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

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

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.

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.

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

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