Course Updates. Reminders: 1) Assignment #13 due Monday. 2) Mirrors & Lenses. 3) Review for Final: Wednesday, May 5th

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1 Coure Update Reminder: ) Aignment #3 due Monday 2) Mirror & Lene 3) Review for Final: Wedneday, May 5th

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4 h R- R θ θ -R h

5 Spherical Mirror Infinite ditance,, R/2 image appear at ½ radiu of curvature. + ' 2 R Equation + ' 2 R Nomenclature; focal length, fr/2, i image length when object i at infinity. + ' f Real image formed by converging ray. Can be viewed on creen. Virtual image ray do not go through. Can not be hown on creen. Concave mirror: can have real or virtual image.

6 Lateral Magnification; pherical mirror Magnification y ' y ' Remark; note that y - y, ince the arrow i upide down and that,, and y are poitive. So the magnification by thi definition i negative, ince y i upide down.

7 Convex mirror For a convex mirror, the radiu of curvature i inide the mirror. We have another RULE, that when the curvature center C i on the ame ide of the outgoing ray, then the radiu i poitive. For the convex mirror we have NEGATIVE radiu. Alo from our rule for, we oberve thi i negative in the above drawing. Uing ame recipe a we ued for concave mirror, we would find ame formula: + ' 2 R Again, note and R are negative Magnification (thi i poitive) y ' y '

8 Quetion The diagram below how three light ray reflected off of a concave mirror. Which ray i NOT correct? A) C) R B) f A) B) C)

9 Quetion The diagram below how three light ray reflected off of a concave mirror. Which ray i NOT correct? A) C) R B) f A) B) C)

10 A) C) X R B) f Ray A goe through focal pt and i reflected parallel to the axi. Ray B ha angle incidence angle reflection Ray C goe through center of phere. Therefore it ha normal incidence Should be reflected traight back

11 Quetion 2 The image produced by a concave mirror of a real object i a) alway real. b) alway virtual. c) ometime real and ometime virtual.

12 Quetion 2 The image produced by a concave mirror of a real object i a) alway real. b) alway virtual. c) ometime real and ometime virtual. I image of a real object from a concave mirror real or virtual? It depend on the poition of the object relative to the focal point! Draw Ray or.. / /f / (concave implie f > 0)

13 Quetion 3 The image produced by a concave mirror of a real object i a) alway upright. b) alway inverted. c) ometime upright and ometime inverted.

14 Quetion 3 The image produced by a concave mirror of a real object i a) alway upright. b) alway inverted. c) ometime upright and ometime inverted. I image of a real object from a concave mirror upright or inverted? Once again, it depend on poition relative to focal point! If > 0, real and inverted If < 0, virtual and upright

15 Y&F Example 34.4 >R image Inverted m / R m- R/2f m <R/2 m /> cometic mirror

16 Quetion 4 The image produced by a convex mirror of a real object i a) alway real. b) alway virtual. c) ometime real and ometime virtual. and ometime inverted.

17 Quetion 4 The image produced by a convex mirror of a real object i a) alway real. b) alway virtual. c) ometime real and ometime virtual. and ometime inverted. I image of a real object from a convex mirror real or virtual? Same PROCEDURE a for concave mirror we did earlier! Draw Ray or.. / /f / (convex implie f < 0)

18 Quetion 5 The image produced by a convex mirror of a real object i a) alway upright. b) alway inverted. c) ometime upright and ometime inverted.

19 Quetion 5 The image produced by a convex mirror of a real object i a) alway upright. b) alway inverted. c) ometime upright and ometime inverted. I image of a real object from a convex mirror upright or inverted? Once again, depend on ign of (real/inverted or virtual/upright) Here < 0 ALWAYS therefore virtual and upright

20 Quetion 6 In order for a real object to create a real, inverted enlarged image, a) we mut ue a concave mirror. b) we mut ue a convex mirror. c) neither a concave nor a convex mirror can produce thi image.

21 Quetion 6 In order for a real object to create a real, inverted enlarged image, a) we mut ue a concave mirror. b) we mut ue a convex mirror. c) neither a concave nor a convex mirror can produce thi image. A convex mirror can only produce a virtual image ince all reflected ray will diverge. Therefore, b) i fale. To create a real image with a concave mirror, the object mut be outide the focal point. The example we jut did gave a real, inverted reduced image. I it poible to chooe the parameter θ uch that the image i enlarged?? h θ The anwer: h i a real image. Therefore conider the OBJECT to be h. The IMAGE will be h -R R- h R

22 h f h

23 Refraction on Spherical Surface R n n n n a b b a + ' Magnification θ θ θ θ θ θ in tan in in tan tan b b a a b a n n y y For mall angle n n y y m y n y n b a b a

24 Lene A len i a piece of tranparent material haped uch that parallel light ray are refracted toward a point, a focu: Poitive f Convergent Len light moving from air into gla will move toward the normal light moving from gla back into air will move away from the normal real focu light moving from air into gla will move toward the normal light moving from gla back into air will move away from the normal virtual focu Divergent Len Negative f

25 The Len Equation We now derive the len equation which determine the image ditance in term of the object ditance and the focal length. Convergent Len: h f h Ray Trace: Ray through the center of the len (light blue) pae through undeflected. Ray parallel to axi (white) pae through focal point f. Thee are principal two et of imilar triangle: ray!!! eliminating h /h: f f h h + h f f h f ame a mirror eqn if we define > 0 f > 0 magnification: alo ame a mirror eqn!! M < 0 for inverted image. M

26 A parallel laer beam of width w i incident on a two len ytem a hown below. w 2 Each len i converging. The econd len ha a larger focal length than the firt (f 2 > f ). What doe the beam look like when it emerge from the econd len? a) The beam i converging b) The beam i diverging c) The beam i parallel to the axi with a width < w d) The beam i parallel to the axi with a width w e) The beam i parallel to the axi with a width > w

27 Len Equation ummary Draw ome ray diagram: convergent len example h f h + ' f ' f f M ' ' h h

28 The len in your eye a) i alway a poitive (i.e., converging) len b) i alway a negative (i.e., diverging) len c) i ometime poitive, and ometime negative, depending on whether you are looking at an object near or far away d) i poitive if you are near-ighted and negative if you are farighted The image on the back of your retina i a) inverted b) noninverted The image on the back of your retina i a) real b) virtual The image on the back of your retina i a) enlarged b) reduced

29 Summary of Lene and Mirror We have derived, in the paraxial (and thin len) approximation, the ame equation for mirror and lene: + f M when the following ign convention are ued: Variable f > 0 f < 0 > 0 < 0 > 0 < 0 Mirror concave convex real (front) virtual (back) real (front) virtual (back) Len converging diverging real (front) virtual (back) real (back) virtual (front) Principal ray connect object and image one goe through the center of the len or mirror the other goe parallel to the optic axi and then i refracted or reflected through a focal point the third one i like the econd one.

30 For next time Homework #3 due Monday One more lecture: optic/optical phenomenon Lat quiz now!

31 Spherical Mirror Concave Mirror Point C, center of curvature. Suppoe object at P, then out Going ray pae through P. α + θ φ ; φ + θ β α + β 2φ tanα h δ ; tan β h h α β ; ' h ' δ Aume, angle mall, δ 0, paraxial ray, approx. parallel to axi. Note and poitive. h R ; tanφ h R δ + ; φ ' R 2