Wave Optics PYQs Set 10 (PDF)

Set 10 of 10 · Questions 271-295 of 295

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Optics · Set 10 (Q271-295)
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271. $Two coherent monochromatic point sources S_{1} and S_{2} of wavelength λ = 600 nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is Δθ. Which of the following options is/are correct ?$ (1) $The total number of fringes produced between P_{1} and P_{2} in the first quadrant is close to 3000$ (2) $A dark spot will be formed at the point P_{2}$ (3) $At P_{2} the order of the fringe will be maximum$ (4) $The angular separation between two consecutive bright spots decreases as we move from P_{1} to P_{2} along the first quadrant$ 272. $In Young's double slit experiment, a third slit is made in between the double slits. Then$ (1) $fringes of unequal width are formed$ (2) $contrast between bright and dark fringes is reduced$ (3) $intensity of fringes totally disappears$ (4) $only bright light is observed on the screen.$ 273. $While conducting the Young's double slit experiment, a student replaced to two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources (S_{1}, S_{2}) emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0) at a distance D = 3 m from the mid-point of S_{1} S_{2}, as shown schematically in the figure. The distance between the sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S_{1} S_{2} . Which of the following is(are) true of the intensity pattern on the screen ?$ (1) $Semi circular bright and dark bands centered at point O$ (2) $Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction$ (3) $The region very close to the point O will be dark$ (4) $Straight bright and dark bands parallel to the x-axis$ 274. $Electric field in a plane electromagnetic wave is given by E = 50 sin (500 x - 10 \times 1 0^{10} t) V / m . The velocity of electromagnetic wave in this medium is : (Given C = speed of light in vacuum)$ (1) $\frac{3}{2} C$ (2) $C$ (3) $\frac{2}{3} C$ (4) $\frac{C}{2}$ 275. $In a Young's double slit experiment, two slits are illuminated with a light of wavelength 800 nm. The line joining A_{1} P is perpendicular to A_{1} A_{2} as shown in the figure. If the first minimum is detected at P, the value of slits separation 'a' will be: The distance of screen from slits D = 5 cm$ (1) $0.4 mm$ (2) $0.5 mm$ (3) $0.2 mm$ (4) $0.1 mm$ 276. $Light emerges out of a convex lens when a source of light kept at its focus. The shape of wave front of the light is:$ (1) $both spherical and cylindrical$ (2) $plane$ (3) $spherical$ (4) $cylindrical$ 277. $On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :$ (1) $becomes narrower$ (2) $goes horizontally without any deflection$ (3) $bends downwards$ (4) $bends upwards$ 278. $An unpolarised light beam of intensity 2 I_{0} is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is$ (1) $\frac{I _{0}}{4}$ (2) $\frac{I _{0}}{2}$ (3) $\frac{3 I _{0}}{4}$ (4) $\frac{3 I _{0}}{2}$ 279. $The interference pattern is obtained with two coherent light sources of intensity ratio 4:1. And the ratio \frac{I _{ma x} + I _{min}}{I _{ma x} - I _{min}} is \frac{5}{x} . Then, the value of x will be equal to :$ (1) $3$ (2) $4$ (3) $2$ (4) $1$ 280. $Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is , then Brewster's angle for the light propagating from glass to air is Statement II : The Brewster's angle for the light propagating from glass to air is where is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both Statements I and Statement II are true.$ (2) $Statement I is true but Statement II is false.$ (3) $Both Statement I and Statement II arc false.$ (4) $Statement I is false but Statement II is true.$ 281. $A cylindrical tube of length 0.2 m and radius R with sugar solution of concentration ' C' produce a rotation of θ in the plane of vibration of a plane polarized light. The same sugar solution is transferred to another tube of length 0.3 m of same radius. The remaining gap is filled by distilled water. Now the optical rotation produced is$ (1) $θ$ (2) $\frac{2 θ}{3}$ (3) $\frac{3 θ}{2}$ (4) $\frac{9 θ}{4}$ 282. $Which of the following phenomena support the wave theory of light?1.Scattering2.Interference3.Diffraction4.Velocity of light in a denser medium is less than the velocity of light in the rarer medium$ (1) $1, 2, 3$ (2) $1, 2, 4$ (3) $2, 3, 4$ (4) $1, 3, 4$ 283. $Consider the following statements in case of Young's double slit experiment. (1) A slit S is necessary if we use an ordinary extended source of light. (2) A slit S is not needed if we use an ordinary but well collimated beam of light. (3) A slit S is not needed if we use a spatially coherent source of light. Which of the above statements are correct?$ (1) $(1), (2) and (3)$ (2) $(1) and (2)$ (3) $(2) and (3)$ (4) $(1) and (3)$ 284. $In single slit experiment, the width of the slit is reduced. Then, the linear width of the principal maxima...$ (1) $increases but becomes less bright$ (2) $decreases but becomes more bright$ (3) $increases but becomes more bright$ (4) $decreases but becomes less bright.$ 285. $In Young's double slit experiment the source is white light. One slit is covered with red filter and the other with blue filter. There shall be$ (1) $alternate red and blue fringes$ (2) $alternate dark and pink fringes$ (3) $alternate dark and yellow fringes$ (4) $no interference.$ 286. $Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is 2.5 \times 10^{- 3} m and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is$ (1) $12.2 m$ (2) $24.4 m$ (3) $2.44 m$ (4) $1.22 m$ 287. $Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A: The beam of electrons shows wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below :$ (1) $A is correct but R is not correct$ (2) $A is not correct but R is correct$ (3) $Both A and R are correct but R is Not the correct explanation of A$ (4) $Both A and R are correct and R is the correct explanation of A$ 288. $In a double-slit experiment, green light falls on a double slit having a separation of and a width of The number of bright fringes between the first andthe second diffraction minima is :$ (1) $10$ (2) $05$ (3) $04$ (4) $09$ 289. $The light waves from two coherent sources have same intensity I_{1} = I_{2} = I_{0} . In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?$ (1) $I_{0}$ (2) $2 I_{0}$ (3) $5 I_{0}$ (4) $4 I_{0}$ 290. $Two coherent point sources S_{1} and S_{2} are separated by a small distance 'd' as shown. The fringes obtained on the screen will be :$ (1) $points$ (2) $straight lines$ (3) $semi-circles$ (4) $concentric circles$ 291. $As shown in the figure, in Young's double slit experiment, a thin plate of thickness t = 10 m and refractive index =1.2 is inserted infront of slit . The experiment is conducted in air (= 1) and uses a monochromatic light of wavelength = 500 nm. Due to the insertion of the plate, central maxima is shifted by a distance of is the fringe-width before the insertion of the plate, The value of the x is_____.$ 292. $Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium -1) and 6.8 (medium -2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be the value of is ______. (Given for dielectric media, )$ 293. $Two light waves of wavelengths 800 and 600 nm are used in Young's double slit experiment to obtain interference fringes on a screen placed 7 m away from plane of slits. If the two slits are separated by 0.35 mm, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ mm.$ 294. $A plane electromagnetic wave with frequency of 30MHz travels in free space. At particular point in space and time, electric field is 6V/m. The magnetic field at this point will be x \times 1 0^{- 8} T . The value of x is .....$ 295. $In a Young's double slit experiment, the intensities at two points, for the path difference \frac{λ}{4} and \frac{λ}{3} (λ, being the wavelength of light used) are I_{1} and I_{2} respectively. If Io denotes the intensity produced by each one of the individual slits, then \frac{I _{1} + I _{2}}{I _{0}} = ...$