Physics 102: Lecture 18 Snell’s Law, Total Internal Reflection, Brewster’s Angle, Dispersion, Lenses 1

Summary of today’s lecture Examples of refraction 1) Total internal reflection 2) Brewster’s angle 3) Dispersion (rainbows) 4) Lenses

Demo: Snell’s Law n1 sin(q1)= n2 sin(q2) When light travels from one medium to another the speed changes v=c/n, but the frequency is constant. So the light bends: n1 sin(q1)= n2 sin(q2) incident reflected refracted q1 q2 qr n2 n1 > n2  q2 > q1 Light bent away from normal as it goes in medium with lower n Demo 281: Snell’s Law n1 > n2

1) Total Internal Reflection Snell’s Law: n1 sin(q1)= n2 sin(q2) (n1 > n2  q2 > q1 ) normal q1 = sin-1(n2/n1) then q2 = 90 q1 q2 “critical angle” n2 qc qi > qc qr Light incident at a larger angle will only have reflection (qi = qr) n1 > n2 Demo 281: Snell’s Law Only possible if n1>n2 For water/air: n1=1.33, n2=1 q1 = sin-1(n2/n1) = 48.80

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 Laser surgery Total Internal Reflection only works if noutside < ninside

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 2) No

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 ACT, then demo 1129 (ball in tub of water)

horiz. and vert. polarized 2) Brewster’s angle Reflected light is usually unpolarized (mixture of horizontally and vertically polarized). But… qB qB horiz. polarized only! n1 n2 horiz. and vert. polarized 90º 90º – qB When angle between reflected beam and refracted beam is exactly 90 degrees, reflected beam is 100% horizontally polarized ! n1 sin qB = n2 sin (90-qB) n1 sin qB = n2 cos (qB)

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. ACT, then demo 664

Preflight 18.3, 18.4 Polarizing sunglasses are often considered to be better than tinted glasses because they… block more light are safer for your eyes block more glare are cheaper Polarizing sunglasses (when worn by someone standing up) work by absorbing light polarized in which direction? horizontal vertical

3) Dispersion The index of refraction n depends on color! In glass: nblue = 1.53 nred = 1.52 nblue > nred qred qi qblue qblue < qred White light Blue light gets deflected more Prism

Wow look at the variation in index of refraction! Rainbow: Preflight 18.5 Wow look at the variation in index of refraction! Which is red? Which is blue? refraction, reflection, refraction 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!

LIKE SO! In second rainbow pattern is reversed

4) Lenses Converging lens: “Plano-convex” Converging lens: – Rays parallel to P.A. converge on focal point q2 q1 F P.A. q1 Diverging lens: – Rays parallel to P.A. diverge as if emerging from focal point behind lens q2 F P.A. Start this by :35 Lens in water has larger focal length since n2/n1 is smaller! “Plano-concave” Focal point determined by geometry and Snell’s Law: n1 sin(q1) = n2 sin(q2) Larger n2/n1 = more bending, shorter focal length. Smaller n2/n1 = less bending, longer focal length. n1 = n2 => No Bending, f = infinity

Converging & Diverging Lenses Converging lens: – Rays parallel to P.A. converge on focal point = = “Plano-convex” “Double convex” “Concave-convex” Converging = fat in the middle Diverging lens: – Rays parallel to P.A. diverge as if emerging from focal point behind lens Start this by :35 Lens in water has larger focal length since n2/n1 is smaller! = = “Plano-concave” “Double concave” “Convex-concave” Diverging = thin in the middle

Converging Lens Principal Rays Example F Image P.A. Object 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). Key assumptions: • monochromatic light incident on a thin lens. • rays are all “near” the principal axis.

Converging Lens Preflight 18.6 All rays parallel to principal axis pass through focal point F. Double Convex P.A. F Preflight 18.6 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? nlens > noutside P.A. F At F Inside F Outside F

3 Cases for Converging Lenses Object Image Past 2F Inverted Reduced Real This could be used in a camera. Big object on small film Between F & 2F Image Object Inverted Enlarged Real This could be used as a projector. Small slide on big screen Demo 71 Image Object Inside F Upright Enlarged Virtual This is a magnifying glass

ACT: Converging Lens Which way should you move object so image is real and diminished? (1) Closer to lens (2) Further from lens (3) Converging lens can’t create real diminished image. F Object P.A. Demo 71

Diverging Lens Principal Rays Example F P.A. Image Object F 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 for diverging lens: Image is always virtual, upright, and reduced.

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