Read
Read pages 677-679 of the textbook for more explanations and help in drawing ray diagrams for thin lenses.

 

The Lens Equation

 

While ray diagrams are useful tools for revealing image characteristics, they can also be used to derive a mathematical equation for finding and identifying image characteristics.  The derivation of the lens equation, which is identical to the mirror equation in Lesson 3, can be seen on page 680 of your textbook.

 

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

 

Expressed as an equation, it is as follows:

 

 

Quantity

Symbol

SI Unit

object position relative to the optical centre

d o

m

image position relative to the optical centre

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.
  • Converging lenses have a real focal length that is positive.
  • Diverging lenses 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 noted sign conventions.

 

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


Read
Read "Equations for Thin Lenses" on page 680 of the textbook.


Try This
Complete "Practice Problems" 1-3 on page 681 of the textbook.