Physics Photo of the Week

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 beer.

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 beverage.

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 left-right reversal.

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.

Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department.  These photos feature interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation.  Atmospheric phenomena are especially welcome.  Please send any photos to dcollins@warren-wilson.edu.

All photos and discussions are copyright by Donald Collins or by the person credited for the photo and/or discussion.  These photos and discussions may be used for private individual use or educational use.  Any commercial use without written permission of the photoprovider is forbidden.