Chapter 23:Mirrors and Lenses Flat Mirrors Homework assignment : 20,24,42,45,51  Image of a point source P P’ The reflected rays entering eyes look as though they had come from image P’. Light rays radiate from a point object at P in all directions. virtual image

 Image of a point source on a flat mirror (cont’d)

 Image formation on a flat mirror s’ (s) is the image (object) distance: |s| =|s’| Sign Rules: (1)Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative. (2) Sign rule for the image distance: When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance s’ is positive. Otherwise it is negative. (3) Sign rule for the radius of curvature of a spherical surface: When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative. Flat Mirrors s’

Multiple image due to multiple Reflection by two mirrors h h’ m = h’/h=1 lateral magnification image is erect image is virtual  Image of an extended object on a flat mirror S’1S’1 S’2S’2 S’3S’3 Flat Mirrors

 Rotation of mirror When a flat mirror is rotated, how Much is the image rotated? Flat Mirrors

Solution x/2 (h-x)/2 h-x x What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length? The minimum length of mirror for a woman to see her full height h Is h/2 as shown in the figure right. Flat Mirrors  Example

Image Formed by Spherical Mirrors  Concave and convex mirrors

 Focal points at concave and convex mirror Focal point or focus: Point F at which rays from a source point are brought together (focused) to form an image. Focal length: Distance f from mirror where focus occurs. f=R/2 where R is the radius of a spherical mirror. Image Formed by Spherical Mirrors

 Focal points at a concave mirror s’ h d object image If Image Formed by Spherical Mirrors

 Image of an extended object at a concave mirror Principle rays: Light rays that can be traced (more easily) from the source to the image: 1. Parallel to optical axis 2. Passing through the focal point 3. Passing through the center of curvature 4. Passing through the center of the mirror surface or lens real image Image Formed by Spherical Mirrors

 Magnification of image at a concave mirror h h’ When s,s’ >0, m<0 inverted s/s’ 0 upright or erect Image Formed by Spherical Mirrors

 Example with a concave mirror real image virtual image Image Formed by Spherical Mirrors

 Example with a concave mirror Image Formed by Spherical Mirrors

 Image at a convex mirror ss’ f f R s positive s’ negative (virtual image) R negative f negative Image Formed by Spherical Mirrors

 Magnification of image at a convex mirror s’ For a convex mirror f < 0 m > 1 magnified m < 1 minimized m > 0 image upright m < 0 image inverted Image Formed by Spherical Mirrors

Refraction at a spherical surface  Refraction at a convex spherical surface For small angles     

Refraction at a spherical surface  Refraction at a concave spherical surface For a concave surface, we can use the same formula But in this case R < 0 and f < 0. Therefore the image is virtual.

Refraction at a spherical surface  Relation between source and image distance at a convex spherical surface s’ For a convex (concave) surface, R >(<) 0. Snell’s law

Refraction at a spherical surface  Example of a convex surface

Refraction at a spherical surface  Example of a concave surface

Refraction at a spherical surface  Example of a concave surface

Refraction at a spherical surface  Example of a concave surface

Convex Lens  Sign rules for convex and concave lens: Sign Rules: (1)Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative. (2) Sign rule for the image distance: When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance i is positive (real image). Otherwise it is negative (virtual image). (3) Sign rule for the radius of curvature of a spherical surface: When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative.

Convex Lens  Lens-makers (thin lens) formula surface 1 surface 2 Image due to surface 1: s’ 1 becomes source s 2 for surface 2: s 1 = s and s’ 2 = s’: s’ Parallel rays (s=inf.) w.r.t. the axis converge at the focal pioint R 1 >0R 2 <0

Convex Lens  Magnification s’ same as for mirrors

Convex Lens  Object between the focal point and lens A virtual image

Convex Lens  Object position, image position, and magnification real inverted image m < 1 real inverted image m >1 virtual erect image m >1

Lens  Types of lens

Lens  Two lens systems

Lens  Two lens systems (cont’d)

Lens  Two lens systems (cont’d)

Lens  Two lens systems (cont’d)

Aberration sphereparaboloid

Chromatic aberration

Gravitational lens

Exercises Problem (focal length of a zoom lens) Solution I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)<s’ 2 f (a) f1f1 (b) (c) ray bundle Find the effective focal length f of the combination lens. d x r0r0 f1f1 s2s2