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 In Young’s double-slit experiment using monochromatic light of wavelength l, the intensity of light at a point on the screen where path difference is l, is K units. What is the intensity of light at a point where path difference is l/3?

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