Practice Questions

Q23.A transparent cube of side d, made of a material of refractive index μ2 , is immersed in a liquid of refractive index μ1 ( μ1 < μ2). A ray is incident on the face AB at an angle θ (shown in the figure). Total internal reflection takes place at the point E on the face BC. Then, θ must satisfy (1) (2) θ > sin−1 μ2 θ < sin−1 2 −1 √μ2μ21 μ1 (3) θ < sin−1 μ1 (4) 2 μ2 θ > sin−1 −1 √μ2μ21

Q23.An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is 𝑎 and distance of its centre from the wire is 𝑑 𝑑≫𝑎. If the loop applies a force 𝐹 on the wire then: 2 (1) 𝐹∝𝑎 (2) 𝐹= 0 𝑑 𝑎 (3) 𝐹∝𝑎2 (4) 𝐹∝ 𝑑 𝑑3

Q23.The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10A to 25A in 1s , the change in the energy of the inductance is: (1) 637.5 J (2) 740 J (3) 437.5 J (4) 540 J

Q23.A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 V m-1 along y-direction. Its corresponding magnetic field component, B would be: (1) 2 × 10-8 T along z- (2) 2 × 10-8 T along y- (3) 6 × 10-8 T along z- (4) 6 × 10-8 T along x- direction direction direction direction

Q23.Sunlight of intensity 50 W m−2 is incident normally on the surface of a solar panel. Some part of incident energy ( 25%) is reflected from the surface and the rest is absorbed. The force exerted on 1 m2 surface area will be close to (c = 3 × 108 m s−1) (1) 15 × 10−8 N (2) 20 × 10−8 N (3) 10 × 10−8 N (4) 35 × 10−8 N

Q23.The energy associated with electric field is (UE) and with magnetic field is (UB) for an electromagnetic wave in free space. Then: (1) UE > UB (2) UE = UB (3) UE = UB2 (4) UE < UB

Q23.An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s the speed and direction of the image will be (1) 2.26 × 10−3 m/s away from the lens (2) 0.92 × 10−3 m/s away from the lens (3) 3.22 × 10−3 m/s towards the lens (4) 1.16 × 10−3 m/s towards the lens

Q23.A coil of self inductance 10 mH and resistance of 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω . After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [ln5 = 1.6] (1) 0.103 s (2) 0.002 s (3) 0.324 s (4) 0.016 s

Q23.A circuit connected to an ac source of emf e = e0sin⁡100𝑡 with t in seconds, gives a phase difference of 𝜋 4 between the emf 𝑒 and current i . Which of the following circuits will exhibit this? (1) RC circuit with R = 1 kΩ and C = 1 μF (2) RL circuit with R = 1 kΩ and L = 1 mH (3) RL circuit with R = 1 kΩ and L = 10 mH (4) RC circuit with R = 1 kΩ and C = 10 μF

Q23.The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to: (1) L (2) 1 L2 (3) 1 (4) L2 L JEE Main 2019 (09 Apr Shift 1) JEE Main Previous Year Paper →

Q23.A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 mV , then the amplitude of the electric field for the wave propagating in the glass medium will be: (1) 30 mV (2) 6 mV (3) 24 mV (4) 10 mV

Q24.A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is: (1) 2√3 a + 2b (2) 2a + 2b (3) 2a + 2b (4) 2a + 2b3 √3

Q24.Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen? (1) Image disappears (2) Magnified image (3) Erect real image (4) No change JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q24.A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33 ) (1) 13.4 cm (2) 8.8 cm (3) 6.7 cm (4) 11.7 cm

Q24.The graph shows how the magnification 𝑚 produced by a thin lens varies with image distance 𝑣. The focal length of the lens used is (1) 𝑏 (2) 𝑎 𝑐 𝑐 (3) 𝑏2𝑐 (4) 𝑏2 𝑎 𝑎𝑐

Q24.Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) and parallel to the first mirror (M1). The angle between the two mirrors will be: (1) 60o (2) 45o (3) 90o (4) 75o

Q24.A system of three polarizers P1, P2, P3 is set up such that the pass axis of P3 is crossed with respect to that of P1 . The pass axis of P2 is inclined at 60o to the pass axis of P3. When a beam of unpolarized light of intensity Io is incident on P1, the intensity of light transmitted by the three polarizers is I . The ratio (Io/I) equals (nearly): (1) 5.33 (2) 16.00 (3) 1.80 (4) 10.67

Q24.A conducting circular loop made of a thin wire has area 3.5 × 10-2 m2 and resistance 10 Ω It is placed perpendicular to a time-dependent magnetic field 𝐵𝑡= 0.4 Tsin50𝜋𝑡 The field is uniform in space. Then the net charge flowing through the loop during 𝑡= 0 s and 𝑡= 10 ms is close to (1) 1.4 𝑚𝐶 (2) 7 𝑚𝐶 (3) 21 𝑚𝐶 (4) 6 𝑚𝐶

Q24.The magnetic field of an electromagnetic wave is given by: →B = 1.6 × 10-6cos⁡ 2 × 107𝑧+ 6 × 1015𝑡 2^𝑖+ ^𝑗 Wb m2 The associated electric field will be: (1) →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 -2 ^𝑗+ ^𝑖 V(2) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 ^𝑖- 2 ^𝑗 V m m (3) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 -^𝑖+ 2^𝑗V →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 2^𝑖+ ^𝑗V m(4) m

Q24.The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if Dm is the angle of minimum deviation? JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q24.A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is : (1) 90∘ (2) 30∘ (3) 60∘ (4) 45∘

Q24.The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by the → → expression E(x, y) = 10ˆjcos(6x + 8z). The magnetic field B(x, z, t) is given by ( c is the velocity of light.) (1) 1 + cos(6x + 8z −10 ct) c (6ˆk −8ˆi) cos(6x + 8z + 10 ct) (2) 1c (6ˆk 8ˆi) (3) 1 + + 8z −10 ct) c (6ˆk 8ˆi) cos(6x −8z + 10 ct) (4) 1c (6ˆk −8ˆi)cos(6x

Q24.A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x1 and x2(x1 > x2) from the lens. The ratio of x1 and x2 is: (1) 2 : 1 (2) 5 : 3 (3) 4 : 3 (4) 3 : 1

Q24.What is the position and nature of image formed by lens combination shown in figure? ( f1, f2 are focal lengths) (1) 40 cm from point B at right; real (2) 203 cm from point B at right, real (3) 70 cm from point B at right; real (4) 70 cm from point B at left; virtual JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q24.In figure, the optical fiber is 𝑙= 2 m long and has a diameter of d = 20 μm . If a ray of light is incident on one end of the fiber at angle θ1 = 40° , the number of reflections it makes before emerging from the other end is close to: (refractive index of fiber is 1.31 , sin 40° = 0.64 and sin-1⁡0.49 = 30° .) (1) 55000 (2) 57000 (3) 45000 (4) 66000