9 11 Practical examples of interference Blooming of

9. 11 Practical examples of interference • Blooming of lenses • Parallel-sided thin film • Wedge-shaped air film • Oil film and soap film • Newton’s ring © Manhattan Press (H. K. ) Ltd. 1

9. 11 Practical examples of interference (SB p. 94) Blooming of lenses light incident on film light refracted light reflected at A (phase change of ) light reflected at B (phase change of ) Reflected light from A and B are in phase We do not want there is reflection from film (destructive interference occurs) n – refractive index of film © Manhattan Press (H. K. ) Ltd. 2

9. 11 Practical examples of interference (SB p. 94) Blooming of lenses For white light - use mean value of (greenish-yellow light) to calculate thickness of film - Green and yellow light not reflected - Red and blue light reflected - Give magenta in colour - lenses with “bloomed” look magenta in colour © Manhattan Press (H. K. ) Ltd. 3

9. 11 Practical examples of interference (SB p. 95) Parallel-sided thin film 1. For reflection ray 1 reflected (phase change of ) ray 2 reflected (no phase change) Go to More to Know 3 © Manhattan Press (H. K. ) Ltd. 4

9. 11 Practical examples of interference (SB p. 96) Parallel-sided thin film 2. For transmission rays 3 & 4 transmitted (no phase change) Note: A “thin” film should be used for an interference pattern to be observed. This is because the optical path in the film must © Manhattan Press (H. K. ) Ltd. be smaller than the coherent length of light. 5

9. 11 Practical examples of interference (SB p. 96) Wedge-shaped air film 1. Set-up of apparatus air wedge between glass slide and glass block © Manhattan Press (H. K. ) Ltd. 6

9. 11 Practical examples of interference (SB p. 97) Wedge-shaped air film 2. Theory ray 1 reflected (no phase change) © Manhattan Press (H. K. ) Ltd. ray 2 reflected (phase change of ) Note: When m = 0, it gives rise to the first dark fringe. 7

9. 11 Practical examples of interference (SB p. 97) Wedge-shaped air film 2. Theory © Manhattan Press (H. K. ) Ltd. 8

9. 11 Practical examples of interference (SB p. 98) Wedge-shaped air film 2. Theory Note: 1. The fringe separation is proportional to wavelength. 2. If white light is used, colour fringes will be observed. Red light is further apart as its wavelength is longer. 3. If the angle θ is too great, the fringes will be too close that no interference is observed. © Manhattan Press (H. K. ) Ltd. 9

9. 11 Practical examples of interference (SB p. 98) Wedge-shaped air film 2. Theory Note: 4. At the touched end of slides, it is a dark fringe. Despite the path difference of the two reflected rays at the edge is zero, there is a 180°phase change on the reflected wave from the glass block. Therefore, destructive interference occurs. 5. Since the reflected lights from other surface are not coherent , they usually cannot interfere each other. Go to © Manhattan Press (H. K. ) Ltd. More to Know 4 10

9. 11 Practical examples of interference (SB p. 98) Wedge-shaped air film 2. Theory Applications: 1. Measure thickness of thin foil; 2. Measure the coefficient of expansion; 3. Test for flatness of an optical surface; and 4. Measure the refractive index of a liquid by trapping the liquid in the wedge. © Manhattan Press (H. K. ) Ltd. 11

9. 11 Practical examples of interference (SB p. 98) Wedge-shaped air film 3. Testing flatness of surface - = constant, d = constant (equally spaced dark and bright fringes) - Uneven parts of testing surface, interference pattern distorts © Manhattan Press (H. K. ) Ltd. 12

9. 11 Practical examples of interference (SB p. 98) Oil film and soap film 1. Oil film Interference pattern of colours on oil film on water surface - film thickness varies - path difference is different - colour pattern © Manhattan Press (H. K. ) Ltd. 13

9. 11 Practical examples of interference (SB p. 99) Oil film and soap film 2. Soap film held vertically - Variable thickness of soap film (wedge-shaped liquid) - Thinner on top, thicker at bottom (by gravitation) - Violet on top, red at bottom for each colour band Go to Example 17 © Manhattan Press (H. K. ) Ltd. 14

9. 11 Practical examples of interference (SB p. 100) Newton’s ring 1. Set-up apparatus air wedge between lens and glass block © Manhattan Press (H. K. ) Ltd. 15

9. 11 Practical examples of interference (SB p. 100) Newton’s ring 1. Set-up apparatus a series of dark and bright rings formed (Newton’s rings) © Manhattan Press (H. K. ) Ltd. 16

9. 11 Practical examples of interference (SB p. 101) Newton’s ring 2. Theory ray 1 reflected ( no phase change) ray 2 reflected (phase change of ) For dark rings r 2 = m. R © Manhattan Press (H. K. ) Ltd. 17

9. 11 Practical examples of interference (SB p. 102) Newton’s ring 2. Theory Note: 1. By , as the thickness of the air film increases gradually outwards non-uniformly, the separation between the fringes decreases. 2. If white light is used, coloured rings will be observed. For a given ring, the inner side is violet and outer side is red. This is because the radius is proportional to the square root of wavelength and red light has longer wavelength. Go to © Manhattan Press (H. K. ) Ltd. More to Know 5 18

9. 11 Practical examples of interference (SB p. 102) Newton’s ring 2. Theory Note: 3. It is a dark spot at the centre of the lens. The path difference of the two reflected light is zero, but there is a 180°phase change on ray 2. Therefore, an half wavelength path difference exists between the two rays. Thus, destructive interference occurs at centre. 4. If the interference pattern is viewed from below the glass block, reversed bright and dark fringes will be observed, i. e. the centre becomes a bright spot. This is because of the two 180°phase changes due to the ray reflected twice by an optically denser medium. Thus, the transmitted rays are in phase. © Manhattan Press (H. K. ) Ltd. 19

9. 11 Practical examples of interference (SB p. 95) Normal incidence Practically, it is difficult to observe the interference pattern if the light is incident on the parallel-sided thin film normally. For this case, only a single bright or dark patch can be seen. Return to © Manhattan Press (H. K. ) Ltd. Text 21

9. 11 Practical examples of interference (SB p. 98) Liquid film If some liquid is trapped between the slide and the glass block, the separation of fringes will decrease. Since where n = refractive index, becomes smaller. © Manhattan Press (H. K. ) Ltd. Return to Text 22

9. 11 Practical examples of interference (SB p. 99) Q: The figure shows a drop of oil (refractive index noil = 1. 20) floating on the surface of water (refractive index nwater = 1. 33) and the reflected light is observed on the top. (a) Explain whether the outer region (which is the thinnest) corresponds to a bright or dark fringe. (b) If blue light of wavelength 450 nm is incident on the oil drop, estimate thickness of the oil at the position of the third bright fringe from the outside. (c) Explain why the interference fringes cannot be seen when the thickness of the oil increases. Solution © Manhattan Press (H. K. ) Ltd. 23

9. 11 Practical examples of interference (SB p. 99) Solution: (a) In the figure above, for light reflected at A, a phase change of π radians occurs since light is reflected at the oil surface (note that oil is optically denser than air). At B, the reflected light also experiences a phase change of π radians because light is reflected from water and nwater > noil. Hence, the two reflected rays are in phase. If t = thickness of the oil film, then the path difference between the two reflected light rays is 2 nt where n = refractive index of oil. At the outer edge, t = 0. Hence the path difference = 0 and a bright fringe is observed. © Manhattan Press (H. K. ) Ltd. 24

9. 11 Practical examples of interference (SB p. 100) Solution (cont’d): (b) For the third bright fringe from the edge, m = 3. From the equation 2 nt = mλ = 3λ ∴ Thickness of the oil film, t = = = 560 nm (c) As the oil film gets thicker, the separation between neighbouring fringes gets smaller until the eye is not able to resolve them. Return to © Manhattan Press (H. K. ) Ltd. Text 25

9. 11 Practical examples of interference (SB p. 102) Energy conservation As the rings produced by the transmitted light are complementary to that by the reflected light, i. e. constructive interference on one side of the film while destructive interference on the other side, it shows that energy is conserved. Return to © Manhattan Press (H. K. ) Ltd. Text 26