Reflection and Refraction of Light

1. Physics 102: Lecture 17 Reflection and Refraction of Light

2. Exam 2 results • Raw mean = 87.8 / 115 (76.3%) • Scaled mean = 76.3% • Raw mean improved by 10% compared to Exam 1 • Answers will be posted after March 18 • Concerned? Diagnose the issue • Physics understanding? • Test taking? • Contact me: ychemla@illinois.edu • Oh by the way... • Next exam April 18

3. qi qr Last Time Today q1 n1 n2 q2 Recall from last time…. Reflection: qi = qr Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex Refraction: n1 sin(q1)= n2 sin(q2)

4. #1 #2 #3 I Concave Mirror Principal Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. O f c • Image is (in this case): • Real (light rays actually cross) • Inverted (Arrow points opposite direction) • Reduced (smaller than object) **Every other ray from object tip which hits mirror will reflect through image tip

5. 15% 43% 41% Preflight 17.1 Which ray is NOT correct? Ray through center should reflect back on self. p.a. 1) C f 2) 3)

6. Mirror Equation do f I di Works for concave, convex, or flat O c • do = distance object is from mirror: • Positive: object in front of mirror • Negative: object behind mirror • di = distance image is from mirror: • Positive: real image (in front of mirror) • Negative: virtual image (behind mirror) • f = focal length mirror: • Positive: concave mirror +R/2 • Negative: convex mirror –R/2

7. Mirror Equation: Preflight 17.3 The image produced by a concave mirror of a real object is: 46% 16% 38% • Always Real • Always Virtual • Sometimes Real, Sometimes Virtual Concave mirror: f > 0 Real Object means in front of mirror: do > 0  di is positive if d0 > f; negative is d0 < f.

8. ACT: Concave Mirror Where in front of a concave mirror should you place an object so that the image is virtual? Mirror Equation: • Close to mirror • Far from mirror • Either close or far • Not Possible • Concave mirror: f > 0 • Object in front of mirror: do > 0 • Virtual image means behind mirror: di < 0 • When do < f then di < 0 virtual image.

9. C C C F F F Object Image Image Object Object Image 3 Cases for Concave Mirrors Virtual Inside F Real Between C&F Real Past C

10. Magnification Equation q do do q Angle of incidence I di ho q di -hi q Angle of reflection O • ho = height of object: • Positive: always • hi = height of image: • Positive: image is upright • Negative: image is inverted • m = magnification: • Positive / Negative: same as for hi • < 1: image is reduced • > 1: image is enlarged

11. Preflight 17.2 Compared to the candle, the image will be: • Larger • Smaller • Same Size Example Solving Equations A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. di = + 3 cm (in front of mirror) Real Image! p.a. C f 25% 66% 9%

12. ACT: Magnification A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2. • What is the size of the image? • 2 inches • 4 inches • 8 inches 4 inches Magnitude gives us size. • What direction will the image arrow point? • Up 2) Down (-) sign tells us it’s inverted from object

13. C C C F F F Object Image Image Object Object Image 3 Cases for Concave Mirrors Upright Enlarged Virtual Inside F Inverted Enlarged Real Between C&F Inverted Reduced Real Past C

14. Demo: optical illusion f image object • Demo: • two identical spherical mirrors • each mirror is positioned at the focal point of the other

15. #1 #2 #3 Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. O I f c Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object) (always true for convex mirrors!):

16. Virtual Image! Image is Upright! Example 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? di = - 2 cm (behind mirror) m = + 1/3 hi = + 3 cm

17. di is negative! do is positive f is negative Preflight 17.4 Mirror Equation: The image produced by a convex mirror of a real object is • always real • always virtual • sometimes real and sometimes virtual • Convex mirror: f < 0 • Object in front of mirror: do > 0 • di < 0 means virtual image! • Image is always between F and mirror |di|<|f|

18. Mirror Summary • Angle of incidence = Angle of Reflection • Principal Rays • Parallel to P.A.: Reflects through focus • Through focus: Reflects parallel to P.A. • Through center: Reflects back on self • |f| = R/2

19. Index of Refraction Recall speed of light c = 3x108 m/s is in vacuum In a medium (air, water, glass...) light is slower c l1 l2 v < c Frequency is the same, wavelength decreases v = lf vacuum glass n is a property of the medium: nvacuum = 1 nair = 1.0003 nwater = 1.33 nglass = 1.50 “Index of refraction” n ≥ 1 Speed of light in medium v = c/n Speed of light in vacuum

20. Snell’s law of Refraction When light travels from one medium to another, v (and l) changes (v = c/n). So the light bends! l1 n1 sin(q1)= n2 sin(q2) Incident wave q1 qr Reflected wave n1 l2 < l1 n2 > n1 q2 Refracted wave

21. 1 r Example Snell’s Law Practice Usually, there is both reflection and refraction! 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 qr = 60. The other part of the beam is refracted. What is q2? q1 = qr = 60 sin(60) = 1.33 sin(q2) q2 = 40.6 degrees n1 n2 normal

22. Apparent depth: d apparent fish d actual fish Apparent Depth n2 n1

23. See you after break!