Lenses ---------------------------------- Joseph F. Alward, PhD Department of  Physics University of the Pacific

Applets used in this eLecture:  Converging Lens  Diverging Lens

 Convex Lens (Converging Lens)   

  Spherical Aberration             

Non-paraxial rays are not focused at the focal point.

 Chromatic Aberration   

 Concave Lens (Diverging Lens)  

  Convex Lens is Inverse  
 of Concave Lens                

  Ray Displacement           

 Center Rays                                                                       

  Rays Through Center of Lenses                                                     

   Rays Through Focal Point                                                              

Any ray aimed at a focal point will be bent parallel to the principal axis.

 Paraxial Rays                                                                                              

Paraxial rays are really bent through the focal point in a converging lens; they are virtually bent through the focal point for a diverging lens.

  Object and Image Distances           

  Sign Conventions                                      

Mirror Rule: "If it's in front, it's positive." Except for object distances, which are always positive, the rule for lenses is the opposite of the rule for mirrors. ---------------------------------------------------------------------------- Convex   Lenses:   f is positive                   (convex   mirrors have negative focal lengths) Concave Lenses:   f is negative                   (concave mirrors have positive focal lengths) ---------------------------------------------------------------------------- Lens images have positive distances if they're on the side opposite to the object.

 Thin Lens Equation    

1/do + 1/di = 1/f ---------------------------------- Rules: Convex:    f is positive Concave:  f is negative Image in back is positive

Convex Lens as Magnifier     

   Magnification with the Converging Lens                 

The Lens Equation:   1/do + 1/di = 1/f  M = -di / do ------------------------------ Convex:  f is positive Given:  f   = 20 cm do = 12 cm ----------------------------- 1/12 + 1/di = 1/20 Solve:  di = - 30 cm M = - (-30)/12      =  2.5

   The De-Magnifier

  De-Magnifying Glass                                                              

The Lens Equation:   1/do + 1/di = 1/f  M = -di / do -------------------------------- Concave:  f is negative Given:  f    = -20 cm do =   30 cm ------------------------------- 1/30 + 1/di = 1/(-20) Solve:  di = - 12cm M = - (-12)/30      =  0.4

  Convex Lens Real Images                                                                              

Real images like this one are required if images are to be placed on screens or camera film.

The Lens Equation:   1/do + 1/di = 1/f -----------------------------  f    =  20 cm do =   30 cm ----------------------------- 1/30 + 1/di = 1/(20) Solve:  di = 60 cm M = - (60)/30      =  -2 (Image is inverted)

  Film Projectors                                                              

  Camera Lens Geometry                                                    

Image is small and real, and is suitable for placement on camera film, which requires a real image, not virtual.

The Lens Equation:   1/do + 1/di = 1/f -----------------------  f    =  5 cm do =   500 cm ----------------------- 1/500 + 1/di = 1/5 Solve:  di = 5.05 cm M = - (5.05)/500      =  -0.0101 (Image is inverted)

  Camera Film Image          

                                                            

1.  Converging Lens Interactive Applet    2.  Diverging Lens Interactive Applet

  Example Problem 1                                                    

At which of the points A, B, C, D, or E is the image located?  Note:  the focal point   F on the right of the lens is the only one shown.

  Example Problem 2                             

A 6.0 cm object is placed 30.0 cm from a lens.   The resulting image height has magnitude of 2.0 cm and is upright.  What is the focal length of the lens?

M = 1/3 -di /do = 1/3 di = -10 cm 1/30 + 1/(-10) = 1/f f = -15 cm

 Microscope      

  Microscope Geometry                                                                   

If object or virtual object is between convex lens and focal point, it will be magnified.

  Telescope Geometry                                                   

  Farsighted Eye                                                                                             

Near objects are focused behind the retina  in far-sighted persons. Their vision is called "far-sighted" because their lens is relaxed only while looking at objects far away. As one ages, books and newspapers must be held farther and farther away with each passing year. Converging lenses will correct farsightedness.

  Nearsighted Eye                                                                        

This lens sees near objects better than far objects.