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BLE THICKNESS (WEDGE-SHAPED) FILM, , study the interference of light in a film of varying thickness. A thin film having, sat one end and progressively increasing to a particular thickness at the other end is, e. A thin wedge of air film can be formed by two glass slides resting on each other at, eparated by a thin spacer at the opposite edge., , angement for observing the interference pattern in a wedge shaped film is shown in, he wedge angle is usually very small and of the order of a fraction of a degree. When, n Of monochromatic light illuminates the wedge from above, the rays reflected from, ding surfaces will not be paralle!. They appear to diverge from a point near the film. The, nce between the rays reflected from the upper and lower surfaces of the air film varies, igth due to variation in film thickness. Therefore, alternate bright and dark fringes are, is top surface (see Fig. 15.9b). The fringes are localized at the top surface of the, , , , , , , , , , , , , , , , , , , , , , ithe light is incident on the wedge from above, it gets partly reflected from the glass-to, tt the top of the air film. Part of the light is transmitted through the air film and gets, ly at the air-to-glass boundary, as shown in Fig. 15.10. The two rays BC and DE, thus, op and bottom of the air film, are coherent as they are derived from the same ray, of amplitude. The rays are close enough if the thickness of the film is of the, 1 of light. For small film thickness the rays interfere producing darkness ¢, on the phase difference. The thickness of the glass plates is large comp

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gAnowivs & 2HIOw, , count the gain of half-wave due, np of t radians in the phase of the, , =m A. Ifthe difference in the optical, n the two rays is equal to an integral, full waves, then the rays meet each other, [he crests of one wave falls on the crests, ers and the waves interfere —, vely. This needs that, , | Fig. 15.10, A= 2u t cos r—/2 aie aul :, , No 7 change, , nima occur when the optical path difference is A = (2 m + 1) A/2. If the difference |, , tween the two rays is equal to an odd integral number of half-waves, then the, ach ther in opposite phase. The crests of one wave falls on the troughs of the others, fere destructively. It needs that it ach ag, , 2u tcosr=mh. ’ ris, , . ze 3) Yee, ig.15.11, let us say a dark fringe occurs at A where the relation 5 ,

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(15.20), m eq. (15.20), we, , , , . (15.21), (4-4) =BC, , (15.22), i, (AB) tan 0 735 (15.23), , the distance between successive dark fringes and it also equals the separation of the, bright fringes, It is, therefore, called the fringe width, B® That is AB = B, We may write, , | 23) as, , For small values of 0, tan = 6. *, , “B= (15.25), , the quantities on the right side of the above equation are all constant, B is constant for a, angle. According to equ.(15.25), an increase in the angle 6 makes the fringes move, , Rs ceeeenieniee 52, , , , ence pattern has the following salient features., , , , Scanned with CamScanner