Thin Films, Diffraction, and Double slit interference

Young's Experiment Construction is reinforcement (adding) Suppose you have two waves with the same phase at point P, and l1 and l2 are the length the waves have traveled The waves differ by one wavelength So l1 = 2¼ and l2 = 3¼ So whenever l2-l1 = m, where m = 1,2,3,…, there is constructive interference

Cont. Destruction is cancellation (subtraction) Suppose you have two waves that are out of phase at point P, and l 1 and l 2 are the length the waves have traveled The waves differ by one-half a wavelength So l 1 = 2¾ and l 2 = 3¼ So whenever l 2 -l 1 = (m + ½), where m = 0,1,2,3…, there is destructive interference

Coherent Sources Two sources are coherent if the waves they emit maintain a constant phase relation. This means the wave do not shift relative to one another Lasers are coherent, incandescent bulbs are non coherent

Young In 1801, Thomas Young demonstrated the wave nature of light by overlapping light waves and showing interference He was also able to determine the wavelength of light When the path difference is =, a bright fringe is made When the path difference an odd multiple of ½, a dark fringe is made

Cont For Bright Fringes, For Dark Fringes,

Thin film interference Young double slit experiment is one form of interference Light is reflected off of both boundaries, but one ray travels further than the other This causes the waves to “construct,” 0 o, or 360 o phase difference or “ destruct,” 180 o phase difference. The determining factor is the number of whole wavelengths

Cont. Using index of refraction n=c/v Stating c = f and v film = f When light travels to a more refractive material (e.g. air to gasoline), relection at the boundary occurs along with a phase change that is ½ of a wavelength in the film

Cont. When light travels to a less refractive material, there is no phase change Example 3 pg 827 Let “t” represent the thickness of the film Since light goes from air to gasoline there is a 1/2 phase shift, so: 2t + 1/2  =  1/2  3/2  5/2  subtracting ½ 2t = 1,2,3...so t = m /2, m = 1,2,3

Cont. Multicolored films If the thickness is different at different parts of the film then different colors subtract, green subtraction would look magenta, red subtraction would look cyan

Diffraction The bending of light around obstacles Christian Huygens ( ) describes that Every point on a wave front acts as a source of tine wavelet that move forward with the same speed as the wave. The wave front at a later instant is the surface that is tangent to the wavelets. The amount of bending is determined by / W, where W is the width of the opening For dark fringes sin  = m /W

Diffraction Grating