OPTICS Wave optics. Interference. Diffraction. Polarization 1. Young's Double Slit Experiment Constructive interference: Screen 8 = k) = 2k- х, Destructive interference: 8 = (2k + 1) Coordinates of bright and dark fringes on the screen: Ymax =± -k; Ymin =± Here 8 is path difference (m), 1 is wavelength of light (m), l is distance from the slits to the screen (m), k = 0, 1, 2, 3 ... is minimum or maximum order number, d is distance between the slits (m), Ymax are coordinates of bright fringes on the screen (m), ymin are coordinates of dark fringes on the screen (m), Ay is width of the fridges (m). 2. Interference in thin films: Air Constructive interference: Film 21 V n2 – sin? a (2k + 1) 2 Destructive interference: Air 21 Vn² – sin? a = k) Here n is refractive index of the film, a is angle of light incidence, k = 0, 1, 2, 3 ... is minimum or maximum order number, 1 is wavelength of light (m), l is thickness of the film (m). 3. Single-Slit Diffraction Constructive: sine - 2à/a sine -/a a sin© = ±(2k + 1), sine0 Destructive: sine-A/a - sine --2/a a sinº = ±ka a is the slit width, k = 0, 1, 2, 3 ... is minimum or maximum order Viewing screen number, A is wavelength of light (m), 0 is the angle on corresponding minimum or maximum. 4. Diffraction grating: d sin ±kX d = '/N is period of diffraction grating and N is number of lines per unit length, o is angle on corresponding minimum or maximum, k = 0, 1, 2... is minimum or maximum order number, 1 is wavelength of light (m). 5. Resolution of the optical instruments Limiting angle of resolution 0min: S1 1.22A Өmin Omin = D Minimum separation distance d: d = L0min a is wavelength of light (m), D is aperture diameter, for human eye pupil diameter (m). 10. Georges Seurat, a post-impressionist French painter, used a technique of painting with small dots of color placed close together on a canvas. From sufficiently far away, the dots cannot be distinguished and the painting looks normal in appearance. If the dots on the painting are separated by 1.5 mm and the painting is observed under light of 550 nm wavelength with eyes having a pupil diameter of 2 mm, find the minimum distance you must stand from the painting so that the individual dots cannot be resolved.