6. Interference by thin films t No phase shift (if n 2 < n 1 ) Phase shift -_____ (if n 2 > n 1 ) If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference. This can be seen in soap bubbles and oil slicks, for example. The wavelength of the light will be different inside and outside the film: An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.

A similar effect takes place when a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton’s rings. Examples: One can also create a thin film of air by creating a wedge-shaped gap between two pieces of glass.

Example: White light, with uniform intensity across the visible range of 400 to 700 nm, is perpendicularly incident on a water film, of index of refraction n=1.33 and thickness t=320nm, that is suspended in air. At what wavelength is the light reflected by the film brightest to an observer? For m=1: For m=2: - ultraviolet For m=0: - infrared

Example: A drop of oil on a pond appears bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of refraction of the oil? At the edge of the oil drop, the film is so thin that the path difference between the light reflecting off of the top surface and the light going through the oil and reflecting off of the bottom surface is so small that we can consider it to be zero. Thus, the two different rays of light must be in phase when they reach our eyes. We know that the phase of the light being reflected off of the top surface of the oil must have been flipped 180°, since the index of refraction of oil is greater than that of air. Thus, the reflection off of the bottom surface of the film (where it touches the water), must also have flipped the phase of the light 180°. This tells us that the index of refraction of the water is higher than that of the oil. Thus, we know that the index of refraction of the oil is greater than that of air and less than that of water: 1.00 < n < 1.33.

6. Polarization (review) (Polarizeation of transverse waves) 1) Waves on string (polarisation and polrizing filters)

3) Unpolarized light (a)Unpolarized light consist of waves with randomly directed electric fields. Here the waves are all traveling along the same axis, directly out of the page, and all have the same amplitude E. (b)A second way of representing unpolarized light – the light is the superposition of two polarized waves whose planes of oscillation are perpendicular to each other. - intensity of unpolarized light 2) Electromagnetic waves (polarized light) z direction of motion of wave x y e.m. waves are transverse waves This wave is polarized in y direction Light is polarized when its electric fields oscillate in a single plane, rather than in any direction perpendicular to the direction of propagation.

When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is plane-polarized, the outgoing intensity is: 4) Polarisation of light (Malus’s law) Example (two sheets): The light transmitted by polarizing sheet P 1 is vertically polarized, as represented by the vertical double arrow. The amount of that light that is transmitted by polarizing sheet P 2 depends an the angle between the polarization direction of that light and the polarizing direction of P 2

Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction. This means that if initially unpolarized light passes through crossed polarizers, no light will get through the second one. Example (three sheets):

Polarization by reflection (Brewster’s law) Light is also partially polarized after reflecting from a nonmetallic surface. At a special angle, called the polarizing angle or Brewster’s angle, the polarization is 100%. n1n1 n2n2