Chapter 36:  Geometric Optics

 

Learning Goals

  1. Understand how flat mirrors form images.
  2. Understand how curved mirrors form real and virtual images.
  3. Understand how thin lenses form real and virtual images.

 

Lensmaker’s Formula

With the proper sign conventions (see text), the same formula may be used to analyze images formed by thin lenses and mirrors:

 

where so is the object distance, si is the image distance, and f is the focal length. Negative image distances correspond to virtual images, and positive image distances correspond to real images.

The accuracy of this equation is subject to the validity of the paraxial approximation which requires that the focal length be much greater that the diameter of the optic.

 

Focal Lengths

Spherical mirrors have focal lengths given by

 

Thin lenses have focal lengths given by

 

Focal lengths of converging optics are positive, and focal lengths of diverging optics are negative.

Note: focal lengths for all problems in this section are given as positive quantities. When working with the lensmaker's formula, it is your responsibility to assign negative values to focal lengths of diverging optics.

 

Magnification

Magnification is calculated the same way for both mirrors and lenses:

 

 where h denotes the image and object heights, and s denotes the image and object distances. Negative magnifications correspond to inverted images and positive magnifications correspond to upright images.

Single optics always give inverted real images and upright virtual images.