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<ul><li> 1. Reflection and Refraction of Light Physics 102:Lecture 17</li></ul> <p> 2. Recall from last time. Reflection: Refraction: Flat Mirror:image equidistant behind Spherical Mirrors: Concave or Convex i= r n 1sin( 1 )= n 2sin( 2 ) Today Last Time i r 1 2 n 2 n 1 3. O Concave Mirror Principal Rays f c 1) Parallel to principal axis reflects through f. 3) Through center. </p> <ul><li>Image is (in this case): </li></ul> <ul><li>Real (light rays actually cross) </li></ul> <ul><li>Inverted (Arrow points opposite direction) </li></ul> <ul><li>Reduced (smaller than object) </li></ul> <p>**Every other ray from object tip which hits mirror will reflect through image tip 2) Through f, reflects parallel to principal axis. #1 #3 #2 I 4. C f 1) 2) 3) p.a. Preflight 17.1 Ray through center should reflect back on self. Which ray is NOT correct? 20% 45% 35% 5. O Mirror Equation c </p> <ul><li>d o= distance object is from mirror: </li></ul> <ul><li><ul><li><ul><li>Positive:objectin frontof mirror </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Negative:objectbehindmirror </li></ul></li></ul></li></ul> <ul><li>d i= distance image is from mirror: </li></ul> <ul><li><ul><li><ul><li>Positive:realimage (in front of mirror) </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Negative:virtualimage (behind mirror) </li></ul></li></ul></li></ul> <ul><li>f = focal length mirror: </li></ul> <ul><li><ul><li><ul><li>Positive:concavemirror+R/2 </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Negative:convexmirrorR/2 </li></ul></li></ul></li></ul> <p>Works for concave, convex, or flat I f d o d i 6. Preflight 17.3 </p> <ul><li>The image produced by a concave mirror of a real object is: </li></ul> <ul><li>Always Real </li></ul> <ul><li>Always Virtual </li></ul> <ul><li>Sometimes Real, Sometimes Virtual </li></ul> <p> 7. ACT: Concave Mirror </p> <ul><li>Where in front of a concave mirror should you place an object so that the image is virtual? </li></ul> <ul><li>Close to mirror </li></ul> <ul><li>Far from mirror </li></ul> <ul><li>Either close or far </li></ul> <ul><li>Not Possible </li></ul> <p> 8. 3 Cases for Concave Mirrors Inside F Between C&amp;F Past C Real Virtual Real C F Object Image C F Object Image C F Object Image 9. O Magnification Equation </p> <ul><li>h o= height of object: </li></ul> <ul><li><ul><li><ul><li>Positive:always </li></ul></li></ul></li></ul> <ul><li>h i= height of image: </li></ul> <ul><li><ul><li><ul><li>Positive:image isupright </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Negative:image isinverted </li></ul></li></ul></li></ul> <ul><li>m = magnification: </li></ul> <ul><li><ul><li><ul><li>Positive / Negative:same as for h i </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>&lt; 1:image isreduced </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>&gt; 1:image isenlarged </li></ul></li></ul></li></ul> <p>I d o d o h o Angle of incidence d i -h i Angle of reflection d i 10. Solving Equations </p> <ul><li>A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. </li></ul> <p>d i= + 3 cm (in front of mirror) Real Image! Example C f p.a. Preflight 17.2 Compared to the candle, the image will be: </p> <ul><li>Larger </li></ul> <ul><li>Smaller </li></ul> <ul><li>Same Size </li></ul> <p> 11. ACT: Magnification </p> <ul><li>A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of 2.</li></ul> <ul><li>What is the size of the image? </li></ul> <ul><li>2 inches </li></ul> <ul><li>4 inches </li></ul> <ul><li>8 inches </li></ul> <ul><li>What direction will the image arrow point? </li></ul> <ul><li>Up 2)Down </li></ul> <p>4 inches 12. 3 Cases for Concave Mirrors Inside F Between C&amp;F Past C Inverted Enlarged Real Upright Enlarged Virtual Inverted Reduced Real C F Object Image C F Object Image C F Object Image 13. f image object </p> <ul><li>Demo:</li></ul> <ul><li>two identical spherical mirrors </li></ul> <ul><li>each mirror is positioned at the focal point of the other </li></ul> <p>Demo: optical illusion 14. O Convex Mirror Raysc 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. Image is: Virtual (light rays dont really cross) Upright(same direction as object) Reduced(smaller than object) ( alwaystrue for convex mirrors!): f #2 I #3 #1 15. Solving Equations A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. Determine the magnification of the candle. If the candle is 9 cm tall, how tall does the image candle appear to be? Example 16. Preflight 17.4 </p> <ul><li>The image produced by a convex mirror of a real object is</li></ul> <ul><li>always real </li></ul> <ul><li>always virtual </li></ul> <ul><li>sometimes real and sometimes virtual </li></ul> <p> 17. Mirror Summary </p> <ul><li>Angle of incidence = Angle of Reflection </li></ul> <ul><li>Principal Rays </li></ul> <ul><li><ul><li>Parallel to P.A.: Reflects through focus </li></ul></li></ul> <ul><li><ul><li>Through focus: Reflects parallel to P.A. </li></ul></li></ul> <ul><li><ul><li>Through center: Reflects back on self </li></ul></li></ul> <ul><li>|f| = R/2 </li></ul> <p> 18. Index of Refraction Frequency is thesame , wavelengthdecreases Recall speed of light c = 3x10 8m/s isin vacuum In a medium (air, water, glass...) light isslower n is a property of the medium: n vacuum= 1 n air= 1.0003 n water= 1.33 n glass= 1.50 v=c / n n 1 c = /f v &lt; c c vacuum glass 1 2 Speed of light in vacuum Speed of light in medium Index of refraction 19. Reflected wave Refracted wave Incident wave n 1 n 2&gt; n 1 Snells law of Refraction n 1sin( 1 )= n 2sin( 2 ) When light travels from one medium to another, v (and ) changes (v = c/n). So the light bends! 2&lt; 1 1 1 r 2 20. n 1 n 2 Snells Law Practice normal 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.The other part of the beam is refracted.What is 2 ? sin(60) = 1.33 sin( 2 ) 2= 40.6 degrees 1= r= Usually, there is bothreflectionandrefraction ! Example 1 r 21. Apparent Depth n 2 n 1 50 d d Apparent depth: actual fish apparent fish </p>