Radius of Curvature Plane

A plane mirror is a spherical mirror with an infinite radius of curvature. O Height = I Height

Spherical DEMO Focal Points of Spherical Mirrors DEMO Concave Mirror: (e.g. make up mirror) Concave: Parallel rays close to Center of curvature is in front of mirror central axis reflect through a Field of view is smaller than for plane common point F. mirror F is called the focal point. Object Height < Image Height f is the focal length (distance from center of mirror to F). R f = 2 Convex: The extensions of the Convex Mirror: (e.g. surveillance mirror) reflected rays pass through a Center of curvature is behind mirror common point behind the mirror. Field of view is larger than for plane mirror Object Height > Image Height

Sign Convention: r & f are positive for concave mirror.

10/25/11 3 10/25/11 r & f are negative for convex mirror. 4 DEMO Images from Spherical Mirrors Spherical Mirrors (a)! O is inside the focal point:

*image appears behind the mirror •! So > 0 *S is negative i •! Real images form on the same side of a *virtual image mirror as the object (Si > 0). *same orientation •! Virtual images form on the opposite side (Si (b) O at the focal point: < 0). *image is ambiguous 1 1 1 *rays do not cross to form image + = For a spherical mirror So Si f (c) O is outside the focal point:

*image is inverted & in front of the mirror f > 0 concave mirror

*Si is positive f < 0 convex mirror *real image

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Magnification Location of Images by Drawing Rays Size of an object or image is measured to the mirror’s central axis & is

called the image height, hi.

h - height of object Si o m = ! So hi - height of image h S Magnification produced by a mirror: m = i m = i ho So If m < 0, image is inverted.

For plane mirror : Si = !So For Spherical mirror: m 1 = + 1 1 1 fSo + = " Si = Use with next slide. Image is upright. S0 Si f So ! f S ! f m = ! i " m = So So ! f

10/25/11 7 10/25/11 8 Location of Images by Drawing Rays Summary 1 1 1 S For concave mirrors: You can graphically locate the + = m = ! i •! Equations for mirrors : S S f image of any off-axis point of the object by drawing a o i So diagram with any two of four special rays through when the following sign conventions are used: the point: Mirror Object Image Location Image Type Image Sign of 1.! A ray that is parallel to the central axis reflects through the Type Location Orientation f r s’ m focal point F. Plane Anywhere Opposite side of Virtual Same ! ! - + mirror from orientation 2.! A ray that reflects from the mirror after passing through the object as object focal point emerges parallel to the central axis. Concave Inside F Opposite side of Virtual Same + + - + mirror from orientation 3.! A ray that reflects from the mirror after passing through the object as object center of curvature C returns along itself. Concave Outside F Same side as Real Inverted + + + - object 4.! A ray that reflects from the mirror at its intersection with the central axis is reflected symmetrically about that axis. Convex Anywhere Opposite side of Virtual Same - - - + mirror from orientation object as object

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Last Lecture: Geometric Thin Lenses: Converging Lens In situations in which the length scales are >> than the light’s wavelength, light propagates as rays incident reflected ray ray !1 !r n : !i = !r 1 n2 !2 Refraction: n1 sin!1 = n2 sin!2 refracted ray •!Parallel rays refract twice 1 ' 1 1 $ = (n !1)% ! " •!Converge at F a distance f from f & r1 r2 # If n1 > n2 then !2 > !1 Refracted ray bends away from normal 2 center of lens n !1 > 0 because nglass > nair r 0 because obj. facing convex surface •!F2 is a real focal pt because rays 1 >

If n2 > n1 then !1 > !2 Refracted ray bends toward the normal pass through r2 < 0 because obj. facing concave surface •!f > 0 for real focal points

10/25/11 11 10/25/11 12 Thin Lenses: Diverging Lens Ray Tracing For Lenses

•!Rays diverge, never pass through a common point f < 0 for virtual focal points •!F2 at a distance f

•!F2 is virtual focal point

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Lens Equation Extra Slides

10/25/11 15 10/25/11 16 Spherically Refracting Surfaces Spherically Refracting Surfaces If the refracted ray is directed toward the central n > n axis, a real image will form 2 1 on that axis. Bends toward normal Real (virtual) images are Real image formed formed when obj. is relatively far (near) from refracting surface If the refracted ray is directed away from the central axis, it CANNOT form a real image. n1 < n2 However, backward extension of the ray can Bends away from normal form a virtual image. Real image formed 10/25/11 17 10/25/11 18

Spherically Refracting Surfaces Summary: Spherically Refracting Surfaces 1.! Real Images form on the side of a refracting surface that is opposite the object. n > n 2 1 2.! Virtual Images form on the same side as the object Ray directed away from 3. For light rays making only small angles with the central axis: central axis ! Virtual image formed n n n ! n 1 = 2 = 2 1 So Si r

n1 > n2 4.! When the object faces a convex refracting surface, the radius of curvature is positive. Bends away from normal and central axis 5.! When object faces a concave surface, radius of curvature is negative. Virtual image formed

10/25/11 19 10/25/11 20 Example: Mosquito in Amber 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 1) Si = !5 mm b/c obj. and image are on same convex with a radius of curvature 3.0 mm. The mosquito head happens to side of refracting surface (image be on the central axis of that surface, is virtual) and when viewed along the axis appears to be buried 5.0 mm into the 2) n1 =1.6 (use convention that obj. is in medium with index n1) amber. How deep is it really? n2 =1 (air) Draw Picture 3) r = !3 mm (negative b/c obj. faces concave surface)

n1 n2 n2 ! n1 1.6 1 1!1.6 + = " + = " S0 = 4 mm So Si r So !5 !3

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