Today5/1 Questions? Waves (review) phase shifts interference reftaction lenses/mirrors etc..

Interference in 2-D Sources “in phase” Crest meets trough and trough meets crest, destructive, no sound or dark Crest meets crest and trough meets trough, constructive, loud sound or bright light Crest Trough

Interference in 2-D Sources “in phase” Constructive at a point if it is the same distance from each source Destructive at a point if it is 1/2 farther away from one source Crest Trough

Interference in 2D Sources “out of phase” Crest meets crest and trough meets trough, constructive, loud sound or bright Crest meets trough and trough meets crest, destructive, no sound or dark Crest Trough

Interference in 2-D Sources “out of phase” Constructive at a point if the point is 1/2 farther away from one source Destructive at a point if the point is the same distance from each source Crest Trough

Reflections at Boundaries Four situations Fixed end Light to heavy Free end Heavy to light

Fixed End Reflections Crest turns into trough Leading edge is the same Same velocity, length, and amplitude See “Wave Interference” handout for how the string looks during the reflection.

Free End Reflections Crest stays a crest Leading edge is the same Same velocity, length, and amplitude See “Wave Interference” handout for how the string looks during the reflection.

Light to Heavy Both transmission and reflection Boundary feels like a fixed end to the light string Reflection just like fixed end, inverted Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave. Slower, so not as far from boundary Inverted wave Shorter, “bunched up”

Heavy to Light Both transmission and reflection Boundary feels like a free end to the heavy string Reflection just like free end, not inverted Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave. Faster, farther from boundary Wave not inverted Longer, “spread out”

Light: Glass to Air Faster, farther from boundary Same as incoming wave Longer, “spread out” Light: Air to Glass Slower, so not as far from boundary Inverted wave Shorter, “bunched up”

Two slit geometry (screen far away) PLD = d sin (d = slit separation) d  Screen PLD  d (close enough) 

Two slit geometry PDL = d sin (d = slit separation) Screen  d sin = m constructive interference d sin = (m+ 1/2) destructive interference When the sources (slits) are “in phase”

A simpler picture Two slits very close together (d) Screen very far away (L)  d sin = m constructive interference d sin = (m+ 1/2) destructive interference When the sources (slits) and “in phase”

The m’s d sin = m d sin = (m+ 1/2) 0 “zeroth order” fringe 1 “first order” fringe m = 0 m = 1 m = 2 2 “second order” fringe d sin = m d sin = (m+ 1/2)

Thin Films The wavelength is different in the film. Wavelength () Film thickness (PLD) Index of refraction (n) Phase shifts film = vacuum /nfilm Eyeball

Thin Film Problems Draw picture Consider reflected wave phase shifts none, one, or both can be shifted Find  in the film Chose m or (m + 1/2) (use  in the film) Constructive or destructive? Phase shifts? PLD = 2t for thin films

Total internal reflection Air - index of refraction nA = 1.0 nAsin A = nWsin W As W increases, so does A A until A becomes 90°. C is called the “critical angle”. If W is greater that C no light will escape the water and all will be “internally reflected.” C Total internal reflection only happens when light goes from high n to low n and it depends on both n’s! nAsin 90 = nWsin C or nA = nWsin C W Water - index of refraction nW = 1.33

Example: n2 = n1sin C sin C = n2/n1 = 0.752 C = 48.8° C What is the critical angle for light traveling from water into air? sin C = n2/n1 = 0.752 n2 = 1.0 C = 48.8° C Note that there is no critical angle for light from low index to higher index. n1 = 1.33

Example: n2 = n1sin C 50° 1 = 50° What happens if the angle of incidence is greater than 48.8°? n2 = 1.0 50° 1 = 50° n1 = 1.33

Example: n2 = n1sin C n2sin 2 = n1sin 1 g = 42.8 1 = 50 What happens if I place a sheet of glass on the water, ng = 1.5? No internal reflection possible-low to high n! n2 = 1.0 1.5sin g = 1.33sin50° g = 42.8° Now what happens? C = Arcsin1/1.5 = 41.8° g = 42.8 ng = 1.5 The light reflected back into the glass. 1 = 50 n1 = 1.33

Diverging Lens-Ray Diagrams Bend the ray at the middle of the lens In parallel-out as if from left focus In as if toward right focus-out parallel Also straight through the center of the lens f f di For lenses (both types) di is positive on the right. Here di will be a negative number. f is negative for diverging lenses.

Diverging Lens-Ray Diagrams and Math d0 = +12 cm, f = -4 cm find di, m, hi f f di

Virtual and Real Images A screen placed at the image will produce an image. A screen placed at the image will not produce an image. All image forming rays actually pass through the image. At most only one image forming ray will pass through the image.

Example: f = + 6 cm and - 18 cm lenses are 1 cm apart do = + 12 cm Math minus sign because “virtual object” First lens do = 9, f = 6 di = ? di = 18 First image m1 = -18/9 = -2 Second lens do = -9, f = -18 di = ? di = 18 Total m = -2(2) = -4 Second image m2 = -18/-9 = +2 Inverted and real do do di di