Text Reference: Chapter 32.1 through 32.2 LECTURE 24: Light Text Reference: Chapter 32.1 through 32.2

Types of Images Virtual Images Real Images DEMO 7A-05 Candle & water reflection 1/18/2019

Plane Mirror O = Object = Point source of light S = distance from O to mirror S’ = distance from mirror to point of intersections of extensions I = point image is a virtual image because the rays don’t pass through I. What is the distance between O & I? *Object distance is taken as positive. *Image distance is taken as negative. 1/18/2019

Extended Objects s’ = -s 1/18/2019

Mirrors DEMO 7A-09 O I A plane mirror is a spherical mirror with an infinite radius of curvature. Object Height = Image Height Concave Mirror: Center of curvature is in front of mirror Field of view is smaller than for plane mirror Object Height < Image Height C O I Concave & convex mirros C O I Convex Mirror: Center of curvature is behind mirror Field of view is larger than for plane mirror Object Height > Image Height 1/18/2019

Focal Points of Spherical Mirrors DEMO 7A-01 C F Concave: Parallel rays close to central axis reflect through a common point F. Geometric optics & white board C F Convex: The extensions of the reflected rays pass through a common point behind the mirror. Sign Convention: r & f are positive for concave mirror. r & f are negative for convex mirror.

Images from Spherical Mirrors DEMO 7A-10 F O I Images from Spherical Mirrors O is inside the focal point: *image appears behind the mirror *same orientation F O (b) O at the focal point: *image is ambiguous Light bulb on rail & concave mirror F O I (c) O is outside the focal point: *image is inverted & in front of the mirror 1/18/2019

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Spherical Mirrors Real images form on the same side of a mirror as the object. Virtual images form on the opposite side. For a spherical mirror 1/18/2019

Magnification Size of an object or image is measured to the mirror’s central axis & is called the image height, h’. h - height of object h’ - height of image Magnification produced by a mirror: For plane mirror: For Spherical mirror: 1/18/2019

Location of Images by Drawing Rays Use with next slide. 1/18/2019

Location of Images by Drawing Rays For concave mirrors: You can graphically locate the image of any off-axis point of the object by drawing a ray diagram with any two of four special rays through the point: A ray that is parallel to the central axis reflects through the focal point F. A ray that reflects from the mirror after passing through the focal point emerges parallel to the central axis. A ray that reflects from the mirror after passing through the center of curvature C returns along itself. A ray that reflects from the mirror at its intersection with the central axis is reflected symmetrically about that axis. 1/18/2019

Location of Images by Drawing Rays Use with next slide. C O I C O I 1/18/2019

Summary Equations for mirrors : when the following sign conventions are used: Mirror Type Object Location Image Location Image Type Image Orientation Sign of f r s’ m Plane Anywhere Opposite side of mirror from object Virtual Same orientation as object Concave Inside F Outside F Same side as object Real Inverted Convex 1/18/2019

Example: Concave Mirror A concave spherical mirror has a focal point of 12 cm. If an object is placed 6 cm in front of the mirror, the image position is

Example: Convex Mirror In a subway station, a convex mirror allows the attendant to view activity on the platform. A woman 1.64 m tall is standing 4.5 m from the mirror. The image formed of the woman is 0.500 m tall. What is the radius of curvature of the mirror? 
 (1) 3.9 m; (2) 4.5 m; 3.9 m

Quiz lecture 24 An arrow is located in front of a convex spherical mirror of radius R = 50cm. R = 50 y x What is the focal length of the mirror? f = 50cm f = 25cm f = -50cm f = -25cm 1/18/2019

Quiz lecture 24 A moth at about eye level is 10 cm in front of a plane mirror; you are behind the moth, 30 cm from the mirror. What is the distance between your eyes and the apparent position of the moth’s image in the mirror? 10 cm 20 cm 30 cm 40 cm 60 cm 1/18/2019

LECTURE 25: Spherical Refracting Surfaces

Previous Lecture: Geometric Optics In situations in which the length scales are >> than the light’s wavelength, light propagates as rays incident ray reflected 1 r n1 refracted 2 n2 Reflection: Refraction: If n1 > n2 then 2 > 1 Refracted ray bends away from normal If n2 > n1 then 1 > 2 Refracted ray bends toward the normal 1/18/2019

Spherically Refracting Surfaces If the refracted ray is directed toward the central axis, a real image will form on that axis. Real (virtual) images are formed when obj. is relatively far (near) from refracting surface O C I Real n1 n2 s s’ r If the refracted ray is directed away from the central axis, it CANNOT form a real image. However, backward extension of the ray can form a virtual image. O C I Virtual n1 n2 s r s’ 1/18/2019

Spherically Refracting Surfaces O C I Real n1 n2 s s’ r n2 > n1 Bends toward normal Real image formed I C O Real n2 n1 s’ s r n1 > n2 Bends away from normal Real image formed 1/18/2019

Spherically Refracting Surfaces n2 > n1 Ray directed away from central axis Virtual image formed O C I Virtual n1 n2 C Virtual n2 n1 O I n1 > n2 Bends away from normal and central axis Virtual image formed 1/18/2019

Summary: Spherically Refracting Surfaces Real Images form on the side of a refracting surface that is opposite the object. Virtual Images form on the same side as the object For light rays making only small angles with the central axis: When the object faces a convex refracting surface, the radius of curvature is positive. When object faces a concave surface, radius of curvature is negative. 1/18/2019

Example: Mosquito in Amber A mosquito is embedded in amber with an index of refraction of 1.6. One surface of the amber is spherically convex with a radius of curvature 3.0 mm. The mosquito head happens to be on the central axis of that surface, and when viewed along the axis appears to be buried 5.0 mm into the amber. How deep is it really? Draw a Picture I Virtual n2 n1 O C 1/18/2019

Example: Mosquito in Amber 1/18/2019

Quiz lecture 24 A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n. If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? 2.0 1.5 1.0 0.5 1/18/2019