Physics 102: Lecture 20 Interference 1

Phys 102 recent lectures Light as a wave Light as a ray Lecture 14 – EM waves Lecture 15 – Polarization Lecture 20 & 21 – Interference & diffraction Light as a ray Lecture 16 – Reflection Lecture 17 – Spherical mirrors & refraction Lecture 18 – Refraction & lenses Lecture 19 – Lenses & your eye

Constructive Interference Superposition Constructive Interference t +1 -1 + t +1 -1 In Phase t +2 -2

Destructive Interference Superposition Destructive Interference +1 t -1 + +1 Out of Phase 180 degrees t -1 t +2 -2

ACT: Superposition + Different f 1) Constructive 2) Destructive 3) Neither

Interference Requirements Need two (or more) waves Must have same frequency Must be coherent (i.e. waves must have definite phase relation)

Demo: Interference for Sound … For example, a pair of speakers, driven in phase, producing a tone of a single f and l: hmmm… I’m just far enough away that l2-l1=l/2, and I hear no sound at all! l1 l2 Demo 440 Sound Interference But this won’t work for light--can’t get coherent sources

Interference for Light … Can’t produce coherent light from separate sources. (f  1014 Hz) Need two waves from single source taking two different paths Two slits Reflection (thin films) Diffraction* Today’s lecture Next lecture

Young’s double slit/rays Monochromatic light travels through 2 slits onto a screen What pattern emerges on the screen? Bright spots Shadow This is not what is actually seen!

Young’s double slit/Huygens Recall Huygens’ principle: Every point on a wave front acts as a source of tiny wavelets that move forward. • Bright and dark spots on screen! Constructive = bright • Destructive = dark Wave crests in phase = constructive interference

Young’s double slit: Key idea Consider two rays traveling at an angle q: • • θ Bottom ray travels a little further (2l in this case) Key for interference is this small extra distance.

Young’s double slit: Quantitative Consider two rays traveling at an angle q Assume screen is very far away (L>>d): ≈ ≈ θ θ d ≈ m = +2 Path length difference = dsin(q) L Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l where m = 0, 1, 2 Need l < d

Young’s double slit: Quantitative Assume screen is very far away (L>>d), angles q are small: m = 0 m = +1 m = -1 m = -2 m = +2 y θ θ d dsin(q) L sin(q)  tan(q) = y/L Constructive: dsin(q) = ml Destructive: dsin(q) = (m+1/2)l y ≈ mlL/d y ≈ (m+1/2)lL/d m = 0, 1, 2

ACT: Preflight 20.3 When this Young’s double slit experiment is placed under water, the separation y between minima and maxima: m = 0 m = +1 m = -1 m = -2 m = +2 y θ θ d dsin(q) L 1) increases 2) same 3) decreases

Preflight 20.2 In the Young double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light? 1) Yes 2) No

Thin Film Interference Light is incident normal to a thin film Note: angles exaggerated for clarity 1 2 n0=1.0 (air) t n1 (thin film) n2 Demo 70 soap film Get two waves by reflection off two different interfaces: interference! Ray 2 travels approximately 2t further than ray 1.

Reflection & Phase Shifts Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change. Reflected Reflected Incident Incident n1 n1 n2 n2 Refracted Refracted If n1 > n2 – no phase change upon reflection If n1 < n2 – 180º phase change upon reflection (shift by l/2)

Note: this is wavelength in film! (lfilm= lo/n1) Thin Film Summary Determine d, number of extra wavelengths for each ray. 1 2 n = 1.0 (air) n1 (thin film) t n2 This is important! Reflection Distance Note: this is wavelength in film! (lfilm= lo/n1) Ray 1: d1 = 0 or ½ + 0 Ray 2: d2 = 0 or ½ + 2 t/ lfilm If |d2 – d1| = 0, 1, 2, 3 …. (m) constructive If |d2 – d1| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

ACT: Thin Film Practice Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2 n = 1.0 (air) n1 (thin film) t n2 A) d1 = 0 B) d1 = ½ C) d1 = 1 What is d1, the total phase shift for ray 1

Thin Film Practice Example Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2 n = 1.0 (air) n1 (thin film) t n2 Is the interference constructive or destructive or neither? d1 = d2 = Phase shift = |d2 – d1| =

ACT: Thin Film Practice II Example Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of plastic (n2 = 1.8). 1 2 n = 1.0 (air) n1 (thin film) t n2 Is the interference : 1) constructive 2) destructive 3) neither? d1 = d2 = Phase shift = |d2 – d1| =