From Last time…

1. From Last time… Two-source interference: Diffraction grating Diffraction = interference from many sources Thin-film interference Please pick up pack of color sheets

2. Single slit diffraction Important parameter: • Interference-like pattern from a single slit. Wavelength compared to size of aperture Long wavelength:wide pattern Short wavelengthnarrow pattern

3. Diffraction: single slit interference • Huygen’s principle: each portion of the slit acts as a source of waves • These sources interfere according to path-length difference.

4. Overlapping diffraction patterns Angularseparation • Two independent point sources will produce two diffraction patterns. • Too much overlap, resolution is lost. • Image shows two sources clearly resolved. 

5. Diffraction-limited resolution Easily resolved ( > min ) diffraction limit ( = min ) not resolved ( < min ) • For a circular aperture (e.g. lens)

6. Waves and geometry • Interference and diffraction demonstrate that light is a wave. • Doesn’t always appear as a straight ‘ray’ of light … but sometimes it almost does! Geometric optics: Tracing the path of light rays

7. Wavefronts (crests of waves) What is a light ray? • Light ray is a line in the direction along which light energy is flowing. Ray enters eye -> you can see the light source

8. What does a light ray do? • Light rays travel forever in straight line unless they interact with matter (reflection, refraction, absorption)

9. What about diffraction? • Light really behaves as a wave • The concept of a light ray is an approximation i.e. a lie Wavelength << aperture size, rays are good approximation

10. Light rays from point source • Light rays are not always parallel. • E.g. light bulb visible from all directions • Rays must be traveling in all directions Light ray perpendicular to local wavefront (crest of wave).

11. Reflection/refraction occur at interfaces between different materials Interaction of light with matter Absorption Reflection Refraction And all occur simultaneously

12. Inter-face Reflection and Refraction • Direction of light can be changed by • Reflection (lets you see an object) • Refraction (transmits light thru object) … at an interface between different materials • Ray  is the incident ray • Ray  is the reflected ray • Ray  is refracted into the lucite • Ray  is reflected inside the lucite • Ray  is refracted as it enters the air from the lucite Air Plastic

13. When are materials different? • For reflection/refraction • materials are different if they have different index of refraction • Light propagates at different speed in different materials. • Due to interaction of electromagnetic wave with atoms in material. c=speed of light in vacuum

14. What do you think? Pyrex stirring rod (n=1.46) dipped into beaker of Wesson oil (n=1.46). What happens to the rod? Appears dark Appears bright Appears invisible Appears curved Appears inverted Beaker of Wesson oil Pyrex stirring rod No reflection/refraction if index of refraction is same.

15. i r Incidentray Reflectedray Reflection • Angle of incidence = angle of reflection • Multiple reflections • Apply i=r at each surface • trace ray

16. r Why i=r? • Christian Huygens modeled this in 1690 • Said that each point on wavefront acts as source of spherical wavelets • Superposition of wavelets gives reflected plane wave such that i=r i

17. i,1 r n1 n2 2 Angle of refraction What about refraction? • Refraction occurs when light moves into medium with different index of refraction. • Result: light direction bends according to Snell’s law

18. r 2 Why Snell? • Can analyze in exactly the same way • Light moves at different speed in different media i n1 n2>n1 v2<v1

19. n1 Reflected ray v2>v1 n2 < n1 Refraction angle n1 Reflected ray v2<v1 n2 >n1 slower in medium 2 faster in medium 2 n2>n1Refracted ray bent toward normal n2<n1Refracted ray bent away from normal

20. A B C Quick quiz Which of these fluids has the smallest index of refraction(highest light speed)? Fluid A Fluid B Fluid C All equal

21. Numerical Example A beam of light is traveling underwater, aimed up at the surface at 45˚ away from the surface normal. Part of it is reflected back into the water, and part is transmitted into the air. Airn2=1.00 2 Watern1=1.33 1=45˚

22. Quick quiz n2=1.0 A trout looks up through the surface at the setting sun, and at the moon directly overhead. He sees n1=1.33 Moon directly overhead, sun ~ parallel to water surface Moon directly overhead, sun ~ 40˚ above water surface Moon ~ 40˚ from vertical, sun ~ parallel to water surface Moon and sun aligned at 40˚ from vertical.

23. For water: Total Internal Reflection • Is possible when light is directed from n1 > n2  refracted rays bend away from the normal • Critical angle: angle of incidence that will result in an angle of refraction of 90° (sin = 1)

24. Optical Fibers The cladding has a lower n than the core • Plastic or glass light pipes • Applications: • Medicine: endoscope (light can be directed even if bent and the surgeon can view areas in the body using a camera.) • Telecommunications