Chapter 24

Light propagates \(2 \mathrm{~cm}\) distance in glass of refractive index \(1.5\) in time \(t_{0}\). In the same time \(t_{0}\), light propagates a distance of \(2.25 \mathrm{~cm}\) in a medium. The refractive index of the medium is (a) \(4 / 3\) (b) \(3 / 2\) (c) \(8 / 3\) (d) None of these

The ratio of intensities of two waves is \(9: 1\). They are producing interference. The ratio of maximum and minimum intensities will be (a) \(10: 8\) (b) \(9: 1\) (c) \(4: 1\) (d) \(12: 1\)

The ratio of intensities of two waves is \(9: 1\). They are producing interference. The ratio of maximum and minimum intensities will be (a) \(10: 8\) (b) \(9: 1\) (c) \(4: 1\) (d) \(12: 1\)

Interference was observed in interference chamber when air was present, now the chamber is evacuated and if, the same light is used, a careful observer will see (a) interference in which width of the fringe will be slightly increased (b) interference with bright band (c) interference with dark band (d) All of the above

In a Young's double-slit experiment, the slits are separated by \(0.28 \mathrm{~mm}\) and the screen is placed \(1.4 \mathrm{~m}\) away. The distance between the central bright fringe and the fourth bright fringe is measured to be \(1.2 \mathrm{~cm}\). Determine the wavelength of light used in the experiment. [NCERT] (a) \(4 \times 10^{-9} \mathrm{~m}\) (b) \(5 \times 10^{-10} \mathrm{~m}\) (c) \(3 \times 10^{-7} \mathrm{~m}\) (d) \(6 \times 10^{-7} \mathrm{~m}\)

Consider sunlight incident on a slit of width \(10^{4} \mathrm{~A}\). The image seen through the slit shall [NCERT Exemplar] (a) be a fine sharp slit white in colour at the centre (b) a bright slit. white at the centre diffusing to zero intensities at the edges (c) a bright slit white at the centre diffusing to regions of different colours (d) Only be a diffused slit white in colour

A stone thrown into still water, creates a circular wave pattern moving radially outwards. If, \(r\) is the distance measured from the centre of the pattern, the amplitude of the wave varies as (a) \(r^{-3 / 2}\) (b) \(\underline{r^{-1 / 2}} \quad\) (c) \(r^{-1}\) (d) \(r^{1 / 3}\)

Monochromatic light of wavelength \(589 \mathrm{~nm}\) is incident from air on a water surface. What are the wavelength and speed of refracted light? Refractive index of water is \(1.33 .\) (NCERT] (a) \(4.20 \times 10^{-6}\) and \(4.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\) (b) \(3.68 \times 10^{-9} \mathrm{~m}\) and \(3.02 \times 10^{7} \mathrm{~m} / \mathrm{s}\) (c) \(1.9 \times 10^{-10} \mathrm{~m}\) and \(3.2 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (d) \(4.42 \times 10^{-7} \mathrm{~m}\) and \(2.25 \times 10^{6} \mathrm{~m} / \mathrm{s}\)

If, an interference pattern has maximum and minimum intensities in \(36: 1\) ratio, then what will be the ratio of amplitudes? (a) \(4: 5\) (b) \(7: 5\) (c) \(6: 5\) (d) \(3: 4\)

The waves of wavelength 5900 A emitted by any atom or molecule must have some finite total length which is known as coherent length. For sodium light, this length is \(2.4 \mathrm{~cm}\). The number of oscillations in this length will be(a) \(4.068 \times 10^{5}\) (b) \(4.068 \times 10^{6}\) (c) \(4.068 \times 10^{7}\) (d) \(4.068 \times 10^{4}\)

In Young's double slit experiment, the spacing between the slits is \(d\) and wavelength of light used is \(6000 \mathrm{~A}\). If the angular width of a fringe formed on a distance screen is \(1^{\circ}\), then value of \(d\) is (a) \(1 \mathrm{~mm}\) (b) \(0.05 \mathrm{~mm}\) (c) \(0.03 \mathrm{~mm}\) (d) \(0.01 \mathrm{~mm}\)

In a certain double slit experimental arrangement interference fringes of width \(1.0 \mathrm{~mm}\) each are observed when light of wavelength \(5000 \mathrm{~A}\) is used. Keeping the setup unaltered, if the source is replaced by another source of wavelength \(6000 \AA\), the fringe width will be (a) \(1.2 \mathrm{~mm}\) (b) \(1.5 \mathrm{~mm}\) (c) \(1.8 \mathrm{~mm}\) (d) \(2.0 \mathrm{~mm}\)

In Young's double slit experiment, when violet light of wavelength \(4358 \AA\) is used, the 84 fringes are seen in the field of view, but when sodium light of certain wavelength is used, then 62 fringes are seen in the field of view, the wavelength of sodium light is (a) \(6893 \mathrm{~A}\) (b) \(5904 \mathrm{~A}\) (c) \(5523 \mathrm{~A}\) (d) \(6429 \mathrm{~A}\)

In a certain double slit experimental arrangement interference fringes of width \(1.0 \mathrm{~mm}\) each are observed when light of wavelength \(5000 \mathrm{~A}\) is used. Keeping the setup unaltered, if the source is replaced by another source of wavelength \(6000 \AA\), the fringe width will be (a) \(1.2 \mathrm{~mm}\) (b) \(1.5 \mathrm{~mm}\) (c) \(1.8 \mathrm{~mm}\) (d) \(2.0 \mathrm{~mm}\)

Consider a ray of light incident from air into a slap of glass (refractive index \(n\) ) of width \(d\), at an angle \(\theta\). The phase difference between the ray reflected by the top surface of the glass and the bottom surface is [NCERT Exemplar] (a) \(\frac{4 \pi n d}{\lambda}\left(1-\frac{1}{n^{2}} \sin ^{2} \theta\right)^{-1 / 2}+\pi\) (b) \(\frac{4 \pi d}{\lambda}\left(1-\frac{1}{n^{2}} \sin ^{2} \theta\right)^{12}\) (c) \(\frac{4 \pi d}{\lambda}\left(1-\frac{1}{n^{2}} \sin ^{2} \theta\right)^{1 / 2}+\frac{\pi}{2}\) (d) \(\frac{4 \pi d}{\lambda}\left(1-\frac{1}{n^{2}} \sin ^{2} \theta\right)^{12}+2 \pi\)

\(\begin{array}{lllll}\text { In } & \text { Young's } & \text { double-slit } & \text { experiment } & \text { using }\end{array}\) monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\) i.e., \(K\) units. What is the intensity of light at a point where path difference is N3? [NCERT] (a) \(\frac{K}{4}\) (b) \(\frac{K}{5}\) (c) \(\frac{K}{7}\) (d) \(\frac{K}{2}\)

In Young's double slit experiment, we get 60 fringes in the field of view of monochromatic light of wavelength \(4000 \AA\). If we use monochromatic light of wavelength \(6000 \AA\), then the number of fringes obtained in the same field of view are (a) 60 (b) 90 (c) 40 (d) \(1.5\)

The maximum intensity in the case of \(n\) identical incoherent waves, each of intensity \(2 \mathrm{Wm}^{-2}\) is \(32 \mathrm{Wm}^{-2}\). The value of \(n\) is (a) 4 (b) 16 (c) 32 (d) 64

The phenomenon which does not take place in sound waves is (a) scattering (b) diffraction (c) interference (d) polarisation

In an interference pattern the position of zeroth order maxima is \(4.8 \mathrm{~mm}\) from a certain point \(P\) on the screen. The fringe width is \(0.2 \mathrm{~mm}\). The position of second maxima from point \(P\) is (a) \(5.1 \mathrm{~mm}\) (b) \(5 \mathrm{~mm}\) (c) \(40 \mathrm{~mm}\) (d) \(5.2 \mathrm{~mm}\)

Two Nicol prisms are first crossed and then one of them is rotated through \(60^{\circ}\). The percentage of incident light transmitted is (a) \(\underline{1.25}\) (b) \(25.0\) (c) \(37.5\) (d) 50

\(S_{1}\) and \(S_{2}\) are two coherent sources, The intensity of both sources are same. If the intensity at the point of maxima is \(4 \mathrm{Wm}^{-2}\), the intensity of each source is (a) \(1 \mathrm{Wm}^{-2}\) (b) \(2 \mathrm{Wm}^{-2}\) (c) \(3 \mathrm{Wm}^{-2}\) (d) \(4 \mathrm{Wm}^{-2}\)

Two Nicol prisms are first crossed and then one of them is rotated through \(60^{\circ}\). The percentage of incident light transmitted is (a) \(\underline{1.25}\) (b) \(25.0\) (c) \(37.5\) (d) 50

\(S_{1}\) and \(S_{2}\) are two coherent sources, The intensity of both sources are same. If the intensity at the point of maxima is \(4 \mathrm{Wm}^{-2}\), the intensity of each source is (a) \(1 \mathrm{Wm}^{-2}\) (b) \(2 \mathrm{Wm}^{-2}\) (c) \(3 \mathrm{Wm}^{-2}\) (d) \(4 \mathrm{Wm}^{-2}\)

Find the thickness of a plate which will produce a change in optical path equal to half the wavelength \(\lambda\) of the light passing through it normally. The refractive index of the plate \(\mu\) is equal to (a) \(\frac{\lambda}{4(\mu-1)}\) (b) \(\frac{2 \lambda}{4(\mu-1)}\) (c) \(\frac{\lambda}{(\mu-1)}\) (d) \(\frac{\lambda}{2(\mu-1)}\)

Light of wavelength \(2 \times 10^{-3} \mathrm{~m}\) falls on a slit of width \(4 \times 10^{-3} \mathrm{~m}\). The angular dispersion of the central maximum will be (a) \(30^{\circ}\) (b) \(60^{\circ}\) (c) \(90^{\circ}\) (d) \(180^{*}\)

\(n\)th bright fringe if red light \(\left(\lambda_{1}=7500 \mathrm{~A}\right)\) coincides with \((n+1)\) th bright fringe of green light \(\left(\lambda_{2}=6000 \AA\right.\) A \()\). The value of \(n\), is (a) 4 (b) 5 (c) 3 (d) 2

In double-slit experiment using light of wavelength \(600 \mathrm{~nm}\), the angular width of a fringe formed on a distant screen is \(0.1^{\circ} .\) What is the spacing between the two slits? (a) \(3.44 \times 10^{-4} \mathrm{~m}\) (b) \(3.03 \times 10^{-4} \mathrm{~m}\) (c) \(4.03 \times 10^{-4} \mathrm{~m}\) (d) \(2.68 \times 10^{-4} \mathrm{~m}\)

A parallel beam of light of intensity \(I_{0}\) is incident on a glass plate, \(25 \%\) of light is reflected by upper surface and \(50 \%\) of light is reflected from lower surface. The ratio of maximum to minimum intensity in interference region of reflected rays is (a) \(\left(\frac{\frac{1}{2}+\sqrt{\frac{3}{8}}}{\frac{1}{2}-\sqrt{\frac{3}{8}}}\right)^{2}\) (b) \(\left(\frac{\frac{1}{4}+\sqrt{\frac{3}{8}}}{\frac{1}{2}-\sqrt{\frac{3}{8}}}\right)^{2}\) (c) \(\frac{5}{8}\) (d) \(\frac{8}{5}\)

A light of wavelength 5890 A falls normally on a thin air film. The minimum thickness of the film such that the film appears dark in reflected light is (a) \(2.945 \times 10^{-7} \mathrm{~m}\) (b) \(3.945 \times 10^{-7} \mathrm{~m}\) (c) \(4.95 \times 10^{-7} \mathrm{~m}\) (d) \(1.945 \times 10^{-7} \mathrm{~m}\)

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 [NCERT Exemplar] (a) there shall be altemate interference patterns of red and blue (b) there shall be an interference pattem for red distirct from that for blue (c) there shall be no interference fringes (d) there shall be an interference pattern for red mixiting

In Young's double slit experiment, a minimum is obtained when the phase difference of super imposing waves is (a) zero (b) \([2 n-1) \pi\) (c) \(n \pi\) (d) \((n+1) \pi\)

In a Young's experiment, one of the slits is covered with a transparent sheet of thickness \(3.6 \times 10^{-3} \mathrm{~cm}\) due to which position of central fringe shifts to a position originally occupied by 30 th fringe. The refractive index of the sheet, if \(\lambda=6000 \AA\), is (a) \(1.5\) (b) \(1.2\) (c) \(1.3\) (d) \(1.7\)

Light waves travel in vacuum along the \(y\)-axis. Which of the following may represent the wavefront? (a) \(y=\) constant (b) \(x=\) constant (c) \(z=\) constant (d) \(x+y+z=\) constant

The velocity of a moving galaxy is \(300 \mathrm{~km} \mathrm{~s}^{-1}\) and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as \(0.5 \mathrm{~nm}\). Then, the actual wavelength of the spectral line is (a) \(3000 \mathrm{~A}\) (b) \(5000 \AA\) (c) \(6000 \mathrm{~A}\) (d) \(4500 \dot{A}\) (e) \(5500 \mathrm{~A}\)

In Young's double slit experiment, if \(d, D\) and \(\lambda\) represent, the distance between the slits, the distance of the screen from the slits and wavelength of light used respectively, then the bandwidth is inversely proportional to (a) \(\underline{\lambda}\) (b) \(d\) (c) \(D\) (d) \(\lambda^{2}\) (e) \(D^{2}\)

Two coherent waves are represented by \(y_{1}=a_{1} \cos \omega t\) and \(y_{2}=a_{2} \sin \omega t\), superimposed on each other. The resultant intensity is proportional to (a) \(\left(a_{1}+a_{2}\right)\) (b) \(\left(a_{1}-a_{2}\right)\) (c) \(\left(a_{1}^{2}+a_{2}^{2}\right)\) (d) \(\left(a_{1}^{2}-a_{2}^{2}\right)\)

In Young's double slit experiment, if \(d, D\) and \(\lambda\) represent, the distance between the slits, the distance of the screen from the slits and wavelength of light used respectively, then the bandwidth is inversely proportional to (a) \(\underline{\lambda}\) (b) \(d\) (c) \(D\) (d) \(\lambda^{2}\) (e) \(D^{2}\)

The maximum intensity of fringes in Young's experiment is \(I .\) If one of the slit is closed, then the intensity at that place becomes \(I_{0}\). Which of the following relation is true? (a) \(I=\bar{I}_{0}\) (b) \(l=2 l_{0}\) (c) \(1=4 l_{0}\) (d) \(I=0\)

In Young's two slit experiment the distance between the two coherent sources is \(2 \mathrm{~mm}\) and the screen is at a distance of \(1 \mathrm{~m}\). If the fringe width is found to be \(0.03 \mathrm{~cm}\), then the wavelength of the light used is (a) \(4000 \mathrm{~A}\) (b) \(5000 \mathrm{~A}\) (c) \(5890 \mathrm{~A}\) (d) \(6000 \dot{A}\)

The equations of two interfering waves are \(y_{1}=b \cos \omega t\) and \(y_{2}=b \cos (\omega t+\phi) .\) For destructive interference the path difference is (a) \(0^{\circ}\) (b) \(360^{*}\) (c) \(180^{\circ}\) (d) \(720^{\circ}\)

The Young's double slit experiment is performed with blue and with green light of wavelengths 4360 Á and \(5460 \mathrm{~A}\) respectively. If, \(x\) is the distance of 4 th maxima from the central one, then[a) \(x\) (blue) \(=x\) (green) (b) \(x\) (blue) \(>x\) (green) (c) \(x(\) blue \()

Two slits separated by a distance of \(1 \mathrm{~mm}\) are illuminated with red light of wavelength \(6.5 \times 10^{-7} \mathrm{~m}\). The interference fringes are observed on a screen place \(1 \mathrm{~m}\) from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to (a) \(0.65 \mathrm{~mm}\) (b) \(1.63 \mathrm{~mm}\) (c) \(3.25 \mathrm{~mm}\) (d) \(4.88 \mathrm{~mm}\)

Two slits separated by a distance of \(1 \mathrm{~mm}\) are illuminated with red light of wavelength \(6.5 \times 10^{-7} \mathrm{~m}\). The interference fringes are observed on a screen place \(1 \mathrm{~m}\) from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to (a) \(0.65 \mathrm{~mm}\) (b) \(1.63 \mathrm{~mm}\) (c) \(3.25 \mathrm{~mm}\) (d) \(4.88 \mathrm{~mm}\)

Two light rays having the same wavelength \(\lambda\) in vacuum are in phase initially. Then the first ray travels a path \(L_{1}\) through a medium of refractive index \(n_{1}\), while the second ray travels a path of length \(L_{2}\) through a medium of refractive index \(n_{2}\). The two waves are then combined to observe interference. The phase difference the two waves is (a) \(\frac{2 \pi}{\lambda}\left(L_{2}-L_{1}\right)\) (b) \(\frac{2 \pi}{\lambda}\left(n_{1} L_{1}-m_{2} L_{2}\right)\) (c) \(\frac{2 \pi}{\lambda}\left(n_{2} L_{1}-n_{1} L_{2}\right)\) (d) \(\frac{2 \pi}{\lambda}\left(\frac{L_{1}}{n_{1}}-\frac{L_{2}}{n_{2}}\right)\)

If white light is used in a biprism experiment, then (a) fringe pattern disappers (b) all fringes will be coloured (c) central fringe will be white while others will be coloured (d) central fringe will be dark

Two waves of same frequency and same amplitude from two monochromatic source are allowed to superpose at a certain point. If in one case the phase difference is \(0^{\circ}\) and in other case is \(\pi / 2\), the ratio of the intensities in the two cases will be (a) \(1: 1\) (b) \(2: 1\) (c) \(4: 1\) (d) None of these

We shift Young's double slit experiment from air to water. Assuming that water is still and clear, it can be perdicted that the fringe pattern will (a) remain unchanged (b) disappear (c) shrink (d) be enlarged

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of \(45^{\circ}\). The percentage of incident light now transmitted through the system is (a) 159 (b) 2596 (c) \(50 \%\) (d) 6096

In Young's double slit experiment, the separation between slit is halved and the distance between the slits and screen is doubled. The fringe width is (a) unchanged (b) halved (c) double (d) quardrupled