Interference Interference l 2 l 1 m Constructive

Interference

Interference • l 2 - l 1 = m λ (Constructive) • l 2 - l 1 = (m+1/2) λ (Destructive) m = 0, 1, 2, 3, 4, ………

Thin film interference 2 t = (m+1/2) λfilm Constructive 2 t = m λfilm Constructive 2 t = (m+1/2) λfilm Destructive λfilm = nvac /nfilm

Phase Change • If light is reflected from a surface where n 1 > n 2 there is a ½ λ phase shift. • Zero or One phase shift 2 t = m λfilm Constructive 2 t = (m+1/2) λfilm Destructive • One phase shift 2 t = (m+1/2) λfilm Constructive 2 t = m λfilm Destructive

Light of wavelength 600 nm impinges upon a soap film (n = 1. 4) on top of glass (n = 1. 5). What is the smallest thickness of film that will produce constructive interference? (Assume the index of refraction of air is n= 1. 0)

Light of wavelength 600 nm impinges upon a soap film (n = 1. 4) on top of plastic (n = 1. 3). What is the smallest thickness of film that will produce constructive interference? (Assume the index of refraction of air is n= 1. 0)

Double slit Sin θ = m λ / d Constructive (bright) Sin θ = (m + ½) λ / d Destructive (dark)

A double slit experiment is setup using light of wavelength, 600 nm with a slit spacing of 2 x 10 -5 m. If the screen is located 5 m from the slits how far from the pattern middle is the first bright, dark spot located?

Single slit/Barrier • Sin θ = m λ / w Dest. (dark) m = 1, 2, 3, 4, ………

Diffraction grating • Sin θ = m λ / d Const. (bright) d = dist. between slits d = 1/# of slits per m.

Missing bright spots in the double slit pattern • Double Slit Sin θ = m λ / d Constructive (bright) • Single slit Sin θ = m λ / w Destructive (dark)