Physics Photo of the
September 23, 2011
Bi-focal Bird Feeder
This summer I noticed these stunning images of
the Willoughby Lake, Vermont in our humming bird feeder.
The feeder was partially filled with colored sugar water,
which the area hummingbirds would consume in about 10 days.
Notice the images through the sugar water. Through the
spherical part of the feeder, we see the distant Mount Pisgah
inverted; through the lower waist of the feeder we see the
mountain erect, but left and right are reversed. The
images through the lens of the birdfeeder are shown in the
close-up photo at right. The lower erect
image can be thought of either the up-down reversal of the
inverted image or the left-right reversal of the original
scene. We often see the images of our dining partner
either inverted or left-right reversed in a glass of wine or
The spherical part of the feeder - or wine glass - converges
the rays of light from the scene in all directions. The
rays of light meet to form an image between the lens and the
viewer. Due to the symmetry of the convergence, the
image is inverted. We see the same effect if we hold a
simple magnifying lens at a distance viewing distant
objects. (See PPOW
for November 30, 2007). The surfaces of a simple
magnifying glass are spherical.
The lower part of the feeder is not spherical but
predominantly cylindrical with a vertical axis. A
cylindrical lens converges light only in the horizontal plane,
perpendicular to the cylindrical axis. Therefore the
image is "inverted" only in the horizontal plane. There
is no convergence in the vertical plane. We would see
the same effect in a cylindrical glass of beer or other clear
If one carefully studies the curvature of the feeder, the
waist part has two different curvatures. In the
horizontal direction the outside of the waist is convex - it
curves away from the observer. For the vertical
direction, the waist is concave, it curves towards the
observer. That actually makes the lens concave for the
vertical direction (it makes the image smaller, but erect, in
the vertical direction). The convex axis performs the
Finally, for calculus students, the fuzzy line demarking the
division between the two images, appears close to the "curve
of inflection" around the feeder that divides upper vertically
convex portion of the lens from the lower vertically concave
portion of the lens.
The mountain with the cliffs is Mount Pisgah overlooking
Willoughby Lake in northern Vermont.
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