Conceptual Physics

converge at the focal point are called paraxial rays.

Lenses produce real and virtual images, just as mirrors do. As with mirrors, a real image

can be projected onto a piece of paper, while a virtual image cannot. However, the

locations of virtual and real images are reversed for lenses and mirrors. With lenses,

virtual images occur on the same side of the lens as the object. Real images occur on

the opposite side of the lens as the object.

The prisms in Concept 1 í the ones stacked base to base í produce a real image on

the opposite side from the object. The ones placed tip to tip create a virtual image, one

on the same side as the object.

As with mirrors, incoming rays that are far from the principal axis of a lens do not

converge precisely at the focal point. This blurs the image and is called spherical

aberration. Diverging lens

Thinner in center, light “spreads out”

33.2 - Converging lens: ray-tracing diagram

As with mirrors, ray-tracing diagrams are used to determine the orientation, and approximate size and location, of an image produced by a

lens. The diagrams in this textbook employ a convention to make them easier to understand: Objects are shown fairly close to lenses that are

relatively thick compared to the distances shown. For the approximations in the theory of thin lenses to hold true, the objects should be quite

far from the lenses and the lenses should be much thinner than shown. Being literal would make for illustrations that would stretch far across

the page or computer screen, so the diagrams are not drawn to scale.

Light that strikes the lens at an angle refracts twice, once upon entering the lens, and again while exiting. However, with a thin lens, we simplify

things by modeling the light ray as changing direction just once as it passes through the lens.

Physicists use three specific rays to analyze the behavior of a lens; these rays differ somewhat from those used to analyze mirrors. A single

converging lens can create different image types based on the position of the object relative to the focal point. In this example, we discuss the

image created by an object more than twice the focal length away from a converging lens.

Ray 1 begins as a horizontal line, parallel to the principal axis, starting at the top of the object. It refracts at the lens and passes through the

focal point on the far side of the lens. (We use “near” to describe the object’s side of the lens, and “far” to describe the other side. We will

typically place objects on the left side of the lens. Images can be created on the near or far side of the lens.)

Ray 2 starts at the top of the object and passes through the center of the lens. It does not change direction.

Rays for a converging lens

What will be the nature of the image?

Ray 1:

Parallel to axis, then passes through far

focal point

Ray 2:

Passes unchanged through center of

lens

(^608) Copyright 2007 Kinetic Books Co. Chapter 33