Physics 102: Lecture 17 Reflection and Refraction of Light Physics 102: Lecture 17, Slide 1
Recall from last time. Today Last Time Reflection: θ i = θ r Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex Refraction: n 1 sin(θ 1 )= n 2 sin(θ 2 ) θ i θ r θ 1 n 1 θ 2 n 2 Physics 102: Lecture 17, Slide 2
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 #3 f c Image is (in this case): Real (light rays actually cross) I Inverted (Arrow points opposite direction) Reduced (smaller than object) **Every other ray from object tip which hits mirror will reflect through image tip Physics 102: Lecture 17, Slide 3 #2
Physics 102: Lecture 17, Slide 4
Preflight 17.1 Which ray is NOT correct? 1) p.a. C f 2) 3) Physics 102: Lecture 17, Slide 5
Mirror Equation 1 d o + 1 d i = 1 f Works for concave, convex, or flat O d o d o = distance object is from mirror: c f Positive: object in front of mirror Negative: object behind mirror I d i = distance image is from mirror: d i Positive: real image (in front of mirror) Negative: virtual image (behind mirror) f = focal length mirror: Positive: concave mirror +R/2 Negative: convex mirror Physics 102: Lecture 17, Slide 6 R/2
Preflight 17.3 The image produced by a concave mirror of a real object is: 1) Always Real 2) Always Virtual 3) Sometimes Real, Sometimes Virtual Physics 102: Lecture 17, Slide 7
Physics 102: Lecture 17, Slide 8
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 2) Far from mirror 3) Either close or far 4) Not Possible Physics 102: Lecture 17, Slide 9
Magnification Equation m h h i o = d d i o O d o h o = height of object: θ Positive: always h i = height of image: Positive: image is upright I θ Negative: image is inverted m = magnification: Angle of incidence h o d i Positive / Negative: same as for h i < 1: image is reduced > 1: image is enlarged θ d o Physics 102: Lecture 17, Slide 10 tan(θ ) = h d o o = h d i i h i θ d i Angle of reflection 25
Solving Equations A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. Preflight 17.2 Compared to the candle, the image will be: Larger p.a. C f Smaller Same Size Physics 102: Lecture 17, Slide 11
Physics 102: Lecture 17, Slide 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? 1) 2 inches 2) 4 inches 3) 8 inches 4 inches What direction will the image arrow point? 1) Up 2) Down Physics 102: Lecture 17, Slide 13
3 Cases for Concave Mirrors Upright C F Object Image Inside F Enlarged Virtual Image C Obje ct F Between C&F Inverted Enlarged Real Obje ct C F Image Physics 102: Lecture 17, Slide 14 Past C Inverted Reduced Real
f image object Demo: two identical spherical mirrors each mirror is positioned at the focal point of the other Physics 102: Lecture 17, Slide 15
Physics 102: Lecture 17, Slide 16
Convex Mirror Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. O #1 #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 17 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. Determine the magnification of the candle. If the candle is 9 cm tall, how tall does the image candle appear to be? Physics 102: Lecture 17, Slide 18
Preflight 17.4 The image produced by a convex mirror of a real object is 1) always real 2) always virtual 3) sometimes real and sometimes virtual Physics 102: Lecture 17, Slide 19
Physics 102: Lecture 17, Slide 20
Physics 102: Lecture 17, Slide 21 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 d o d i f m h i d = i h o d o
Index of Refraction 186,000 miles/second: it s not just a good idea, it s the law! v = c n Speed of light in vacuum Speed of light in medium Index of refraction v < c Physics 102: Lecture 17, Slide 22 so always! n > 1
Snell s Law When light travels from one medium to another the speed changes v=c/n, but the frequency is constant. So the light bends: n 1 sin(θ 1 )= n 2 sin(θ 2 ) n 1 Preflight 17.6 θ 1 1) n 1 > n 2 θ 2 n 2 2) n 1 = n 2 Compare n 1 to n 2. 3) n 1 < n 2 Physics 102: Lecture 17, Slide 23
Physics 102: Lecture 17, Slide 24
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 θ r = 60. The other part of the beam is refracted. What is θ 2? θ 1 θ r n 1 θ 2 = n 2 Physics 102: Lecture 17, Slide 25 normal θ 2 n 1 sin θ 1 = n 2 sin θ 2
Apparent Depth Apparent depth: d = d n 2 n 1 n 2 d d n 1 apparent fish actual fish Physics 102: Lecture 17, Slide 26
Physics 102: Lecture 17, Slide 27