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• Comment that this is “weird” to have a real image. –demo 554, flower mirage
• Note: also works for flat mirrors (f is infinite)
• Demo: 1131; large concave mirror
• Flat mirrors: m=+1
• Demo 296: penny mirage
• Make this mirror almost flat so that it is like your review mirror
• Lect17 handout

1. 1. Reflection and Refraction of Light Physics 102: Lecture 17
2. 2. Recall from last time…. Reflection: Refraction: Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex  i =  r n 1 sin(  1 )= n 2 sin(  2 ) Today Last Time  i  r  1  2 n 2 n 1
3. 3. O Concave Mirror Principal Rays f c 1) Parallel to principal axis reflects through f. 3) Through center. <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>**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. 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. 5. O Mirror Equation c <ul><li>d o = distance object is from mirror: </li></ul><ul><ul><ul><li>Positive: object in front of mirror </li></ul></ul></ul><ul><ul><ul><li>Negative: object behind mirror </li></ul></ul></ul><ul><li>d i = distance image is from mirror: </li></ul><ul><ul><ul><li>Positive: real image (in front of mirror) </li></ul></ul></ul><ul><ul><ul><li>Negative: virtual image (behind mirror) </li></ul></ul></ul><ul><li>f = focal length mirror: </li></ul><ul><ul><ul><li>Positive: concave mirror +R/2 </li></ul></ul></ul><ul><ul><ul><li>Negative: convex mirror –R/2 </li></ul></ul></ul>Works for concave, convex, or flat I f d o d i
6. 6. Preflight 17.3 <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>
7. 7. ACT: Concave Mirror <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>
8. 8. 3 Cases for Concave Mirrors Inside F Between C&F Past C Real Virtual Real C F Object Image C F Object Image C F Object Image
9. 9. O Magnification Equation <ul><li>h o = height of object: </li></ul><ul><ul><ul><li>Positive: always </li></ul></ul></ul><ul><li>h i = height of image: </li></ul><ul><ul><ul><li>Positive: image is upright </li></ul></ul></ul><ul><ul><ul><li>Negative: image is inverted </li></ul></ul></ul><ul><li>m = magnification: </li></ul><ul><ul><ul><li>Positive / Negative: same as for h i </li></ul></ul></ul><ul><ul><ul><li>< 1: image is reduced </li></ul></ul></ul><ul><ul><ul><li>> 1: image is enlarged </li></ul></ul></ul>I d o d o h o Angle of incidence d i -h i Angle of reflection d i    
10. 10. Solving Equations <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>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: <ul><li>Larger </li></ul><ul><li>Smaller </li></ul><ul><li>Same Size </li></ul>
11. 11. ACT: Magnification <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>4 inches
12. 12. 3 Cases for Concave Mirrors Inside F Between C&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. 13. f image object <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>Demo: optical illusion
14. 14. O Convex Mirror Rays c 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object) ( always true for convex mirrors!): f #2 I #3 #1
15. 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. 16. Preflight 17.4 <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>
17. 17. Mirror Summary <ul><li>Angle of incidence = Angle of Reflection </li></ul><ul><li>Principal Rays </li></ul><ul><ul><li>Parallel to P.A.: Reflects through focus </li></ul></ul><ul><ul><li>Through focus: Reflects parallel to P.A. </li></ul></ul><ul><ul><li>Through center: Reflects back on self </li></ul></ul><ul><li>|f| = R/2 </li></ul>
18. 18. Index of Refraction Frequency is the same , wavelength decreases Recall speed of light c = 3x10 8 m/s is in vacuum In a medium (air, water, glass...) light is slower 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 < c c vacuum glass  1  2 Speed of light in vacuum Speed of light in medium “ Index of refraction”
19. 19. Reflected wave Refracted wave Incident wave n 1 n 2 > n 1 Snell’s law of Refraction n 1 sin(  1 )= n 2 sin(  2 ) When light travels from one medium to another, v (and  ) changes (v = c/n). So the light bends!  2 <  1  1  1  r  2
20. 20. n 1 n 2 Snell’s 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 both reflection and refraction ! Example  1  r
21. 21. Apparent Depth n 2 n 1 50 d d  Apparent depth: actual fish apparent fish