The document summarizes key concepts from a Physics 102 lecture on optics, including Snell's law, total internal reflection, Brewster's angle, dispersion, and lenses. Snell's law describes how light bends when passing from one medium to another. Total internal reflection occurs when light hits the boundary between two media at an angle greater than the critical angle. Brewster's angle is when the reflected light is completely polarized. Dispersion is why prisms separate white light into a rainbow spectrum. Lenses use refraction to converge or diverge light rays depending on their shape.

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

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

3. Demo: Snell’s Law n 2 n 1 > n 2 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 > n 2   2 >  1 Light bent away from normal as it goes in medium with lower n  1  2  r incident reflected refracted

4. 1) Total Internal Reflection normal n 2 n 1 > n 2 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 Light incident at a larger angle will only have reflection (  i =  r ) For water/air: n 1 =1.33, n 2 =1  1 = sin -1 (n 2 /n 1 ) = 48.8 0 “ critical angle”  1  2  i >  c  r  c

5. Fiber Optics Telecommunications Arthoscopy Laser surgery Total Internal Reflection only works if n outside < n inside 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. n inside n outside

6. Can the person standing on the edge of the pool be prevented from seeing the light by total internal reflection ? 1) Yes 2) No Preflight 18.1

7. 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

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

9. 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.

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

11. 3) Dispersion Prism Blue light gets deflected more n blue > n red The index of refraction n depends on color! In glass: n blue = 1.53 n red = 1.52 White light  blue <  red  red  i  blue

12. Skier sees blue coming up from the bottom (1) , and red coming down from the top (2) of the rainbow. Rainbow: Preflight 18.5 Wow look at the variation in index of refraction! Which is red ? Which is blue ? Blue light is deflected more!

13. LIKE SO! In second rainbow pattern is reversed

14. 4) Lenses Focal point determined by geometry and Snell’s Law : n 1 sin(  1 ) = n 2 sin(  2 ) Converging lens: – Rays parallel to P.A. converge on focal point Diverging lens: – Rays parallel to P.A. diverge as if emerging from focal point behind lens Larger n 2 /n 1 = more bending, shorter focal length. Smaller n 2 /n 1 = less bending, longer focal length. n 1 = n 2 => No Bending, f = infinity F         “ Plano-convex” “ Plano-concave” P.A. F P.A.

15. Converging & Diverging Lenses Converging lens: – Rays parallel to P.A. converge on focal point Diverging lens: – Rays parallel to P.A. diverge as if emerging from focal point behind lens “ Plano-convex” “ Plano-concave” Converging = fat in the middle Diverging = thin in the middle “ Double concave” “ Double convex” = = = = “ Convex-concave” “ Concave-convex”

16. 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. Converging Lens Principal Rays F F Object P.A. Image is: real, inverted and enlarged (in this case). Example Image Key assumptions: • monochromatic light incident on a thin lens. • rays are all “near” the principal axis.

17. Converging Lens All rays parallel to principal axis pass through focal point F. Double Convex P.A. n lens > n outside F At F Inside F Outside F 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?

18. 3 Cases for Converging Lenses This could be used in a camera. Big object on small film Inverted Reduced Real Past 2F This could be used as a projector. Small slide on big screen Inverted Enlarged Real Between F & 2F This is a magnifying glass Upright Enlarged Virtual Inside F Object Image Image Object Image Object

19. 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 F Object P.A.

20. 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. Diverging Lens Principal Rays F F Object P.A. Only 1 case for diverging lens : Image is always virtual, upright, and reduced . Example Image

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