive index =\[{{\mu }_{1}}\]) and cladding (refractive index =\[{{\mu }_{2}}\])
  A)
  \[{{\mu }_{1}}>{{\mu }_{2}}\] done clear
  B)
  \[{{\mu }_{1}}<{{\mu }_{2}}\] done clear
  C)
  \[{{\mu }_{1}}={{\mu }_{2}}\] done clear
  D)
  \[\frac{{{\mu }_{1}}}{{{\mu }_{2}}}=\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer88)
  An isosceles prism of angle \[120{}^\circ \] has a refractive index 1.44. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerge from the opposite faces
  A)
  are parallel to each other      done clear
  B)
  are diverging                      done clear
  C)
  make an angle \[2\left[ si{{n}^{-1\text{ }}}\left( 0.72 \right)-30{}^\circ  \right]\] with each other                      done clear
  D)
  make an angle \[2\text{ }si{{n}^{-1}}(0.72)\]  with each other done clear
  View Solution play_arrow

• question_answer89)
  In Fig. ABC is the cross section of a right - angled prism and ACDE is the cross section of a glass slab. The value of 9 so that incident normally on the face AB does not cross the face AC is\[\left( \text{given si}{{\text{n}}^{-1}}(3/5)=37{}^\circ  \right)\].    
  A)
  \[\theta \le 37{}^\circ \] done clear
  B)
  \[\theta \le 37{}^\circ \] done clear
  C)
  \[\theta \ge 53{}^\circ \] done clear
  D)
  \[\theta >53{}^\circ \] done clear
  View Solution play_arrow

• question_answer90)
  The diameter of the objective lens of microscope makes an angle P at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscope
  A)
  increases with decreasing value of n done clear
  B)
  increases with decreasing value of \[\beta \] done clear
  C)
  increases with increasing value of n sin \[2\beta \] done clear
  D)
  increases with increasing value of \[\frac{1}{n\sin 2\beta }\] done clear
  View Solution play_arrow

• question_answer91)
  A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle  formed by the image of the tower is \[\theta \], then \[\theta \] is close to :
  A)
  6.1 rad done clear
  B)
  3.2 rad done clear
  C)
  1.5 rad done clear
  D)
  0.2 rad done clear
  View Solution play_arrow

• question_answer92)
  An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 3. What is the distance between the screen and the object?
  A)
  124.5 cm  done clear
  B)
  144.5 cm done clear
  C)
  65.0 cm done clear
  D)
  99.0 cm done clear
  View Solution play_arrow

• question_answer93)
  The focal lengths of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively. The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity. The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectively
  A)
  2.4 and 12.0 done clear
  B)
  2.4 and 15.0 done clear
  C)
  2.0 and 12.0 done clear
  D)
  2.0 and 3.0 done clear
  View Solution play_arrow

• question_answer94)
  In a compound microscope, the intermediate image is               
  A)
  virtual, erect and magnified done clear
  B)
  real, erect and magnified done clear
  C)
  real, inverted and magnified done clear
  D)
  virtual, erect and reduced done clear
  View Solution play_arrow

• question_answer95)
  The focal lengths of objective lens and eye lens of a Galilean telescope are respectively 30 cm and 3.0 cm. telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision from the eye lens. In this condition, the magnifying power of the Galilean telescope should be:
  A)
  +11.2 done clear
  B)
  -11.2 done clear
  C)
  -8.8       done clear
  D)
  +8.8 done clear
  View Solution play_arrow

• question_answer96)
  In a compound microscope, the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be:
  A)
  200   done clear
  B)
  100   done clear
  C)
  400   done clear
  D)
  150 done clear
  View Solution play_arrow

• question_answer97)
  The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focused for distinct vision on a scale distant 2m from its objective, then its magnifying power will be:
  A)
  - 4                                done clear
  B)
  - 8        done clear
  C)
  +8                                done clear
  D)
  - 2    done clear
  View Solution play_arrow

• question_answer98)
  When a ray of light enters a glass slab from air,
  A)
  its wavelength decreases. done clear
  B)
  its wavelength increases. done clear
  C)
  Its frequency decreases. done clear
  D)
  neither its wavelength nor its frequency changes. done clear
  View Solution play_arrow

• question_answer99)
  A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface, the radius of this circle (in cm) is -     
  A)
  \[36\sqrt{5}\] done clear
  B)
  \[4\sqrt{5}\] done clear
  C)
  \[36\sqrt{7}\] done clear
  D)
  \[36/\sqrt{7}\] done clear
  View Solution play_arrow

• question_answer100)
  In a vessel, as shown in Fig. point P is just visible when no liquid is filled in vessel through a telescope in the air. When liquid is filled in the vessel completely, point Q is visible without moving the vessel or telescope. Find the refractive index of the liquid.
  A)
  \[\frac{\sqrt{14}}{3}\] done clear
  B)
  \[\frac{\sqrt{85}}{5}\] done clear
  C)
  \[\sqrt{2}\]         done clear
  D)
  \[\sqrt{3}\] done clear
  View Solution play_arrow