Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Physics 102: Lecture 17 Reflection and Refraction of Light Physics 102: Lecture 17, Slide 1 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: [email protected] • Oh by the way... – Next exam April 18 Physics 102: Lecture 17, Slide 2 Today Last Time Recall from last time…. Reflection: qi = qr qi qr Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex Refraction: Physics 102: Lecture 17, Slide 3 n1 sin(q1)= n2 sin(q2) q1 q2 n1 n2 Concave Mirror Principal Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. O #1 #2 #3 c Image is (in this case): • Real (light rays actually cross) • Inverted (Arrow points opposite direction) • Reduced (smaller than object) Physics 102: Lecture 17, Slide 4 f I **Every other ray from object tip which hits mirror will reflect through image tip Preflight 17.1 Which ray is NOT correct? Ray through center should reflect back on self. p.a. 15% 1) 43% 2) 41% 3) Physics 102: Lecture 17, Slide 5 C f Mirror Equation 1 1 1 do di f do Works for concave, convex, or flat • 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 • Negative: convex mirror Physics 102: Lecture 17, Slide 6 +R/2 –R/2 O f c I di Preflight 17.3 The image produced by a concave mirror of a real object is: 46% 1) Always Real 16% 2) Always Virtual 38% 3) Sometimes Real, Sometimes Virtual Concave mirror: f > 0 Real Object means in front of mirror: do > 0 Mirror Equation: 1 1 1 do di f 1 1 1 = di f d0 di is positive if d0 > f; negative is d0 < f. Physics 102: Lecture 17, Slide 7 ACT: Concave Mirror Where in front of a concave mirror should you place an object so that the image is virtual? 1) Close to mirror Mirror Equation: 2) Far from mirror 3) Either close or far 4) Not Possible • Concave mirror: f > 0 1 1 1 do di f 1 1 1 di f d 0 • Object in front of mirror: do > 0 • Virtual image means behind mirror: di < 0 • When do < f then di < 0 virtual image. Physics 102: Lecture 17, Slide 8 3 Cases for Concave Mirrors Virtual C • • F Object Image Inside F Real Image Object C • C • Object • F • F Image Physics 102: Lecture 17, Slide 9 Between C&F Past C Real Magnification Equation do hi di m ho do O q • ho = height of object: • Positive: q always • hi = height of image: I • Positive: image is upright • Negative: image is inverted • m = magnification: • Positive / Negative: same as for hi Angle of incidence ho q • < 1: image is reduced • > 1: image is enlarged ho hi tan(q ) -hi d o di Physics 102: Lecture 17, Slide 10 di do di q Angle of reflection Solving Equations A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. 1 1 1 6 cm di 2 cm di = + 3 cm (in front of mirror) Real Image! Preflight 17.2 Compared to the candle, the image will be: p.a. 25% • Larger 66% • Smaller 9% • Same Size Physics 102: Lecture 17, Slide 11 C f 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? 1) 2 inches hi m ho 4 inches 2) 4 inches 3) 8 inches Magnitude gives us size. hi mh0 2 4 What direction will the image arrow point? 1) Up 2) Down (-) sign tells us it’s inverted from object Physics 102: Lecture 17, Slide 12 3 Cases for Concave Mirrors Upright C • • F Object Image Inside F Enlarged Virtual Inverted Image C • Object • F Between C&F Enlarged Real Object C • • F Image Physics 102: Lecture 17, Slide 13 Past C Inverted Reduced Real Demo: optical illusion f image object Demo: • two identical spherical mirrors • each mirror is positioned at the focal point of the other Physics 102: Lecture 17, Slide 14 Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. #1 O #2 #3 I f Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object) (always true for convex mirrors!): Physics 102: Lecture 17, Slide 15 c Solving Equations A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. 1 1 1 6 cm di 3 cm di = - 2 cm (behind mirror) Virtual Image! Determine the magnification of the candle. di - 2 cm m do 6 cm m = + 1/3 If the candle is 9 cm tall, how tall does the image candle appear to be? hi 1/ 3 9 cm Physics 102: Lecture 17, Slide 16 hi = + 3 cm Image is Upright! Preflight 17.4 The image produced by a convex mirror of a real object is Mirror Equation: 1) always real 2) always virtual 1 1 1 do di f 3) 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| Physics 102: Lecture 17, Slide 17 1 1 1 di f d 0 di is negative! f is negative do is positive 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 • 1 1 1 do di f • m hi di ho Physics 102: Lecture 17, Slide 18 do 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 “Index of refraction” Speed of light in medium Physics 102: Lecture 17, Slide 19 v = c/n Speed of light in vacuum n is a property of the medium: nvacuum = 1 nair = 1.0003 nwater = 1.33 nglass = 1.50 n≥1 Snell’s law of Refraction When light travels from one medium to another, v (and l) changes (v = c/n). So the light bends! n1 sin(q1)= n2 sin(q2) Incident wave Reflected wave q1 q r l1 n2 > n 1 l2 < l1 Refracted wave Physics 102: Lecture 17, Slide 20 n1 q2 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 q2 = 40.6 degrees n1 normal n2 Physics 102: Lecture 17, Slide 21 q1 = qr = 60 sin(60) = 1.33 sin(q2) n1 sin q1 n2 sin q2 q 2 Apparent Depth Apparent depth: n2 d d n1 n2 n1 d apparent fish d actual fish Physics 102: Lecture 17, Slide 22 See you after break! Physics 102: Lecture 17, Slide 23