PH 103 Dr. Cecilia Vogel Lecture 5

Review  Refraction  Total internal reflection  Dispersion  prisms and rainbows Outline  Lenses  types  focal point  images  thin lens equation  sign conventions

Lenses  Two types  converging  center thicker  sometimes called convex or positive  diverging  edges thicker  sometimes called concave or negative

Converging Lens  Suppose parallel rays of light come into lens.  What happens to it, if it passes through :  center  straight thru (  =0)  top of lens  bent downward  bottom  bent upward  Parallel rays CONVERGE  Demo of converging lens f

Converging Lens  The focal point of a converging lens is the point where PARALLEL rays converge to. Very distant object will form an image at focal pt. f

Diverging Lens  Suppose parallel rays of light come into lens  What happens to it, if it passes through :  center  straight thru (  =0)  top of lens  bent upward  bottom  bent downward  Parallel rays DIVERGE  Demo of diverging lens f (negative)

Diverging Lens  The focal point of a diverging lens is the point where PARALLEL rays seem to diverge from. Very distant object will form an image at focal pt. f

Focal Point and Images  Is focal point the point where light is in focus?  NOT generally  Only if rays come in parallel to converging lens  such as from a very distant object  Image point is point where light appears to come from  If it is a real image, that’s where the light is in focus.  If you have light coming in focus, it is a real image.  Position of image point depends on  position of object  type of lens & focal length of lens

Lens Equations and Sign Conventions  d o = object distance (aka p )  positive for real object, in front  + for any real physical object  negative if virtual, behind  d i = image distance (aka q )  positive for real image, behind (light really goes there!)  negative for virtual image, in front (that’s not where light goes after lens)  f = focal length  positive if converging  negative if diverging  Thin lens equation REMINDER “front” = side that light comes from

Magnification Equation and Sign Conventions  h o & h i = object & image height  positive if upright  negative if inverted  M = magnification = ratio of h’s  positive if lens makes an image that is same side up as object  negative if lens inverts image  M can also be calculated using

View Images  Case I: converging lens, object far from lens  forms an image:  real/behind, inverted, smaller or larger  f >0, d o >f, d i > 0, M < 0  Case II: converging lens, object close to lens  forms image:  virtual/in front, upright, larger  f >0, d o 0, M > 1 & h i > h o.  Case III: diverging lens, object at any distance  forms an image:  virtual/in front, upright, smaller  f 0, M < 1 & h i < h o.