Read
Read pages 658-659 of your textbook for more information on drawing ray diagrams.  Note that in the textbook, the ray through the vertex is replaced with a ray through the centre point.

 

The Mirror Equation

 

Ray diagrams are a useful tool for revealing image characteristics using the law of reflection and basic geometry.  This same tool can also be used to derive a mathematical equation for finding and identifying image characteristics.  The derivation of the mirror equation is on pages 661-662 of your textbook.

 

The mirror equation relates the focal length of a curved mirror to the image and object positions.

 

Expressed as an equation, it is as follows:

 

 

Quantity

Symbol

SI Unit

object position relative to the vertex

d o

m

image position relative to the vertex

d i

m

focal length

f

m

 







The image and object characteristics are also described in these equations using sign conventions.

  • Positive distances describe real images and objects.
  • Negative distances describe virtual images and objects.
  • Converging mirrors have a real focal length that is positive.
  • Diverging mirrors have a virtual focal length that is negative.

Magnification is the ratio of the image height to the object height.  A negative sign is used to accommodate the preceding sign conventions.

  • Negative height describes an inverted image or object.
  • Positive height describes an upright image or object.

 


 

Quantity

Positive if

Negative if

Attitude

h

erect

inverted

Image Type

d

real

virtual

Mirror Type

f

converging (concave)

diverging (convex)

 

Note: If the image type is real, the mirror type must be concave.


Read
Review "Example 13.2" on page 664 of the textbook for an example of how to use the mirror equation.