10.4 In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

10.5 INTERFERENCE OF LIGHT WAVES AND YOUNG’S EXPERIMENT We will now discuss interference using light waves. If we use two sodium lamps illuminating two pinholes (Fig. 10.11) we will not observe any interference fringes. This is because of the fact that the light wave emitted from an ordinary source (like a sodium lamp) undergoes abrupt phase changes in times of the order of 10–10 seconds. Thus the light waves coming out from two independent sources of light will not have any fixed phase relationship and would be incoherent, when this FIGURE 10.11 If two sodium happens, as discussed in the previous section, the lamps illuminate two pinholes intensities on the screen will add up. S1 and S2, the intensities will add The British physicist Thomas Young used an up and no interference fringes will ingenious technique to “lock” the phases of the waves be observed on the screen. emanating from S1 and S2. He made two pinholes S1 and S2 (very close to each other) on an opaque screen [Fig. 10.12(a)]. These were illuminated by another pinholes that was in turn, lit by a bright source. Light waves spread out from S and fall on both S1 and S2. S1 and S2 then behave like two coherent sources because light waves coming out from S1 and S2 are derived from the same original source and any abrupt phase change in S will manifest in exactly similar phase changes in the light coming out from S1 and S2. Thus, the two sources S1 and S2 will be locked in phase; i.e., they will be coherent like the two vibrating needle in our water wave example [Fig. 10.8(a)]. The spherical waves emanating from S1 and S2 will produce interference fringes on the screen GG¢, as shown in Fig. 10.12(b). The positions of maximum and minimum intensities can be calculated by using the analysis given in Section 10.4. (a) (b) FIGURE 10.12 Young’s arrangement to produce interference pattern. 265 Reprint 2025-26 Physics We will have constructive interference resulting in a bright xd region when = nl. That is, D n λD x = xn = ; n = 0, ± 1, ± 2, ... (10.13) d On the other hand, we will have destructive xd 1 interference resulting in a dark region when = (n+ ) l D 2 that is  1 D1829) ) ; n  0,  1,  2 (10.14) x = xn = (n+– 2 d Thomas Young Thus dark and bright bands appear on the screen, (1773 – 1829) English as shown in Fig. 10.13. Such bands are called fringes. physicist, physician and Equations (10.13) and (10.14) show that dark and(1773 Egyptologist. Young worked bright fringes are equally spaced. on a wide variety of scientific problems, ranging from the structure of the eye and the mechanism ofYOUNG vision to the decipherment of the Rosetta stone. He revived the wave theory of light and recognised that interference phenomenaTHOMAS provide proof of the wave properties of light. FIGURE 10.13 Computer generated fringe pattern produced by two point source S1 and S2 on the screen GG¢ (Fig. 10.12); d = 0.025 mm, D = 5 cm and l = 5 × 10–5 cm.) (Adopted from OPTICS by A. Ghatak, Tata McGraw Hill Publishing Co. Ltd., New Delhi, 2000.) 10.6 DIFFRACTION If we look clearly at the shadow cast by an opaque object, close to the region of geometrical shadow, there are alternate dark and bright regions just like in interference. This happens due to the phenomenon of diffraction. Diffraction is a general characteristic exhibited by all types of waves, be it sound waves, light waves, water waves or matter waves. Since the wavelength of light is much smaller than the dimensions of most 266 obstacles; we do not encounter diffraction effects of light in everyday Reprint 2025-26 Wave Optics observations. However, the finite resolution of our eye or of optical instruments such as telescopes or microscopes is limited due to the phenomenon of diffraction. Indeed the colours that you see when a CD is viewed is due to diffraction effects. We will now discuss the phenomenon of diffraction. 10.6.1 The single slit In the discussion of Young’s experiment, we stated that a single narrow slit acts as a new source from which light spreads out. Even before Young, early experimenters – including Newton – had noticed that light spreads out from narrow holes and slits. It seems to turn around corners and enter regions where we would expect a shadow. These effects, known as diffraction, can only be properly understood using wave ideas. After all, you are hardly surprised to hear sound waves from someone talking around a corner! When the double slit in Young’s experiment is replaced by a single narrow slit (illuminated by a monochromatic source), a broad pattern with a central bright region is seen. On both sides, there are alternate dark and bright regions, the intensity becoming weaker away from the centre (Fig. 10.15). To understand this, go to Fig. 10.14, which shows a parallel beam of light falling normally on a single slit LN of width a. The diffracted light goes on to meet FIGURE 10.14 The geometry of path a screen. The midpoint of the slit is M. differences for diffraction by a single slit. A straight line through M perpendicular to the slit plane meets the screen at C. We want the intensity at any point P on the screen. As before, straight lines joining P to the different points L,M,N, etc., can be treated as parallel, making an angle q with the normal MC. The basic idea is to divide the slit into much smaller parts, and add their contributions at P with the proper phase differences. We are treating different parts of the wavefront at the slit as secondary sources. Because the incoming wavefront is parallel to the plane of the slit, these sources are in phase. It is observed that the intensity has a central maximum at q = 0 and other secondary maxima at q l (n+1/2) l/a, which go on becoming weaker and weaker with increasing n. The minima (zero intensity) are at q l nl/a, n = ±1, ±2, ±3, .... FIGURE 10.15 Intensity The photograph and intensity pattern corresponding distribution and photograph of to it is shown in Fig. 10.15. fringes due to diffraction There has been prolonged discussion about at single slit. difference between intereference and diffraction among 267 Reprint 2025-26 Physics scientists since the discovery of these phenomena. In this context, it is interesting to note what Richard Feynman* has said in his famous Feynman Lectures on Physics: No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do is, roughly speaking, is to say that when there are only a few sources, say two interfering sources, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used. In the double-slit experiment, we must note that the pattern on the screen is actually a superposition of single-slit diffraction from each slit or hole, and the double-slit interference pattern. 10.6.210.6.210.6.210.6.210.6.2 SeeingSeeingSeeingSeeingSeeing thethethethethe singlesinglesinglesinglesingle slitslitslitslitslit diffractiondiffractiondiffractiondiffractiondiffraction patternpatternpatternpatternpattern It is surprisingly easy to see the single-slit diffraction pattern for oneself. The equipment needed can be found in most homes –– two razor blades and one clear glass electric bulb preferably with a straight filament. One has to hold the two blades so that the edges are parallel and have a narrow slit in between. This is easily done with the thumb and forefingers (Fig. 10.16). Keep the slit parallel to the filament, right in front of the eye. Use spectacles if you normally do. With slight adjustment of the width of the slit and the parallelism of the edges, the pattern should be seen with its bright and dark bands. Since the position of all the bands (except the central one) depends on wavelength, they will show some colours. Using a filter for red or blue will make the fringes clearer. With both filters available, the wider fringes for red compared to blue FIGUREFIGUREFIGUREFIGUREFIGURE 10.1610.1610.1610.1610.16 can be seen. Holding two blades to In this experiment, the filament plays the role of the first slit S in form a single slit. A bulb filament viewed Fig. 10.15. The lens of the eye focuses the pattern on the screen (the through this shows retina of the eye). clear diffraction With some effort, one can cut a double slit in an aluminium foil with bands. a blade. The bulb filament can be viewed as before to repeat Young’s experiment. In daytime, there is another suitable bright source subtending a small angle at the eye. This is the reflection of the Sun in any shiny convex surface (e.g., a cycle bell). Do not try direct sunlight – it can damage the eye and will not give fringes anyway as the Sun subtends an angle of (1/2)°. In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy. * Richard Feynman was one of the recipients of the 1965 Nobel Prize in Physics 268 for his fundamental work in quantum electrodynamics. Reprint 2025-26 Wave Optics

10.6 A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide? 273 Reprint 2025-26 Physics Chapter Eleven DUAL NATURE OF RADIATION AND MATTER 11.1 INTRODUCTION The Maxwell’s equations of electromagnetism and Hertz experiments on the generation and detection of electromagnetic waves in 1887 strongly established the wave nature of light. Towards the same period at the end of 19th century, experimental investigations on conduction of electricity (electric discharge) through gases at low pressure in a discharge tube led to many historic discoveries. The discovery of X-rays by Roentgen in 1895, and of electron by J. J. Thomson in 1897, were important milestones in the understanding of atomic structure. It was found that at sufficiently low pressure of about 0.001 mm of mercury column, a discharge took place between the two electrodes on applying the electric field to the gas in the discharge tube. A fluorescent glow appeared on the glass opposite to cathode. The colour of glow of the glass depended on the type of glass, it being yellowish-green for soda glass. The cause of this fluorescence was attributed to the radiation which appeared to be coming from the cathode. These cathode rays were discovered, in 1870, by William Crookes who later, in 1879, suggested that these rays consisted of streams of fast moving negatively charged particles. The British physicist J. J. Thomson (1856-1940) confirmed this hypothesis. By applying mutually perpendicular electric and magnetic fields across the discharge 274 tube, J. J. Thomson was the first to determine experimentally the speed Reprint 2025-26 Dual Nature of Radiation and Matter and the specific charge [charge to mass ratio (e/m)] of the cathode ray particles. They were found to travel with speeds ranging from about 0.1 to 0.2 times the speed of light (3 ×108 m/s). The presently accepted value of e/m is 1.76 × 1011 C/kg. Further, the value of e/m was found to be independent of the nature of the material/metal used as the cathode (emitter), or the gas introduced in the discharge tube. This observation suggested the universality of the cathode ray particles. Around the same time, in 1887, it was found that certain metals, when irradiated by ultraviolet light, emitted negatively charged particles having small speeds. Also, certain metals when heated to a high temperature were found to emit negatively charged particles. The value of e/m of these particles was found to be the same as that for cathode ray particles. These observations thus established that all these particles, although produced under different conditions, were identical in nature. J. J. Thomson, in 1897, named these particles as electrons, and suggested that they were fundamental, universal constituents of matter. For his epoch-making discovery of electron, through his theoretical and experimental investigations on conduction of electricity by gasses, he was awarded the Nobel Prize in Physics in 1906. In 1913, the American physicist R. A. Millikan (1868-1953) performed the pioneering oil-drop experiment for the precise measurement of the charge on an electron. He found that the charge on an oil-droplet was always an integral multiple of an elementary charge, 1.602 × 10–19 C. Millikan’s experiment established that electric charge is quantised. From the values of charge (e) and specific charge (e/m), the mass (m) of the electron could be determined.