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2. diffraction in films

3. Diffraction Diffraction is the bending of waves around obstacles or the edges of an opening. Huygens’ principle Every point on a wave front acts as a source of tiny wavelets that move forward with the same speed as the wave; the wave front at a latter instant is the surface that is tangent to the wavelets.

4. Diffraction The extent of the diffraction increases as the ratio of the wavelength to the width of the opening increases.

5. Diffraction

6. This top view shows five sources of Huygens’ wavelets. These wavelets interfere on the right side

7. Diffraction Dark fringes for single slit diffraction width of central bright fringe

8. Diffraction width of central bright fringe: 2y 1 = 0.08m nm W=4x10 -6 first dark fringe: L>>W>>λ: width = ~

9. Resolving Power First minimum of a circular diffraction pattern diameter of hole Width of bright circle

10. Resolving Power Three photographs of an automobile’s headlights, taken at progressively greater distances.

11. Resolving Power Rayleigh criterion Two point objects are just resolved when the first dark fringe in the diffraction pattern of one falls directly on the central bright fringe in the diffraction patter of the other. If θ<θ min the diffraction patterns overlap

12. Diffraction

13. X-Ray Diffraction X-rays are used to study materials (solid crystals) DNA Condition for diffraction λ<<d Solids could not be studied with visible light, λ is too large. X-rays have very small λ (10 -10 m < d~10 -9 m) and do not damage materials significantly. In some cases “electrons” diffraction is used. Condition for diffraction λ<<d Solids could not be studied with visible light, λ is too large. X-rays have very small λ (10 -10 m < d~10 -9 m) and do not damage materials significantly. In some cases “electrons” diffraction is used. From the diffraction pattern it can be calculated the structure of the material From the diffraction pattern it can be calculated the structure of the material

14. Polarization In polarized light, the electric field fluctuates along a single direction.

15. Polarization Polarized light may be produced from unpolarized light with the aid of polarizing material.

16. Polarization MALUS’ LAW intensity before analyzer intensity after analyzer

17. Polarization Example 7 Using Polarizers and Analyzers What value of θ should be used so the average intensity of the polarized light reaching the photocell is one-tenth the average intensity of the unpolarized light?

18. Polarization

19. When Polaroid sunglasses are crossed, the intensity of the transmitted light is reduced to zero. Two crossed polarizers (with perpendicular axes) transmit no light zero

20. Polarization Conceptual Example 8 How Can a Crossed Polarizer and Analyzer Transmit Light? Suppose that a third piece of polarizing material is inserted between the polarizer and analyzer. Does light now reach the photocell?

21. Intensity of Polarized Light, Examples On the left, the transmission axes are aligned and maximum intensity occurs. In the middle, the axes are at 45 o to each other and less intensity occurs. On the right, the transmission axes are perpendicular and the light intensity is a minimum. Section 38.6

22. Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light may be –Completely polarized –Partially polarized –Unpolarized The polarization depends on the angle of incidence. –If the angle is 0°, the reflected beam is unpolarized. –For other angles, there is some degree of polarization. –For one particular angle, the beam is completely polarized. Section 38.6

23. Polarization by Reflection. The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p. Brewster’s law relates the polarizing angle to the index of refraction for the material. tan θ p = n 2 /n 1 θ p may also be called Brewster’s angle. Section 38.6

24. Polarization by Reflection, Partially Polarized Example Unpolarized light is incident on a reflecting surface. The reflected beam is partially polarized. The refracted beam is partially polarized Section 38.6

25. Polarization by Reflection, Completely Polarized Example Unpolarized light is incident on a reflecting surface. The reflected beam is completely polarized. The refracted beam is perpendicular to the reflected beam. The angle of incidence is Brewster’s angle. Section 38.6