Reflection and Refraction of Light Physics 102: Lecture 17 Reflection and Refraction of Light 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: ychemla@illinois.edu Oh by the way... Next exam April 18

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

Concave Mirror Principal Rays 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. 3) Through center. #3 #2 O #1 f c I Image is (in this case): Real (light rays actually cross) Inverted (Arrow points opposite direction) Reduced (smaller than object) Comment that this is “weird” to have a real image. –demo 554, flower mirage **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% 43% 41% 1) C f 2) 3)

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

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 Mirror Equation:  di is positive if d0 > f; negative is d0 < f.

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 Demo: 1131; large concave mirror 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.

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

Magnification Equation do O do ho Angle of incidence ho = height of object: Positive: always q di -hi Angle of reflection I 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 di Flat mirrors: m=+1

Solving Equations Preflight 17.2 Example 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! Preflight 17.2 Compared to the candle, the image will be: Larger Smaller Same Size p.a. C f 25% 66% 9%

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

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

Demo: optical illusion f image object Demo 296: penny mirage Demo: two identical spherical mirrors each mirror is positioned at the focal point of the other

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 c Make this mirror almost flat so that it is like your review mirror Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object) (always true for convex mirrors!):

Solving Equations Example 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) Virtual Image! m = + 1/3 hi = + 3 cm Image is Upright!

Preflight 17.4 The image produced by a convex mirror of a real object is Mirror Equation: always real always virtual sometimes real and sometimes virtual Convex mirror: f < 0 64% got this right Object in front of mirror: do > 0 di is negative! f is negative do is positive di < 0 means virtual image! Image is always between F and mirror |di|<|f|

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

Index of Refraction v = c/n 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

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 q1 qr q2 Reflected wave l1 n1 l2 < l1 n2 > n1 Refracted wave

Snell’s Law Practice Example 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) 1 r q2 = 40.6 degrees n1 n2 normal

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

See you after break!