35 Chapter (& 36) Interference
May 7, 12 2009
Topics to focus on
Two source interference (Ch 35.1) Double slit (Ch 35.2) and Diffraction Grating (Ch 36) Thin Film Interference (Ch 35.4) Skip: 35.3 (Intensity in Interference Patterns) and 35.5 (The Michelson Interferometer)
Two Source Interference
We already did this for sound waves in chapter 16! Constructive interference when the extra path length is integer number of wavelengths: r = m Destructive when r = (m+1/2)
Two Parallel, Narrow Slits
Consider the geometry in figure 35.5 in the text Extra distance is r = d sin
Double Slit Interference
Constructive when: r = m = d sin m Position of bright fringes ym = R tan m Typically many alternating bright and dark fringes Small angle approx: sin tan ym mR/d !!! BE VERY CAREFUL !!! Destructive when r = (m+1/2)
Multiple Slits: The Diffraction Grating
More general case, but geometry almost identical to double slit r = d sin between any two adjacent slits When m = d sin m ALL waves will be in phase ym = R tan m NEVER use small angle approximation!!!
Thin Interference
Film Interesting things happen when light reflects from thin films or thin air gaps The first two reflected rays can interfere constructively (maximum reflection) or destructively (maximum transmission) Rays should be drawn straight up & down, but that makes it harder to see
Thin Air Gap Interference
Extra distance traveled by the second ray is twice the thickness of the air gap
r = 2t path = (2)2t/ = 4t/
There are also phase shifts due to reflection
Reflect low n to high n: refl = Reflect high n to low n: refl = 0
If total phase shift is an even multiple of , constructive reflection, odd multiples are destruct...