Wave Optics PYQs Set 9 (PDF)

Set 9 of 10 · Questions 241-270 of 295

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Mere Teacher · Previous Year Questions JEE Main Physics · Wave Optics · Set 9 (Q241-270)
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241. $A transparent medium shows relation between i and r as shown. If the speed of light in vacuum is c, the Brewster's angle for the sin i medium is$ (1) $60^{\circ}$ (2) $30^{\circ}$ (3) $90^{\circ}$ (4) $45^{\circ}$ 242. $n’ polarizing sheets are arranged such that each makes an angle 45° with the proceeding sheet. An unpolarized light of intensity I is incident into this arrangement. The output intensity is found to be \frac{I}{64} . The value of n will be:$ (1) $3$ (2) $6$ (3) $5$ (4) $4$ 243. $P Q represents a wavefront and AO and BP, the corresponding two rays. Find the condition on O for constructive interference at P between ray BP and reflected ray OP .$ (1) $cos θ = \frac{3 λ}{2 d}$ (2) $cos θ = \frac{λ}{4 d}$ (3) $sec θ - cos θ = \frac{λ}{d}$ (4) $sec θ - cos θ = \frac{4 λ}{d} .$ 244. $In the Young's double slit experiment a monochromatic source of wavelength λ is used. The intensity of light passing through each slit is I_{0} . The intensity of light reaching the screen S_{C} at a point P, a distance x from O is given by (Take d ≪ D)$ (1) $I_{0} cos^{2} (\frac{πD}{λd} x)$ (2) $4 I_{0} cos^{2} (\frac{πd}{λD} x)$ (3) $I_{0} sin^{2} (\frac{πd}{2 λD} x)$ (4) $4 I_{0} cos (\frac{πd}{2 λD} x)$ 245. $Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength λ such that the first minima occurs directly in front of the slit (S_{1}) ?$ (1) $\frac{λ}{2 ( 5 - 2 )}$ (2) $\frac{λ}{( 5 - 2 )}$ (3) $\frac{λ}{2 ( 5 - 2 )}$ (4) $\frac{λ}{( 5 - 2 )}$ 246. $Young’s double slit experiment is carried out by using green, red and blue light, one color at time. The fringe widths recorded are β_{G}, β_{R} and β_{B}, respectively. Then$ (1) $βG > βB > βR$ (2) $βB > βG > βR$ (3) $βR > βB > βG$ (4) $βR > βG > βB$ 247. $A ray of light in vacuum is incident on a glass slab at angle and refracted at angle along as shown in the figure. The optical path length of light ray from to is:$ (1) $\frac{2 3}{a} + 2 b$ (2) $2 a + \frac{2 b}{3}$ (3) $2 a + \frac{2 b}{3}$ (4) $2 a + 2 b$ 248. $Tow beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through 30º makes the two beams appear equally bright. If the initial intensities of the two beams are I_{A} and I_{B} respectively, then \frac{I _{A}}{I _{B}} equals$ (1) $3$ (2) $\frac{3}{2}$ (3) $1$ (4) $\frac{1}{3}$ 249. $The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 μm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)$ (1) $75 μm$ (2) $100 μm$ (3) $25 μm$ (4) $50 μm$ 250. $Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index µ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of µ is:$ (1) $\frac{5}{3}$ (2) $\frac{4}{3}$ (3) $\frac{3}{5}$ (4) $\frac{5}{3}$ 251. $Young's double slit experiment gives interference fringes of width . A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes$ (1) $zero$ (2) $0.45 mm$ (3) $0.3 mm$ (4) $0.15 mm$ 252. $In an experiment, light passing through two slits separated by a distance of 0.3 mm is projected on to a screen placed at 1 m from the plane of slits. It is observed that the distance between the central fringe and the adjacent bright fringe is 1.9 mm . The wavelength of light in nm is$ (1) $450$ (2) $495$ (3) $530$ (4) $570$ 253. $Two coherent sources O_{1} and O_{2} in Young's double slit experiment are illuminated with monochromatic light of wavelength 5000Å . If a second order dark fringe is formed at a point R on the screen, the path difference O_{1} R \sim O_{2} R is$ (1) $7.5 μ m$ (2) $0.75 μ m$ (3) $0.075 μ m$ 254. $Two identical light waves having phase difference φ propagate in same direction. When they superpose, the intensity of resultant wave is proportional to$ (1) $cos^{2} ϕ$ (2) $cos^{2} \frac{ϕ}{2}$ (3) $cos^{2} \frac{ϕ}{3}$ (4) $cos^{2} \frac{ϕ}{4}$ 255. $The box of a pin hole camera, of length L, has hole of radius a. it is assumed that when the hole is illuminated by a parallel beam of light of wavelength the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say ) when :$ (1) $a = λ L and b_{min} = (\frac{2 λ ^{2}}{L})$ (2) $a = λ L and 4 λ L$ (3) $a = \frac{λ ^{2}}{L} and b_{min} = 4 λ L$ (4) $a = \frac{λ ^{2}}{L} and b_{min} = (\frac{2 λ ^{2}}{L})$ 256. $A light source, which emits two wavelengths λ_{1} = 400 nm and λ_{2} = 600 nm, is used in a Young's double slit experiment. If recorded fringe widths for λ_{1} and λ_{2} are β_{1} and β_{2} and the number of fringes for them within a distance y on one side of the central maximum are m_{1} and m_{2}, respectively, then$ (1) $β2 > β1$ (2) $m_{1} > m_{2}$ (3) $From the central maximum, 3rd maximum of λ2 overlaps with 5th minimum of λ1$ (4) $The angular separation of fringes for λ1 is greater than λ2$ 257. $The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. [Geometrical Optics] A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement -1 : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of π Statement -2 : The centre of the interference pattern is dark.$ (1) $Statement-1 is true, statement-2 is false.$ (2) $Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation of Statement-1$ (3) $Statement-1 is true, Statement-2 is true, Statement-2 is not the correct explanation of Statement-1$ (4) $Statement-1 is false, Statement-2 is true$ 258. $Which of the following are true for a single slit diffraction?(A) Width of central maxima increases with increase in wavelength keeping slit width constant.(B) Width of central maxima increases with decrease in wavelength keeping slit width constant.(C) Width of central maxima increases with decrease in slit width at constant wavelength.(D) Width of central maxima increases with increase in slit width at constant wavelength.(E) Brightness of central maxima increases for decrease in wavelength at constant slit width.$ (1) $(A) (C) (E) only$ (2) $(A) (D) only$ (3) $(B) (D) only$ (4) $(B) (C) only$ 259. $Given below are two statements : Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits Statement II: In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength. In the light of the above statements, choose the correct answer from the options given below :$ (1) $Both Statement I and Statement II are false$ (2) $Statement I is false but Statement II is true$ (3) $Both Statement I and Statement II are true$ (4) $Statement I is true but Statement II is false$ 260. $In the Young's double slit experiment, the distance between the slits varies in time as d = d_{0} + a_{0} sin ω t; where d_{0}, ω and a_{0} are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :$ (1) $\frac{2 λ D ( d _{0} )}{( d _{0}^{2} - a _{0}^{2} )}$ (2) $\frac{2 λ D a _{0}}{( d _{0}^{2} - a _{0}^{2} )}$ (3) $\frac{λ D}{d _{0}^{2}} a_{0}$ (4) $\frac{λ D}{d _{0} + a _{0}}$ 261. $Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of \frac{I _{ma x} + I _{min}}{I _{ma x} - I _{min}} is equal to \frac{2 α + 1}{β + 3}, then \frac{α}{β} will be :$ (1) $1.5$ (2) $2$ (3) $0.5$ (4) $1$ 262. $The phenomenon of polarization shows that light has nature.$ (1) $particle$ (2) $transverse$ (3) $longitudinal$ (4) $dual$ 263. $In Young's double slit experiment, if the source of light changes from orange to blue then:$ (1) $the central bright fringe will become a dark fringe.$ (2) $the distance between consecutive fringes will decrease.$ (3) $the distance between consecutive fringes will increase.$ (4) $the intensity of the minima will increase.$ 264. $In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of P_{1} and P_{2} are orthogonal to each other. The polarizer P_{3} covers both the slits with its transmission axis at 45^{\circ} to those of P_{1} and P_{2} . An unpolarized light of wavelength λ and intensity I_{0} is incident on P_{1} and P_{2} . The intensity at a point after P_{3} where the path difference between the light waves from s_{1} and s_{2} is \frac{λ}{3}, is$ (1) $I_{0} 2$ (2) $I_{0} 4$ (3) $I_{0} 3$ (4) $I_{0}$ 265. $If is the intensity of the principal maximum in the single slit diffraction pattern, then what will be the intensity when the slit width is doubled?$ (1) $\frac{I _{0}}{2}$ (2) $I_{0}$ (3) $4 I_{0}$ (4) $2 I_{0}$ 266. $In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm . The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be x \times 10^{- 5} m . The value of x is :$ 267. $A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids P_{1} and P_{2} are so placed in between the source of light and screen that the intensity of light on screen is I/2. P_{2} should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes \frac{3 I}{8}$ 268. $The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is mm. [Refractive index of air =1.0003, wavelength of yellow light in vacuum = 6000 ]$ 269. $In a Young's double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is . The value of is_______$ 270. $Two parallel beams of light P & Q (separation d) containing radiations of wavelengths 4000 Å & 5000 Å (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure. The refractive index of the prism as a function of wavelength is given by the relation, μ (λ) = 1.20 +, where λ is in Å & b is a positive constant. The value of b is such that the condition for total reflection at the face AC is just satisfied for one wavelength & is not satisfied for the other. A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper & the lower beams immediately after transmission from the face AC, are 4I & I respectively, find the resultant intensity at the focus.$