Physics 102 Lecture 18 Snells Law Total Internal

Physics 102: Lecture 18 Snell’s Law, Total Internal Reflection, Brewster’s Angle, Dispersion, Lenses

Snell’s Law: A Quick Review When light travels from one medium to another the speed changes v=c/n, but the frequency is constant. So the light bends: n 1 sin( 1)= n 2 sin( 2) n 1 1 2 Compare n 1 to n 2 ACT: 1 < 2 1) n 1 > n 2 sin 1 < sin 2 2) n 1 = n 2 n 1 > n 2 3) n 1 < n 2 44

Total Internal Reflection Recall Snell’s Law: n 1 sin( 1)= n 2 sin( 2) (n 1 > n 2 2 > 1 ) 1 = sin-1(n 2/n 1) then 2 = 90 “critical angle” 2 Light incident at a larger angle will only have reflection ( i = r) r i c 1 n 2 n 1 normal 06

Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light traveling through the air (n=1) is incident on water (n=1. 33). Part of the beam is reflected at an angle r = 60 o. The other part of the beam is refracted. What is 2? 1 r n 1 normal n 2 48

Snell’s Law Practice Usually, there is both reflection and refraction! A ray of light traveling through the air (n=1) is incident on water (n=1. 33). Part of the beam is reflected at an angle r = 60 o. The other part of the beam is refracted. What is 2? 1 r 1 = r =60 o sin(60 o) = 1. 33 sin( 2) 2 = 40. 6 o n 1 normal n 2 48

Preflight 18. 1 Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection ? 1) Yes 51% 2) No 49% “There are millions of light ’rays’ coming from the light. Some of the rays will be totally reflected back into the water, but most of them will not. ” 10 8

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ACT: Refraction • As we pour more water into bucket, what will happen to the number of people who can see the ball? 1) Increase 2) Same 3) Decrease 11

ACT: Refraction • As we pour more water into bucket, what will happen to the number of people who can see the ball? 1) Increase 2) Same 3) Decrease 11

Fiber Optics At each contact w/ the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber. noutside ninside Telecommunications Arthoscopy Total Internal Reflection only works if noutside < ninside Laser surgery 13

Fiber Optics At each contact w/ the glass air interface, if the light hits at greater than the critical angle, it undergoes total internal reflection and stays in the fiber. noutside ncladding ninside Add “cladding” so outside material doesn’t matter! We can be certain that ncladding < ninside 13

Brewster’s angle Reflected light is usually unpolarized (mixture of horizontally and vertically polarized). But… q. B horiz. polarized only! q. B horiz. and vert. polarized 90º n 1 n 2 90º-q. B When angle between reflected beam and refracted beam is exactly 90 degrees, reflected beam is 100% horizontally polarized ! n 1 sin B = n 2 sin (90 - B) n 1 sin B = n 2 cos ( B) 15

ACT: Brewster’s Angle When a polarizer is placed between the light source and the surface with transmission axis aligned as shown, the intensity of the reflected light: (1) Increases (2) Unchanged (3) Decreases T. A. 19

Preflight 18. 3, 18. 4 Polarizing sunglasses are often considered to be better than tinted glasses because they… 27% • 62% • 9% • • 1% block more light block more glare safer for your eyes are cheaper When glare is around q. B, it’s mostly horiz. polarized! Polarizing sunglasses (when worn by someone standing up) work by absorbing light polarized in which direction? 60% 40% • horizontal • vertical 21

Dispersion The index of refraction n depends on color! In glass: nblue = 1. 53 nblue > nred = 1. 52 prism White light Blue light gets deflected more 23

Rainbow: Preflight 18. 5 W loo ow ka t t h var e in i iation nd ex o f ref rac t n! io Which is red? Which is blue? Skier sees blue coming up from the bottom (1), and red coming down from the top (2) of the rainbow. Blue light is deflected more! 25

LIKE SO! In second rainbow pattern is reversed 25

Flat Lens (Window) Incident ray is displaced, but its direction is not changed. n 2 n 1 q 1 If q 1 is not large, and if t is small, the displacement, d, will be quite small. t d 27

Converging Lens Principal Rays F Object P. A. Image F 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to principal axis. Image is: real, inverted and enlarged (in this case). Assumptions: • monochromatic light incident on a thin lens. • rays are all “near” the principal axis. 35

Converging Lens All rays parallel to principal axis pass through focal point F. Double Convex Preflight 18. 6 F P. A. F A beacon in a lighthouse produces a parallel beam of light. The beacon consists of a bulb and a converging lens. Where should the bulb be placed? 53% • At F 20% • Inside F • Outside F 27% P. A. nlens > noutside F F 30

3 Cases for Converging Lenses Past 2 F Image Object Between F & 2 F Image Object Inside F Image Object Inverted Reduced Real This could be used in a camera. Big object on small film Inverted Enlarged Real This could be used as a projector. Small slide on big screen Upright Enlarged Virtual This is a magnifying glass 40

ACT: Converging Lens Which way should you move object so image is real and diminished? F Object P. A. F (1) Closer to lens (2) Further from lens (3) Converging lens can’t create real diminished image. 40

Diverging Lens Principal Rays F Object F P. A. Image 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Only 1 case dirverging lens: Image is always virtual, upright, and reduced. 45

ACT: Diverging Lenses Which way should you move object so image is real? F Demo Object P. A. F 1) Closer to lens 2) Further from lens 3) Diverging lens can’t create real image. 50

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