1. Physical optics Done by P G LOGAN

2. Physical optics Physical optics deals with phenomena that depend on the wave nature of light. There are three types of physical optics. They are 1) Interference 2) Diffraction 3) Polarization

3. Interference The superposition of two or more coherent waves with each other such that the intensity modifies maxima and minima which results in a new wave pattern.

4. There are two types of interference 1) Constructive interference 2) Destructive interference Constructive interference occurs at point O. The two waves travel the same distance. -Therefore, they arrive in phase As a result, constructive interference occurs at this point and a bright fringe is observed. Interference, cont

5. The lower wave has to travel farther than the upper wave to reach point P. The lower wave travels one wavelength farther. -Therefore, the waves arrive in phase A second bright fringe occurs at this position. Interference, cont

6. The upper wave travels one- half of a wavelength farther than the lower wave to reach point R. The trough of the upper wave overlaps the crest of the lower wave. This is destructive interference. - A dark fringe occurs.

7. Conditions for Interference To observe interference in light waves, the following two conditions must be met: The sources must be coherent.  They must maintain a constant phase with respect to each other. The sources should be monochromatic.  Monochromatic means they have a single wavelength.

8. Interference in thin films by reflection Thin film interference patterns seen in Thin film of soapy waterSeashell A thin layer of oil on the Water of a street puddle

9. Interference in thin films by reflection, cont Consider a film of soap with uniform thickness in air Soap film air t When a beam of light is incident on to the surface of the film, part of incident light is reflected on the top surface and part of that transmitted is reflected on the lower surface. If the film is not too thick, the two reflected beams produces an interference effect.

10. Interference in thin films by reflection, cont  If light travelling in a less dense medium is reflected by a dense medium, the reflected wave is phase-shifted by π.  If light travelling in a dense medium is reflected by a less dense medium, the reflected wave does not experience any phase shift. Constructive interference occurs if the path difference between the two reflected light beams is Where n = 0, 1, 2, …

11. Interference in thin films by reflection, cont Destructive interference occurs if the path difference between the two reflected light beams is Where n = 0, 1, 2, … If the film has a refractive index μ then

12. Interference in thin films by reflection, cont On the other hand, the part reflected at the lower surface must travel the extra distance of 2 t, where t is the thickness of the film. That is, 2t is the path difference between the two reflected beams. If 2t = (n+½) λ then constructive interference occurs. If 2t = nλ then destructive interference occurs. When t is large, several values of λ satisfy the equation. The film will appear to be generally illuminated.

13. Newton’s rings

14. Newton’s rings, cont

16.  When a curved glass surface is placed in contact with a flat glass surface, a series of concentric rings is seen when illuminated from above by monochromatic light. These are called Newton’s rings.  Newton’s rings are due to interference between rays reflected by the top and bottom surfaces of the very thin air gap between the two pieces of glass.  Newton’s rings represent a system of contour fringes with radial symmetry.  The point of contact of the two glass surfaces is dark, which tells us the two rays must be completely out of phase.

17. Diffraction Any bending of a wave around an obstacle or edges of an opening by means other than reflection or refraction.

18. Diffraction, cont  The amount of diffraction (bending) depends on the size of the wavelength compared with the size of the obstruction.  The longer the wavelength is compared to the obstruction, the greater the diffraction.

19. Some diffraction patterns

20. Diffraction through a single slit Diffraction refers to the spreading or bending of waves around edges. The fringe pattern formed by a single slit consists of Alternate bright and dark fringes and the fringes fade away from the centre.

21. Diffraction through a single slit, cont Transcendental equation. Solve graphically To find maxima of a function, take derivative and set equal to 0

22. After the central maximum the next maximum occurs about halfway between the first and second minimum. Diffraction through a single slit, cont

23. Diffraction through a double slit

24. Diffraction through a double slit, cont I = I (double slit interference) x I(diffraction)

25. Diffraction Grating A large number of equally spaced parallel slits is called a diffraction grating. A diffraction grating can be thought of as an optical component that has tiny grooves cut into it. The grooves are cut so small that their measurements approach the wave length of light.

26. Diffraction Gratings, cont A diffraction grating splits a plane wave into a number of subsidiary waves which can be brought together to form an interference pattern.

27. Action of Diffraction Grating If d is the slit spacing then the path difference between the light rays X and Y = d sin θ. For principal maxima, d sin θ = nλ. The closer the slits, the more widely spaced are the diffracted beams. The longer the wavelength of light used, the more widely spaced are the diffracted beams. d Path difference = d sin θ θ θ θ X Y

28. Number of Diffraction beams Since sin θ  1, θ1θ1 θ1θ1 θ2θ2 θ2θ2 n = 0 n = 1 n = 2  The highest order number is given by the value of d/λ rounded down to the nearest whole number.