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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 11601. |
A horizontal ray of light passes through a prism of \[\mu =1.5\] whose apex angle is \[4{}^\circ \] and then strikes a vertical mirror M as shown. For the ray after reflection to become horizontal, the mirror must be rotated through an angle of: |
| A. | \[{{2}^{o}}\] |
| B. | \[{{3}^{\text{o}}}\] |
| C. | \[{{4}^{\text{o}}}\] |
| D. | \[{{1}^{\text{o}}}\] |
| Answer» B. \[{{3}^{\text{o}}}\] | |
| 11602. |
A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index n as a function of wavelength \[\lambda \] for glass and liquid are as shown in the figure. A ray of white light is incident on the prism parallel to the base. Choose the incorrect statement - |
| A. | yellow ray travels without deviation |
| B. | blue ray is deviated towards the vertex |
| C. | red ray is deviated towards the base |
| D. | there is no dispersion |
| Answer» E. | |
| 11603. |
A prism of dispersive power 0.021 and refractive index 1.53 form an achromatic combination with prism of angle \[4.2{}^\circ \] and dispersive power 0.045 having refractive index 1.65. Find the resultant deviation. |
| A. | \[1.12{}^\circ \] |
| B. | \[2.16{}^\circ \] |
| C. | \[3.12{}^\circ \] |
| D. | \[4.18{}^\circ \] |
| Answer» D. \[4.18{}^\circ \] | |
| 11604. |
A vertical microscope is focused on a point at the bottom of an empty tank. Water \[\left( \mu =\frac{4}{3} \right)\] is then poured into the tank. The height of the water column is 4 cm. Another lighter liquid, which does not mix with water and which has refractive index \[\frac{3}{2}\] is then poured over the water. The height of liquid column is 2 cm. What is the vertical distance through which the microscope must be moved to bring the object in focus again? |
| A. | 2.61 m |
| B. | 1.55 m |
| C. | 3.12 m |
| D. | 1.67 m |
| Answer» E. | |
| 11605. |
A ray of light passes from vacuum into a medium of refractive index \[\mu ,\] the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is |
| A. | \[{{\cos }^{-1}}(\mu /2)\] |
| B. | \[2{{\cos }^{-1}}(\mu /2)\] |
| C. | \[2{{\sin }^{-1}}(\mu )\] |
| D. | \[2{{\sin }^{-1}}\,(\mu /2)\] |
| Answer» C. \[2{{\sin }^{-1}}(\mu )\] | |
| 11606. |
Let the \[x-y\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has refractive index of \[\sqrt{2}\] and medium 2 with \[z |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{75}^{o}}\] |
| Answer» C. \[{{60}^{o}}\] | |
| 11607. |
A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of \[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is |
| A. | \[\frac{{{n}_{1}}}{2}\] |
| B. | \[2n\] |
| C. | \[\frac{3{{n}_{1}}}{2}\] |
| D. | \[\frac{2{{n}_{1}}}{3}\] |
| Answer» D. \[\frac{2{{n}_{1}}}{3}\] | |
| 11608. |
Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index 3/2 is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of \[\mu \]for which total internal reflection cannot take place on face AC is |
| A. | \[\frac{3\sqrt{3}}{4}>\mu >\frac{\sqrt{3}}{2}\] |
| B. | \[\mu <\frac{3\sqrt{3}}{4}\] |
| C. | \[\mu >\sqrt{3}\] |
| D. | \[\mu <\frac{\sqrt{3}}{2}\] |
| Answer» C. \[\mu >\sqrt{3}\] | |
| 11609. |
If \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] are the refractive indices of the materials of core and cladding of an optical fibre, then the loss of light due to its leakage can be minimised by having |
| A. | \[{{\mu }_{1}}>{{\mu }_{2}}\] |
| B. | \[{{\mu }_{1}}<{{\mu }_{2}}\] |
| C. | \[{{\mu }_{1}}={{\mu }_{2}}\] |
| D. | None of these |
| Answer» B. \[{{\mu }_{1}}<{{\mu }_{2}}\] | |
| 11610. |
A man in an empty swimming pool has a telescope focused at 4'O clock sun. When the swimming pool is filled with water, the man (now inside the water with his telescope undisturbed) observes the setting sun. Find the refractive index of water, if sun rises and sets at 6'O clock. |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{2}{\sqrt{3}}\] |
| C. | \[\frac{8}{5}\] |
| D. | \[\frac{2}{5}\] |
| Answer» C. \[\frac{8}{5}\] | |
| 11611. |
If the signal is transmitted from an optical fibre core of Refractive Index (RI) \[\sqrt{\frac{12}{5}}\] to an another optical fibre with RI of core and cladding as 1.8 and 1.2 respectively, then the maximum angle of acceptance for 2nd optical fibre is |
| A. | \[30{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] |
| Answer» D. \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] | |
| 11612. |
Statement-1: Beam of white light is incident on a transparent glass hemisphere as shown in figure. The beam is rotated clockwise so that angle \[\theta \] increases, as the refracted beam approaches a direction parallel to the horizontal it appears red. Statement-2: Critical angle for a pair of medium depends on \[Rl's\] of mediums and given by \[{{i}_{c}}={{\sin }^{-1}}\left( \frac{1}{_{R}{{\mu }_{D}}} \right)\And Rl\] in turn depends on wavelength of light. |
| A. | Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 |
| B. | Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1 |
| C. | Statement-1 is True, Statement -2 is False |
| D. | Statement -1 is False, Statement-2 is True |
| Answer» B. Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1 | |
| 11613. |
A man is standing at the edge of a 1 m deep swimming pool, completely filled with a liquid of refractive index \[\sqrt{3/2}\]. The eyes of the man are \[\sqrt{3}m\] above the ground. A coin located at the bottom of the pool appears to be at an angle of depression of \[\text{3}0{}^\circ \] with reference to the eye of man. Then horizontal distance (represented by \[\times \] in the figure) of the coin from the eye of the man is ???.. mm. |
| A. | 2000 |
| B. | 3000 |
| C. | 4000 |
| D. | 8000 |
| Answer» D. 8000 | |
| 11614. |
An isosceles trapezium of reflecting material of refractive index \[\sqrt{2}\] and dimension of sides being 5 cm, 5 cm, 10 cm and 5 cm. The angle of minimum deviation by this when light is incident from air and emerges in air is: |
| A. | \[22\frac{1}{2}{}^\circ \] |
| B. | \[\text{45}{}^\circ \] |
| C. | \[\text{3}0{}^\circ \] |
| D. | \[\text{6}0{}^\circ \] |
| Answer» E. | |
| 11615. |
It is found that all electromagnetic signals sent from A towards B reach point C. The speed of electromagnetic signals in glass cannot be: |
| A. | \[1.0\times {{10}^{8}}m/s\] |
| B. | \[2.4\times {{10}^{8}}m/s\] |
| C. | \[2\times {{10}^{7}}m/s\] |
| D. | \[4\times {{10}^{7}}m/s\] |
| Answer» B. \[2.4\times {{10}^{8}}m/s\] | |
| 11616. |
A transparent solid cylindrical rod has a refractive index of \[\frac{2}{\sqrt{3}}\]. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle \[(\theta )\] for which the light ray grazes along the wall of the rod is: |
| A. | \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\] |
| B. | \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\] |
| C. | \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\] |
| Answer» D. \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\] | |
| 11617. |
A plane mirror is made of glass slab \[({{\mu }_{g}}=1.5)\,2.5\,\text{cm}\] thick and silvered on the back. A point object is placed 5 cm in front of the unsilvered face of the mirror. What will be the position of final image: |
| A. | 12 cm from front face |
| B. | 14.6 cm from front face |
| C. | 5.67 cm from front face |
| D. | 8.33 cm from front face |
| Answer» E. | |
| 11618. |
The critical angle of light going from medium A to medium B is \[\theta \]. The speed of light in medium A is v. The speed of light in medium B is: |
| A. | \[\frac{v}{\sin \theta }\] |
| B. | \[v\,\,\sin \theta \] |
| C. | \[v\,\,\cot \theta \] |
| D. | \[v\,\,\tan \theta \] |
| Answer» B. \[v\,\,\sin \theta \] | |
| 11619. |
A beam of monochromatic light is incident at \[i={{50}^{o}}\] on one face of an equilateral prism the angle of emergence is \[40{}^\circ ,\] then the angle of minimum deviation is- |
| A. | \[{{30}^{o}}\] |
| B. | \[<{{30}^{o}}\] |
| C. | \[\le {{30}^{o}}\] |
| D. | \[\ge {{30}^{o}}\] |
| Answer» C. \[\le {{30}^{o}}\] | |
| 11620. |
In the figure [a] the light is incident at an angle \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\] (slightly greater than the critical angle). Now keeping the incident ray fixed a parallel slab of refractive index \[{{n}_{3}}\] is placed on surface AB. |
| A. | total internal reflection occurs at AB for \[{{n}_{3}}={{n}_{2}}\] |
| B. | total internal reflection occurs at AB for \[{{n}_{3}}>{{n}_{1}}\] |
| C. | the ray will return back to the same medium for all values of \[{{n}_{3}}\] |
| D. | total reflection occurs at CD for \[{{n}_{3}}<{{n}_{1}}\]. |
| Answer» D. total reflection occurs at CD for \[{{n}_{3}}<{{n}_{1}}\]. | |
| 11621. |
A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions 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 Region I Region II Region III Region IV \[\frac{{{n}_{0}}}{2}\] \[\frac{{{n}_{0}}}{6}\] \[\frac{{{n}_{0}}}{8}\] 0 0.2 m 0.6 m |
| A. | \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\] |
| B. | \[{{\sin }^{-1}}\left( \frac{1}{8} \right)\] |
| C. | \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\] |
| Answer» C. \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\] | |
| 11622. |
The refractive index of air is 1.0003. The thickness of air column which will have one more wavelength of yellow light \[(X=\text{ }6000\overset{o}{\mathop{A}}\,)\] than in the same thickness in vacuum is |
| A. | 2 mm |
| B. | 2 cm |
| C. | 2 m |
| D. | 2 km |
| Answer» B. 2 cm | |
| 11623. |
A cylinderical optical fibre (quarter circular shape) of refractive index \[n=2\] and diameter \[d=4\text{ }mm\] is surrounded by air. A light beam is sent into the fibre along its axis as shown in figure. Then the smallest outer radius R (as shown in figure) for which no light escapes after first incident on curved surface of fibre is: |
| A. | 2 mm |
| B. | 4 mm |
| C. | 8 mm |
| D. | 6 mm |
| Answer» C. 8 mm | |
| 11624. |
The human eye can be regarded as a single spherical refracting surface of curvature of radii 7.8 mm. If a parallel beam of light comes to focus at 3.075 cm behind the refracting surface, the refractive index of the eye is |
| A. | 1.34 |
| B. | 1 |
| C. | 1.5 |
| D. | 1.86 |
| Answer» B. 1 | |
| 11625. |
Convex side of a convexo-concave lens is silvered and on its principle axis a point object is moving toward it from concave side then |
| A. | its image will continuously move toward the lens |
| B. | its image may continuously move toward the lens |
| C. | its image will always be real |
| D. | its image may be real |
| Answer» B. its image may continuously move toward the lens | |
| 11626. |
Two plano-convex lenses each of focal length 10 cm & refractive index \[\frac{3}{2}\] are placed as shown. In the space left, water \[\left( R.l=\frac{4}{3} \right)\] is filled. The whole arrangement is in air. The optical power of the system is (in diopters) |
| A. | 6.67 |
| B. | -6.67 |
| C. | 33.3 |
| D. | -33.3 |
| Answer» B. -6.67 | |
| 11627. |
An air bubble in a glass sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If \[_{a}{{\mu }_{g}}=1.5,\] the distance of bubble from refracting surface is |
| A. | 1.2 cm |
| B. | 3.2 cm |
| C. | 2.8 cm |
| D. | 1.6 cm |
| Answer» B. 3.2 cm | |
| 11628. |
A convex lens is placed in contact with a mirror as shown. If the space between them is filled with water, its power will |
| A. | decrease |
| B. | increase |
| C. | remain unchanged |
| D. | increase or decrease depending of the foe length |
| Answer» B. increase | |
| 11629. |
A thin linear object of size 1 mm is kept along the principal axis of a convex lens of focal length 10 cm. The object is at 15 cm from the lens. The length of the image is: |
| A. | 1 mm |
| B. | 4 mm |
| C. | 2 mm |
| D. | 8 mm |
| Answer» C. 2 mm | |
| 11630. |
A thin convergent glass lens \[\mu =1.5\] has a power of + 5.0 D. When this lens is immersed in a liquid of refractive index \[{{\mu }_{1}}\] it acts as a divergence lens of focal length 100 cm. The value of \[{{\mu }_{1}}\] should be |
| A. | 44230 |
| B. | 44259 |
| C. | 44260 |
| D. | 2 |
| Answer» D. 2 | |
| 11631. |
A 35 mm film is to be projected on a 20 m wide screen situated at a distance of 40 m from the film-projector. Calculate the focal length of projection lens. |
| A. | 70 mm |
| B. | 35 mm |
| C. | 40 mm |
| D. | 20 mm |
| Answer» B. 35 mm | |
| 11632. |
A convex lens of focal length 15 cm placed coaxially in front of a convex mirror. The lens is 5 cm from apex of mirror. When an object is placed on the axis at a distance of 20 cm from the lens, it is found that image coincides with object, radius of curvature of mirror is |
| A. | 65 cm |
| B. | 60 cm |
| C. | 55 cm |
| D. | 75 cm |
| Answer» D. 75 cm | |
| 11633. |
The plane of a mirror makes an angle of \[30{}^\circ \] with horizontal. If a vertical ray is incident on a mirror, then what is the angle between mirror and reflected ray? |
| A. | \[60{}^\circ \] |
| B. | \[90{}^\circ \] |
| C. | \[45{}^\circ \] |
| D. | \[30{}^\circ \] |
| Answer» B. \[90{}^\circ \] | |
| 11634. |
Two plane mirrors are kept such that angle between their reflecting surfaces is \[40{}^\circ \]. A point object is kept symmetrically with respect to the mirrors. The total number of images formed by one mirror is: |
| A. | 8 |
| B. | 9 |
| C. | 4 |
| D. | 5 |
| Answer» D. 5 | |
| 11635. |
A dentist wants a small mirror that when placed 2 cm from a tooth, will produce \[3\times \] upright image. What kind of mirror must be used and what must its focal length be? |
| A. | concave mirror, 3.0 cm |
| B. | concave mirror, 1.5 cm |
| C. | convex mirror, 3.0 cm |
| D. | convex mirror, 1.5 cm |
| Answer» B. concave mirror, 1.5 cm | |
| 11636. |
An object O is placed in front of a plane mirror. A person looks into the mirror as shown. At what position is the image of O is observed by person? |
| A. | A |
| B. | B |
| C. | C |
| D. | D |
| Answer» C. C | |
| 11637. |
Two plane mirrors A & B are aligned parallel to each other, as shown in the figure. A light ray is incident to an angle of \[\text{3}0{}^\circ \] 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: |
| A. | 28 |
| B. | 30 |
| C. | 32 |
| D. | 34 |
| Answer» C. 32 | |
| 11638. |
In the figure shown, the image of a real object is formed at point I. AB is the principal axis of the mirror. The mirror must be: |
| A. | concave and placed towards right of I |
| B. | concave and placed towards left of O |
| C. | convex and placed towards right of I |
| D. | convex and placed towards left of I |
| Answer» C. convex and placed towards right of I | |
| 11639. |
The reflecting surface of a plane mirror is vertical. A particle is projected in a vertical plane which is also perpendicular to the mirror. The initial speed of the particle is 10 m/s and the angle of projection is \[60{}^\circ \] from the normal of the mirror. The point of projection is at a distance 5 m from the mirror. The particle moves towards the mirror. Just before the particle touches the mirror, the velocity of approach of the particle and the image is: |
| A. | 10 m/s |
| B. | 5 m/s |
| C. | \[10\sqrt{3}\,m/s\] |
| D. | \[5\sqrt{3}\,m/s\] |
| Answer» B. 5 m/s | |
| 11640. |
A rear mirror of a vehicle is cylindrical having radius of curvature 10 cm. The length of arc of curved surface is also 10 cm. If the eye of the driver is assumed to be at a large distance from the mirror, then the field of view in radians is |
| A. | 0.5 |
| B. | 1 |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 11641. |
The focal length of a concave mirror is f and the distance from the object to the principal focus is \[x\]. Then the ratio of the size of the image to the size of the object is: |
| A. | \[\frac{(f+x)}{f}\] |
| B. | \[\frac{f}{x}\] |
| C. | \[\sqrt{\frac{f}{x}}\] |
| D. | \[\frac{{{f}^{2}}}{{{x}^{2}}}\] |
| Answer» C. \[\sqrt{\frac{f}{x}}\] | |
| 11642. |
An object is moving towards a concave mirror of focal length 24 cm. When it is at a distance of 60 cm from the mirror its speed is 9 cm/s. The speed of its image at the instant is |
| A. | 4 cm/s towards the mirror |
| B. | 9 cm/s towards the mirror |
| C. | 4 cm/s away from the mirror |
| D. | 9 cm/s away from the mirror |
| Answer» D. 9 cm/s away from the mirror | |
| 11643. |
A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency \[9\pi /rps\]. The light reflected by the mirror is received on the wall W at a distance 10m from the axis of rotation. When the angle of incidence becomes \[37{}^\circ \] the speed of the spot (a point) on the wall is: |
| A. | 10 m/s |
| B. | 1000 m/s |
| C. | 500 m/s |
| D. | None of these |
| Answer» C. 500 m/s | |
| 11644. |
A rod 1.5 m long is placed along the principal axis of a convex mirror of focal length 60 cm. The near end of the rod is 1 m from the pole of the convex mirror. The length of the image of the rod is |
| A. | 15 cm |
| B. | 14.44 cm |
| C. | 6.62 cm |
| D. | 10.88 cm |
| Answer» E. | |
| 11645. |
A mobile phone of width 5 cm and length 10 cm, is placed parallel to its lengths, such that one of its lengths is along the principal axis of a concave mirror of focal length 30 cm. The far point of its length is at the centre of curvature of the mirror. The width of the image will be |
| A. | 5 cm |
| B. | varies from 5 to 7.5 cm |
| C. | cannot be found |
| D. | varies from 7.5 to 9 cm |
| Answer» C. cannot be found | |
| 11646. |
Two plane mirrors of length L are separated by distance L and a man \[{{M}_{2}}\] is standing at distance L from the connecting line of mirrors as shown in figure. A man \[{{M}_{1}}\] is walking in a straight line at distance 2L parallel to mirrors at speed u, then man \[{{M}_{2}}\] at O will be able to see image of \[{{M}_{1}}\] for time: |
| A. | \[\frac{4L}{u}\] |
| B. | \[\frac{3L}{u}\] |
| C. | \[\frac{6L}{u}\] |
| D. | \[\frac{9L}{u}\] |
| Answer» D. \[\frac{9L}{u}\] | |
| 11647. |
The focal length of a concave mirror is 30 cm. Find the position of the object in front of the mirror, so that the image is three times the size of the object. |
| A. | 20 cm (only) |
| B. | 40 cm (only) |
| C. | 30 cm (only) |
| D. | 20 cm or 40 cm |
| Answer» E. | |
| 11648. |
The focal length of a concave mirror is f and the distance from the object to the principle focus is x. The ratio of the size of the image to the size of the object is [Kerala PET 2005] |
| A. | \[\frac{f+x}{f}\] |
| B. | \[\frac{f}{x}\] |
| C. | \[\sqrt{\frac{f}{x}}\] |
| D. | \[\frac{{{f}^{2}}}{{{x}^{2}}}\] |
| Answer» C. \[\sqrt{\frac{f}{x}}\] | |
| 11649. |
The field of view is maximum for |
| A. | Plane mirror |
| B. | Concave mirror |
| C. | Convex mirror |
| D. | Cylindrical mirror |
| Answer» D. Cylindrical mirror | |
| 11650. |
Image formed by a convex mirror is [MP PET 1993] |
| A. | Virtual |
| B. | Real |
| C. | Enlarged |
| D. | Inverted |
| Answer» B. Real | |