Table 47-1. Sign conventions for lenses.
Variable C
do real object virtual object
di real image virtual image
ho always —
hi,m upright image inverted image
f converging lens diverging lens
R 1 ,R 2 convex surface concave surface47.3 The Fresnel Lens.
If you examine the path of a light ray through a lens carefully, you’ll notice there is a fair amount of “unused”
glass. The incoming light ray is refracted (bent) when it first hits the surface of the lens, then travels in a
straight line all the way through the lens, then is refracted again on the way out. The surfaces of the lens do
all the work—it seems like all that glass inside the lens is kind of a waste, doing nothing but allowing the
light to travel in a straight line. For a large lens, it might be nice to eliminate all that unused glass; is that
possible?
Yes, we can eliminate all that unused glass, as shown in Fig. 47.3. The result is called aFresnel lens. Its
advantage is that a very large lens can be made very flat—for example, a reading lens can be made the size
of a sheet of paper, with roughly the thickness of a credit card. The disadvantage, as seen from the figure, is
that the process of eliminating the “unused” parts of the lens leaves behind a series of “steps” or ridges that
appear as rings in the lens. A Fresnel lens is therefore not suitable where high-quality optics are needed, but
it can be useful as a reading lens, for an overhead projector, or for making something like a solar furnace that
focuses sunlight to produce heat.
Figure 47.3: Cross section of (1) a Fresnel lens, and (2) the equivalent normal lens. (©GNU-FDL, Wikimedia
Commons.)