Physics 132 4/24/17. April 24, 2017 Physics 132 Prof. E. F. Redish. Outline

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1 Aprl 24, 2017 Physcs 132 Prof. E. F. Redsh Theme Musc: Justn Tmberlake Mrrors Cartoon: Gary Larson The Far Sde 1 Outlne Images produced by a curved mrror Image equatons for a curved mrror Lght n dense meda: Snell s law Snell s law n Newton s model Thn lenses 2 Prof. E. F. Redsh 1

2 What happens when a ray hts a curved mrror? 3 A Sphercal Mrror: Central Rays A few rays are easy to fgure out where they go. All rays satsfy the angle of ncdence = angle of reflecton measured to the normal to the surface center of sphere All rays through the center strke the mrror perpendcular to the surface and bounce back along ther ncomng path. 4 Prof. E. F. Redsh 2

3 A Sphercal Mrror: Central Ray A few rays are easy to fgure out where they go. center of sphere All rays satsfy the angle of ncdence = angle of reflecton measured to the normal to the surface The ray httng the central lne of the dagram s partcularly smple. 5 A Sphercal Mrror: Parallel Rays A few rays are easy to fgure out where they go. center of sphere All rays satsfy the angle of ncdence = angle of reflecton measured to the normal to the surface All rays parallel to and near an axs of the sphere reflect through a sngle pont on the axs (the focal pont) 6 Prof. E. F. Redsh 3

4 Images n a Sphercal Mrror: 1 Physcal center of sphere focal pont 7 Knds of Images: Real In the case of the prevous slde, the rays seen by the eye do n fact converge at a pont. When the rays seen by the eye do meet, the mage s called real. If a screen s put at the real mage, the rays wll scatter n all drectons and an mage can be seen on the screen, just as f t were a real object. 8 Prof. E. F. Redsh 4

5 Mathematcal h o h R h' = h o h' R = h o R = + f o = R / 2 10 f Images n a Sphercal Mrror: 2 Physcal 11 Prof. E. F. Redsh 5

6 Knds of Images: Vrtual In the case of the prevous slde, the rays seen by the eye do not converge at a pont. When the rays seen by the eye extrapolate to a pont but don t actually meet, the mage s called vrtual. In our case, the convergence pont s behnd the mrror. If we look at the vrtual mage from behnd the mrror, what wll we see? 13 Mathematcal h h o h' = h o h' R = h R + o o = f o R f = R / 2 Prof. E. F. Redsh 6

7 Unfyng Equaton for Mrrors If we treat our mrror quanttes as sgned and let the sgns carry drectonal nformaton, we can unfy all the stuatons n a sngle set of equatons = + f o h > 0 h < 0 h < 0 h > 0 h' = h o > 0 o > 0 f = R / 2 < 0 o < 0 f < 0 f > 0 standard arrangement 15 Smulatons Overvew (lots of rays) physlet_resources/dav_optcs/ Examples/optcs_bench.html Optcs bench (3 rays) Physcs-Interactves/Refracton-and- Lenses/Optcs-Bench/Optcs-Bench- Refracton-Interactve Ray optcs sm smulator/ 17 Prof. E. F. Redsh 7

8 Changng meda n Newton s model Newton has lght as lttle fast movng partcles. What happens when they move from ar nto a denser medum? Newton suggested the lght partcles moved faster n a denser medum (lke sound). 18 Snell s Law n Newton s Model Assume that there s a lower (negatve compared to vacuum) PE for lght partcles n a denser medum. Then lght would go faster snce (KE + PE) n vac = (KE + PE) n medum. Assume no frcton as t passes through the boundary. Snce t goes faster but the parallel component of the speed stays the same (N2!) the perpendcular component must be bgger, tppng the drecton toward the normal. 19 v 0 θ 0 θ 1 v 1 v 0 snθ 0 = v 1 snθ 1 Compare to speed n vacuum = c v 0 c snθ 0 = v 1 c snθ 1 n 0 snθ 0 = n 1 snθ 1 Prof. E. F. Redsh 8

9 A ray of lght s movng from one medum (blue) nto another (yellow). Whch of the outgong rays s the most plausble f - both meda have the same n? - n blue > n yellow? - n blue < n yellow? 20 Foothold Ideas 1: The Physcs Certan objects (the sun, bulbs, ) gve off lght. Lght can travel through a vacuum. In a vacuum lght travels n straght lnes (rays). Each pont on a rough object scatters lght, sprayng t off n all drectons. A polshed surface reflects rays back agan accordng to the rule: The angle of ncdence equals the angle of reflecton. When enterng a transparent medum, a lght ray changes ts drecton accordng to the rule n s a property of the medum and n vac =1. n 1 snθ 1 = n 2 snθ 2 21 Prof. E. F. Redsh 9

10 Foothold Ideas 2: The Psycho-physology We only see somethng when lght comng from t enters our eyes. Our eyes dentfy a pont as beng on an object by many mechansms: By tracng rays back to see where they converge. By how they change when we move. By our experence wth objects and the world. 22 Knds of Images Real When the rays seen by the eye do meet, the mage s called real. If a screen s put at the real mage, rays scatter n all drectons and an mage can be seen on the screen, just as f t were a real object. Vrtual When the rays seen by the eye extrapolate to a pont but don t actually meet, the mage s called vrtual. 24 Prof. E. F. Redsh 10

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