Chapter 24

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude \(A\) and wavelength \(\lambda\). In another experiment with the same setup, the two slits are sources of equal amplitude \(A\) and wavelength \(\lambda\) but are incoherent. The ratio of the intensity of light at the mid- point of the screen in the first case to that in the second case is (a) \(2: 1\) (b) \(1: 2\) (c) \(3: 4\) (d) \(4: 3\)

In an experiment, the two slits are \(0.5 \mathrm{~mm}\) apart and the fringes are observed to \(100 \mathrm{~cm}\) from the plane of the slits. The distance of the 11 th bright fringe from the 1st bright fringe is \(9.72 \mathrm{~mm}\). The wavelength is (a) \(4.86 \times 10^{-5} \mathrm{~cm}\) (b) \(5.72 \times 10^{-4} \mathrm{~cm}\) (c) \(5.87 \times 10^{-4} \mathrm{~cm}\) (d) \(3.25 \times 10^{-4} \mathrm{~cm}\)

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude \(A\) and wavelength \(\lambda\). In another experiment with the same setup, the two slits are sources of equal amplitude \(A\) and wavelength \(\lambda\) but are incoherent. The ratio of the intensity of light at the mid- point of the screen in the first case to that in the second case is (a) \(2: 1\) (b) \(1: 2\) (c) \(3: 4\) (d) \(4: 3\)

In a biprism experiment, by using light of wavelength \(5000 \AA, 5 \mathrm{~mm}\) wide fringes are obtained on a screen \(1.0 \mathrm{~m}\) away from the coherent sources. The separation between the two coherent sources is (a) \(1.0 \mathrm{~mm}\) (b) \(0.1 \mathrm{~mm}\) (c) \(0.05 \mathrm{~mm}\) (d) \(0.01 \mathrm{~mm}\)

Two coherent light sources \(S_{1}\) and \(S_{2}(\lambda=6000 \AA)\) are \(1 \mathrm{~mm}\) apart from each other. The screen is placed at a distance of \(25 \mathrm{~cm}\) from the sources. The width of the fringes on the screen should be (a) \(0.015 \mathrm{~cm}\) (b) \(0.013 \mathrm{~cm}\) (c) \(0.01 \mathrm{~cm}\) (d) \(0.10 \mathrm{~cm}\)

Through quantum theory of light we can explain a number of phenomena observed with light, it is necessary to retain the wave nature of light to explain the phenomenon of (a) Photoelectric effect (b) Diffraction (c) Compton effect (d) Black body radiation

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between slits is \(b\) and the screen is at a distance\(d(>>b)\) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing, figure. Some of these missing wavelengths are (a) \(\lambda=\frac{b^{2}}{d}, \frac{2 b^{2}}{3 d}\) (b) \(\lambda=\frac{b^{2}}{2 d}, \frac{3 b^{2}}{2 d}\) (c) \(\lambda=\frac{2 b^{2}}{3 d}\) (d) \(\lambda=\frac{3 b^{2}}{4 d}\)

A beam of unpolarized light having flux \(10^{-3} \mathrm{~W}\) falls normally on a polarizer of cross-sectional area \(3 \times 10^{-4} \mathrm{~m}^{2}\). The polarizer rotates with an angular frequency of \(31.4 \mathrm{rads}^{-1}\). The energy of light passing through the polarizer per revolution will be (a) \(10^{-4} \mathrm{~J}\) (b) \(10^{-3} \mathrm{~J}\) (c) \(10^{-2} \mathrm{~J}\) (d) \(10^{-1} \mathrm{~J}\)

The fringe width at a distance of \(50 \mathrm{~cm}\) from the slits in Young's experiment for light of wavelength 6000 ? is \(0.048 \mathrm{~cm}\). The fringe width at the same distance for \(\lambda=5000 \AA\), will be (a) \(0.04 \mathrm{~cm}\) (b) \(0.4 \mathrm{~cm}\) (c) \(0.14 \mathrm{~cm}\) (d) \(0.45 \mathrm{~cm}\)

In a biprism experiment, 5 th dark fringe is obtained at a point. If a thin transparent film is placed in the path of one of waves, then 7 th bright fringes is obtained at the same point. The thickness of the film in terms of wavelength \(l\) and refractive index, \(\mu\) will be (a) \(\frac{1.5 \lambda}{(\mu-1)}\) (b) \(1.5\) ( \(\mu-1] \lambda\) (c) \(2.5(\mu-1) \lambda\) (d) \(\frac{2.5 \lambda}{(\mu-1)}\)

The equations of displacement of two waves are given as \(y_{1}=10 \sin (3 \pi t+\pi / 3)\) $$ y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t) $$ then what is the ratio of their amplitude? (a) \(1: 2\) (b) \(2: 1\) (c) \(1: 1\) (d) None of these

In Young's double slit experiment, the seventh maximum with wavelength \(\lambda_{1}\) is at a distance \(d_{1}\) and the same maximum with wavelength \(\lambda_{2}\) is at a distance \(d_{2}\). Then, \(d_{1} / d_{2}=\) (a) \(\frac{\lambda_{1}}{\lambda_{2}}\) (b) \(\frac{\lambda_{2}}{\lambda_{1}}\) (c) \(\frac{\lambda_{1}^{2}}{R_{2}}\) (d) \(\frac{\lambda_{2}^{2}}{\lambda_{1}}\)

Light of wavelength \(\lambda\) is incident on a slit width \(d\). The resulting diffraction pattern is observed on a screen at a distance \(D\). The linear width of the principal maximum is equal to the width of the slit, if \(D\) equals (a) \(\frac{d^{2}}{2 \lambda}\) (b) \(\frac{d}{\lambda}\) (c) \(\frac{2 \lambda^{2}}{d}\) (d) \(\frac{2 \lambda}{d}\)

When monochromatic light is replaced by white light in Fresnel's biprism arrangement, the central fringe is (a) coloured (b) white (c) dark (d) None of these

A glass slab of thickness \(8 \mathrm{~cm}\) contains the same number of waves as \(10 \mathrm{~cm}\) of water when both are traversed by the same monochromatic light. If the refractive index of water is \(4 / 3\), the refractive index of glass is (a) \(5 / 4\) (b) \(3 / 2\) (c) \(5 / 3\) (d) \(16 / 15\)

A glass slab of thickness \(8 \mathrm{~cm}\) contains the same number of waves as \(10 \mathrm{~cm}\) of water when both are traversed by the same monochromatic light. If the refractive index of water is \(4 / 3\), the refractive index of glass is (a) \(5 / 4\) (b) \(3 / 2\) (c) \(5 / 3\) (d) \(16 / 15\)

In a double slit interference experiment, the distance between the slits is \(0.05 \mathrm{~cm}\) and screen is \(2 \mathrm{~m}\) away from the slits. The wavelength of light is \(6000 \AA\). The distance between the fringes is (a) \(0.24 \mathrm{~cm}\) (b) \(0.12 \mathrm{~cm}\) (c) \(1.24 \mathrm{~cm}\) (d) \(2.28 \mathrm{~cm}\)

In Young's double slit experiment \(\frac{d}{D}=10^{-4}\) \((d=\) distance between slits, \(D=\) distance of screen from the slits). At a point \(P\) on the screen resultant intensity is equal to the intensity due to individual slit \(I_{0}\). Then the distance of point \(P\) from the central maximum is \((\lambda=6000 \AA \hat{A})\) (a) \(0.5 \mathrm{~mm}\) (b) \(2 \mathrm{~mm}\) (c) \(1 \mathrm{~mm}\) (d) \(4 \mathrm{~mm}\)

The separation between successive fringes in a double slit arrangement is \(x\). If the whole arrangement is dipped under water, what will be the new fringe separation? [The wavelength of light being used is \(5000 \AA\) A] (a) \(1.5 x\) (b) \(x\) (c) \(0.75 x\) (d) \(2 x\)

In a Young's experiment, two coherent sources are placed \(0.90 \mathrm{~mm}\) aprt and the fringes are observed one metre away. If it produces the second dark fringe at a distance of \(1 \mathrm{~mm}\) from the central fringe, the wavelength of monochromatic light used will be (a) \(60 \times 10^{-4} \mathrm{~cm}\) (b) \(10 \times 10^{-4} \mathrm{~cm}\) (c) \(10 \times 10^{-5} \mathrm{~cm}\) (d) \(6 \times 10^{-5} \mathrm{~cm}\)

The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double slit experiment is (a) Infinite (b) 5 (c) 3 (d) zero

The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double slit experiment is (a) Infinite (b) 5 (c) 3 (d) zero

A ray of light travelling in a transparent medium falls on a surface separating the medium from air, at an angle of incidence of \(45^{\circ}\). The ray undergoes total internal reflection. If, \(\mu\) is refractive index of the medium w.r.t. air, select the possible values of \(\mu\) from the following(a) \(1.5\) (b) \(1.6\) [c) \(1.2\) (d) \(1.3\)

Microwaves from a transmitter are directed normally towards a plane reflector. A detector moves along the normal to the reflector. Between positions of 14 successive maxima, the detector travels a distance of \(0.14 \mathrm{~m}\). The frequency of transmitter is (a) \(1.5 \times 10^{10} \mathrm{~Hz}\) (b) \(10^{10} \mathrm{~Hz}\) (c) \(3 \times 10^{10} \mathrm{hz}\) (d) \(6 \times 10^{10} \mathrm{~Hz}\)

In Young's double slit experiment, white light is used. The separation between the slits is \(b\). The screen is at a distance \(d(d \gg b)\) from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are (a) \(\lambda=\frac{b^{2}}{d}\) (b) \(\lambda=\frac{2 b^{2}}{d}\) (c) \(\lambda=\frac{b^{2}}{3 d}\) (d) \(\lambda=\frac{2 b^{2}}{3 d}\)

Two waves having the intensities in the ratio \(9: 1\) produce interference. The ratio of maximum to minimum intensity is equal to (a) \(10: 8\) (b) \(9: 1\) (c) \(4: 1\) (d) \(2: 1\)

In the Young's double slit experiment, the ratio of intensities of bright and dark fringes is 9. This means that (a) the intensities of individual sources are 5 and 4 units respectively (b) the intensities of individual sources are 4 and 1 units respectively (c) the ratio of their amplitudes is 3 (d) the ratio of their amplitudes is 2

In an interference pattern produced by two identical slits, the intensity at the slit of the central maximum is \(I\). The intensity at the same spot when either of the slits is closed is \(I_{0}\). Therefore, (a) \(I=I_{0}\) (b) \(l=2 I_{0}\) (c) \(l=4 l_{0}\) (d) \(I\) and \(I_{0}\) are not related to each other

Consider sunlight incident on a pinhole of width \(10^{3} \mathrm{~A}\). The image of the pinhole seen on a screen shall be \(\quad\) [NCERT Exemplar] (a) a sharp white ring (b) different from a geometrical image (c) a diffused central spot, white in colour (d) diffused coloured region around a sharp central white spot

In a two slits experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by \(5 \times 10^{-2} \mathrm{~m}\) towards the slits, the change in fringe width is \(3 \times 10^{-5} \mathrm{~m}\). If separation between the slits is \(10^{-3} \mathrm{~m}\), the wavelength of light used is (a) \(4500 \mathrm{~A}\) (b) \(3000 \mathrm{~A}\) (c) \(5000 \mathrm{~A}\) (d) \(6000 \AA\)

A light of wavelength \(6000 \AA\) in air enters a medium of refractive index \(1.5 .\) Inside the medium, its frequency is \(v\) and its wavelength is \(\lambda\). Then, (a) \(\mathrm{v}=5 \times 10^{14} \mathrm{~Hz}\) (b) \(v=7.5 \times 10^{14} \mathrm{~Hz}\) (c) \(\lambda=4000 \AA\) (d) \(\lambda=9000 \dot{A}\)

In Young's double slit experiment, the intensity on screen at a point where path difference is \(\lambda\) is \(K\). What will be intensity at the point where path difference is \(\lambda 4\) ? (a) \(\mathrm{K} / 4\) (b) \(K / 2\) (c) \(\bar{K}\) (d) zero

A light of wavelength \(6000 \AA\) in air enters a medium of refractive index \(1.5 .\) Inside the medium, its frequency is \(v\) and its wavelength is \(\lambda\). Then, (a) \(\mathrm{v}=5 \times 10^{14} \mathrm{~Hz}\) (b) \(v=7.5 \times 10^{14} \mathrm{~Hz}\) (c) \(\lambda=4000 \AA\) (d) \(\lambda=9000 \dot{A}\)

Consider the diffraction pattern for a small pinhole. As the size of the hole is increased [NCERT Exemplar] (a) the size decreases (b) the intensity increases (c) the size increases (d) the intensity decreases

Oil floating on water appears coloured due to interference of light. What should be the order of magnitude of thickness of oil layer in order that this effect may be observed? (a) \(1,000 \mathrm{~A}\) (b) \(1 \mathrm{~cm}\) (c) \(10 \AA\) (d) \(100 \mathrm{~A}\)

In Young's double slit experiment, on interference, ratio of intensities of a bright band and a dark band is \(16: 1\). The ratio of amplitudes of interfering waves is (a) 16 (b) \(5 / 3\) (c) 4 (d) \(1 / 4\)

Two \(\quad\) waves \(\quad y_{1}=A_{1} \sin \left(\omega t-\beta_{1}\right) \quad\) and \(y_{2}=A_{2} \sin \left(\omega t-\beta_{2}\right)\) superimpose to form a resultant wave whose amplitude is (a) \(\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \left(\beta_{1}-\beta_{2}\right)}\) (b) \(\sqrt{\left(A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \sin \left(\beta_{1}-\beta_{2}\right)\right.}\) (c) \(A_{1}+A_{2}\) (d) \(\left|A_{1}+A_{2}\right|\)

For light diverging from a point source [NCERT Exemplar] (a) the wavefront is spherical (b) the intensity decreases in proportion to the distance squared (c) the wavefront is parabolic (d) the intensity at the wavefront does not depend on the distance

In Young's double slit experiment, 12 fringes are obtained in a certain segment of the screen when light of wavelength \(600 \mathrm{~nm}\), is used. If the wavelength of light is changed to \(400 \mathrm{~nm}\), number of fringes observed in the same segment of the screen is given by (a) 12 (b) 18 (c) 24 (d) 30

In Young's double slit experiment, distance between two sources is \(0.1 \mathrm{~mm}\). The distance of screen from the sources is \(20 \mathrm{~cm}\). Wavelength of light used is \(5460 \AA\). Then angular position of first dark fringe is (a) \(0.08^{\prime}\) (b) \(0.16^{\circ}\) (c) \(0.20^{\circ}\) (d) \(032^{\circ}\)

Two beams of light having intensities \(I\) and \(4 I\) interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\pi / 2\) at point \(A\) and \(\pi\) at point \(B\). Then the difference between the resultant intensities at \(A\) and \(B\) is (a) \(2 l\) (b) 41 [c) 51 (d) 71

In a Young's double slit experiment using red and blue lights of wavelengths \(600 \mathrm{~nm}\) and \(480 \mathrm{~nm}\) respectively, the value of \(n\) from which the \(n\)th red fringe coincides with \((n+1)\) the blue fringes is (a) 5 (b) 4 (c) 3 (d) 2

The light waves from two coherent sources are represented by \(y_{1}=a_{1} \sin \omega t\) and \(y_{2}=a_{2} \sin (\omega t+\pi / 2)\) The resultant amplitude will be (a) \(a_{1}\) (b) \(a_{2}\) [c) \(a_{1}+a_{2}\) (d) \(\sqrt{a_{1}^{2}+a_{2}^{2}}\)

In a Young's double slit experiment using red and blue lights of wavelengths \(600 \mathrm{~nm}\) and \(480 \mathrm{~nm}\) respectively, the value of \(n\) from which the \(n\)th red fringe coincides with \((n+1)\) the blue fringes is (a) 5 (b) 4 (c) 3 (d) 2

In Young's double slit experiment, distance between source is \(1 \mathrm{~mm}\) and distance between the screen and source is \(1 \mathrm{~m}\). If the fringe width on the screen is \(0.06 \mathrm{~cm}\), then \(\lambda\) is (a) \(6000 \dot{A}\) (b) \(4000 \hat{A}\) (c) \(1200 \mathrm{~A}\) (d) \(2400 \mathrm{~A}\)

Two slits, \(4 \mathrm{~mm}\) apart are illuminated by light of wavelength \(600 \AA\). What will be the fringe width on a screen placed \(2 \mathrm{~m}\) from the slits? (a) \(0.12 \mathrm{~mm}\) (b) \(0.3 \mathrm{~mm}\) (c) \(3.0 \mathrm{~mm}\) (d) \(4.0 \mathrm{~mm}\)

The widths of two slits in YDSE are in the ratio \(1: 4\). The ratio of amplitudes of light waves from two slits will be (a) \(9: 1\) (b) \(4: 1\) (c) \(1: 2\) (d) \(1: \sqrt{2}\)

In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there should be no interference fringe (b) there should be an interference pattern for red mixing with one for blue (c) there should be altemate interference patterns of red and blue (d) None of the above

Match the following column I with column II. Column I \(\quad\) Column II 1\. Polarization A. Depends on nature of material II. \(\mu=\tan i_{\rho}\) B. Reciprocal of power of lens III. Interference C. Brewster's law IV. Focal length of a D. Coherent sources lens Code (a) \(1-\mathrm{C}, \mathrm{II}-\mathrm{C}, \mathrm{III}-\mathrm{D}, \mathrm{IV}-\mathrm{A}, \mathrm{B}\) (b) \(1-A, \|-C, I I I-D, I V-B\), (c) \(1-\mathrm{A}, \mathrm{II}-\mathrm{B}, \mathrm{III}-\mathrm{C}, \mathrm{IV}-\mathrm{D}\) (d) \(1-\mathrm{D}, \mathrm{II}-\mathrm{C}, \mathrm{III}-\mathrm{A}, \mathrm{IV}-\mathrm{C}_{+} \mathrm{D}\)

Three waves of equal frequency having amplitudes \(10 \mu \mathrm{m}, 4 \mu \mathrm{m}, 7 \mu \mathrm{m}\) arrive at a given point with successive phase difference of \(\frac{\pi}{2}\), the amplitude of the resulting wave (in \(\mu \mathrm{m}\) ) is given by (a) 4 (b) 5 (c) 6 (d) 7