Geometric Optics. Flat Mirrors Spherical Mirrors Images Formed by Refraction Thin Lenses Optical Instruments

Transcription

1 Geometric Otics Flat Mirrors Sherical Mirrors Images Formed by efraction Thin Lenses Otical Instruments

2 Images - Terminology : Object Distance : Image Distance Magnification M Image Height Object Height eal Images: When light rays ass through and diverge from the image oint. Virtual Images: When light rays do not ass through but aear to diverge h h from the image oint.

3 Images Formed by Flat Mirrors The image is virtual For flat mirrors, M The image distance is eual to the object distance. The image is unmagnified, virtual and uright. The image has front-back reversal.

4 Concet Question An observer O, facing a mirror, observes a light source S. Where does O erceive the mirror image of S to be located? Some other location. 6. The image of S cannot be seen by O when O and S are located as shown.

5 Some Examles Multile Images Formed by Two Mirrors earview Mirror

6 Concave Sherical Mirrors Sherical Concave Mirror A real image is formed by a concave mirror Paraxial Aroximation: Only consider rays making a small angle with the rincial axis Sherical Aberration

7 h h tanθ h h M h h tanα h h + Focal Point f f + Image Formation

8 Convex Sherical Mirrors The image formed is uright and virtual M h h + f

9 Sign Conventions for Mirrors is ositive if object is in front of mirror (real object). is negative if object is in back of mirror (virtual object). is ositive if image is in front of mirror (real image). is negative if image is in back of mirror (virtual image). Both f and are ositive if center of curvature is in front of mirror (concave mirror). Both f and are negative if center of curvature is in back of mirror (convex mirror). If M is ositive, image is uright. If M is negative, image is inverted.

10 ay Diagrams For Mirrors ay is drawn from the to of the object arallel to the rincial axis and is reflected through the focal oint F. ay is drawn from the to of the object through the focal oint and is reflected arallel to the rincial axis. ay 3 is drawn from the to of the object through the center of curvature C and is reflected back on itself.

11 Concave Mirror ( > ) Image is real, inverted and smaller than the object

12 Concave Mirror ( < f) Image is virtual, uright and larger than the object

13 Convex Mirror Image is virtual, uright and smaller than the object

14 Image From a Mirror f +0 cm Concave Mirror (a) 5 cm (b) 0 cm (c) 5 cm + f cm 0cm M h h M h h

15 Images Formed By efraction

16 n n Sinθ nsinθ θ nθ θ α + β β θ + γ nα + nγ ( n n )β tanα α tan β β tanγ γ d d d d d n + n n + d ( n n ) ( n n ) n

17 Sign Conventions for efracting Surfaces is ositive if object is in front of surface (real object). is negative if object is in back of surface (virtual object). is ositive if image is in back of surface (real image). is negative if image is in front of surface (virtual image). is ositive if center of curvature is in back of convex surface. is negative if center of curvature is in front of concave surface.

18 Flat efracting Surface n + n 0 n n The image is on the same side of the surface as the object.

19 Aarent Deth d n n.33 d 0.75d The image is virtual

20 Thin Lenses The image formed by the first surface acts as the object for the second surface ( ) n n + ( ) n n + where, < 0 t + ( ) n n + ( ) + n ( ) + n ( ) n f Lens Makers Euation f + h h M

21 Concet Question A arallel beam of light is sent through an auarium. If a convex glass lens is held in the water, it focuses the beam. closer to the lens than. at the same osition as 3. farther from the lens than outside the water.

22 Lens Tyes Converging Lenses f : object focal oint f : image focal oint Diverging Lenses

23 Sign Conventions for Thin Lenses is ositive if object is in front of lens (real object). is negative if object is in back of lens (virtual object). is ositive if image is in back of lens (real image). is negative if image is in front of lens (virtual image). and are ositive if center of curvature is in back of lens. and are negative if center of curvature is in front of lens. f is ositive if the lens is converging. f is negative if the lens is diverging.

24 ay Diagrams for a Converging Lens ay is drawn arallel to the rincial axis. After being refracted, this ray asses through the focal oint on the back side of the lens. ay is drawn through the center of the lens and continues in a straight line. ay 3 is drawn through the focal oint on the front side of the lens (or as if coming from the focal oint if < f) and emerges from the lens arallel to the rincial axis.

25 The image is real and inverted The image is virtual and uright

26 ay Diagrams for a Diverging Lens ay is drawn arallel to the rincial axis. After being refracted, this ray emerges such that it aears to have assed through the focal oint on the front side of the lens. ay is drawn through the center of the lens and continues in a straight line. ay 3 is drawn toward the focal oint on the back side of the lens and emerges from the lens arallel to the rincial axis.

27 The image is virtual and uright

28 Examles A diverging lens with f -0 cm h cm, 30 cm f cm M h h 0 h M h 0.8cm The image is virtual and uright A converging lens with f 0 cm (a) 30 cm 5 + M cm (b) 0 cm (c) 5 cm The image is real and inverted The image is at infinity + M cm The image is virtual and uright

29 Java Alet for Lens and Mirrors htt://

30 Combination of Thin Lenses First find the image created by the first lens as if the second lens is not resent. Then draw the ray diagram for the second lens with the image from the first lens as the object. The second image formed is the final image of the system. I O I f f

31 Examle 0 cm 0 cm I I O 0 cm f 0 0cm f 0 cm 0 + f 0 cm M f M cm M M M ( )( )

32 The Camera A lens is used to form an image of an object on the film (or detector array). The amount of light entering the camera is controlled by the aerture. The exosure is controlled by the shutter seed. I D f f # f number f D

33 The Eye Light is refracted by the cornea (which includes an aueous humor and lens) and its intensity is regulated by the iris. Light ideally focuses on the retina which has a set of recetors called the rods and cones. The recetors send otical information to the brain via the otical nerve. Focusing is done by changing the shae (curvature) of the lens. The closest oint of focus is the near oint (~ 5 cm).

34 The Simle Magnifier Use a lens near the eye to make an object seem larger (occuy a larger angle at the eye). m θ θ θ m θ 5cm f

35 Comound Microscoe Use a lens combination to make small objects near the objective seem more visible. m L f o M mmθ L f 5cm o f e

36 For Next Class Midterm 3 eview on Monday Midterm 3 on Tuesday eading Assignment for Wednesday Chater 37: Interference of Light Waves WebAssign: Assignment 4