4. c = 300.000 km/sec

7. I F = I 0 x (cosθ) 2

8. Superposition of two waves: 1) same amplitude and wavelength, 2) polarized in two perpendicular planes, 3) oscillate in the same phase.

9. Superposition of two waves: 1) same amplitude and wavelength, 2) polarized in two perpendicular planes, 3) oscillate with 90 o phase difference. A phase difference of 90° means that when one wave is at its peak then the other one is just crossing the zero line. Special electromagnetic wave. At any fixed point in space that is in the line of the propagation of this wave, the electric field vector rotates in a circle while its length remains constant. Such waves are called Circularly polarized waves. As the 3D picture shows, a circularly polarized wave can be visualized with a spiral line; the wave propagates as a function describing a spiral instead of one describing a sinus curve.

10. Superposition of two waves: 1) same amplitude and wavelength, 2) polarized in two perpendicular planes, 3) oscillate with -90 o phase difference.

11. Superposition of two circularly polarized light beams: 1) same amplitude and wavelength, 2) Left and right polarised waves, Any plane polarized light wave can be obtained as a superposition of a left circularly polarized and a right circularly polarized light wave, whose amplitude is identical

12. The interaction of light and matter If light enters matter, its properties may change. Namely, its intensity (amplitude), polarization, velocity, wavelength, etc. may alter. The two basic phenomena of the interaction of light and matter are absorption (or extinction) and a decrease in velocity. Absorption means that the intensity (amplitude) of light decreases in matter because matter absorbs a part of the light. (Intensity is the square of amplitude.) The decrease in velocity (i.e. the slowdown) of light in matter is caused by the fact that all materials (even materials that do not absorb light at all) have a refraction index, which means that the velocity of light is smaller in them than in vacuum. The refraction index is the ratio of the velocities of light measured in vacuum and in the given material.

13. A plane-polarized wave traverses a medium that absorbs light but does not refract it (refraction index= 1) After exiting the material, the field vector oscillates the same way as before entering it but its amplitude is only about 36% of the earlier value.

14. A circularly polarized wave traverses a medium that absorbs light but does not refract it (refraction index= 1) After exiting the material, the field vector oscillates the same way as before entering it but its amplitude is only about 36% of the earlier value.

15. A plane-polarized wave traverses a medium that does not absorb light but refracts it (refraction index> 1) When the light beam enters the piece of material, it slows down because the refracting index of the material is greater than 1.0. Its ν does not change, therefore its λ decreases (the product of the frequency and the wavelength should be equal to c). In these animations, we used a refraction index n=2.2. This means that in c the medium is 1/2.2 times the c in vacuum, and its λ also decreases to 1/2.2 times the original value. The two field vectors at the intersecting planes do not oscillate in the same phase any longer

16. A circularly polarized wave traverses a medium that does not absorb light but refracts it (refraction index> 1) The two field vectors at the intersecting planes do not oscillate in the same phase any longer

17. Some materials possess a special property: they absorb left circularly polarized light to a different extent than right circularly polarized light. This phenomenon is called circular dichroism. REMEMBER: Any plane polarized light can be obtained as the superposition of a left circularly polarized and a right circularly polarized light wave. If linearly polarized light traverses a medium that shows circular dichroism, its properties will change (the medium absorbs the two circularly polarized components to a different extent.) The red component traverses the medium unchanged while the green gets fainter: its intensity decreases to ~ 36% of the original value. The superposition of the two components is no longer a linearly polarized wave: the resulting field vector does not oscillate along a straight line but it rotates along and ellipsoid path. Such a light wave is called an elliptically polarized light. e.g. Does NOT absorb red Highly absorbs green

18. The big axis of the ellipse is parallel to the polarization plane of the original light wave. This is always the case, regardless of which circular component is absorbed more by the medium Of course, it is very unusual for a material not to absorb one circular component at all. Real materials usually absorb both components, to a different extent How elliptical the plane-polarized wave becomes after traversing the medium is determined by the difference between the absorptions of the two circularly polarized components. In the most extreme case, the material almost completely extincts one component--and then the plane-polarized wave almost becomes a perfect circularly polarized light because the other circular component disappears. circular dichroism makes plane-polarized light elliptically polar

19. There are materials having another special property: their refraction index is different for left and right circularly polarized light. This phenomenon is called circular birefringence. A plane-polarized light wave (indicated by light blue color) traverses a medium that does not slow down the left circularly polarized component (this is the circular wave shown in red) of the wave at all but slows down the right circularly polarized component (this is the circular wave shown in green) somewhat (n=1.05). circular birefringence rotates the plane of polarization of plane-polarized light.

20. The component shown in red traverses the medium unchanged while the component shown in green gets slower and its wavelength decreases in the medium. This slowdown and the decreased wavelength is hard to see in the figure because the refraction index (1.05) is close to 1.0. But as a result of this refraction index, the wave shown in green makes 4.2 full periods in the medium instead of 4 full periods, therefore its field vector will further on its rotating path than if the medium were not present circular birefringence rotates the plane of polarization of plane-polarized light.

21. In reality, it rarely occurs that a material exhibits circular dichroism but no circular birefringence or it exhibits circular birefringence but no circular dichroism with respect to light of a certain wavelength. The incident light suffers two modifications here: 1)because of the circular dichroism, it becomes elliptical; 2)because of the circular birefringence, its polarization gets rotated. Since the exiting light is no longer plane-polarized, it is not the plane of polarization that gets rotated but the big axis of the ellipse of polarization of the elliptically polarized light.

22. The ellipticity of the light exiting the medium is determined by the difference between the absorptions with respect to the left and right circularly polarized components. The angle made by the big axis of the ellipse with respect to the original polarization plane is determined by the difference between the refraction indices with respect to the left and right circularly polarized components. With the appropriate instrument, the ellipticity and the angle of rotation of the polarization plane of light can be measured. From those data, the difference between absorptions and refraction indices with respect to left and right circularly polarized lights can be calculated.

23. Circular dichroism and circular birefringence are caused by the asymmetry of the molecular structure of matter. The optical activity of solutions of biological macromolecules provides information about the structural properties of the macromolecules