Geometry of Young’s Double Slit Experiment Particle theory What actually happened (wave theory) X d sinθ = m tanθ = L

Where d = distance between the slits θ = angular separation m = order maximum (bright bands)  = wavelength X = distance from the zeroth order maximum to the mth order maximum L = distance from the slits to the screen m=0 x for m=5 m=5 m=5

Single slit diffraction X w sinθ = m tanθ = L Where w = width of the slit θ = angular separation m = order minimum (dark bands)  = wavelength X = distance from the center of the central bright band to the mth order minimum L = distance from the slits to the screen x for m=3 m=3 m=3

Diffraction grating – has more than two slits grating constant – number of slits per unit length thus d = (grating constant)-1 Example: if the grating constant is 717 lines per mm d = 1.395 x 10-3 mm

Units d and  must match !!!!!!!!!!!! w and  must match !!!!!!!!!!!!   color wavelength red  690 nm orange  620 nm yellow  580 nm green  530 nm blue  450 nm violet  390 nm d and  must match !!!!!!!!!!!! w and  must match !!!!!!!!!!!! X and L must match !!!!!!!!!!!! Calculator must be in degrees!!! 2.48 mm 2) 297 nm 3) 3357 lines/cm 4) 4 : 1 5) 1.8° 6) 4.32 x 10-5 m 7) 1.72 cm 8) 84.5 nm 9) green (532 nm)

Thin Film Interference

Thin Film Interference

Thin Film Interference

Thin Film Interference Ray 1 travels into the film and back it travels 2t (twice the thickness of the film). The path difference between the rays when they come out of the film is 2t.

Condition for Constructive Interference: The reflected rays coming out of the film (5) and the rays that reflected on the film interface with the air(2), must have a path difference of an integer multiple of l/2. This is because (2) flipped going from a less dense to a more dense medium. Note: l is the wavelength in the film.

Condition for Constructive Interference Path Difference= 2t =#lfilm /2 where # =1,3, 5… t is the thickness of the film. minimum thickness occurs when # = 1.

Problem Calculate the minimum thickness of a soap bubble that results in constructive interference when a light of wavelength 500nm shines on it. Answer: 93.7 nm