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Name: Alexandra G.
Status: student
Grade: 9-12
Location: IL
Country: USA
Date: Winter 2011-2012


Question:
I am learning geometric optics and find it very interesting. I have always been fascinated by the human eye, and I hope to become an ophthalmologist. The ray tracings in the text and many other places:

http://www.internal.schools.net.au/edu/lesson_ideas/optics/
optics_w ksht2_p1.html

or similarly for a camera, show parallel light rays coming in an imaging on the retina (or pixels). It is a single point. I understand that for an object at infinity (for the human eye or a camera this should easily be satisfied at several miles, like looking at the Chicago skyline from Lake Michigan) will image in a point. But then how do you see the skyline? It should not be resolved in anything but a point. But indeed I DO see an image of the skyline, so it must be an inverted image on the retina. So where is the focal point? I am confused, and the more I look at the ray tracing diagrams the more perplexing I find all of this to be. I think some of the diagrams are wrong. My physics teacher said that there are rays coming in to form an image that are not parallel to the optical axis, but also said that would not necessarily apply to something several miles away. My question: Are the common ray diagrams I see correct? If so, how do I see a skyline . . . or the Grand Canyon? If not, where might I find the correct drawings?

Replies:
The rays coming from a single point an infinite distance away are all parallel. However, there are many points an infinite distance away. It's not really "infinite"; the points really are indifferent directions from you. So, for the purposes of ray tracing, the rays coming from a single point (say, the top of a skyscraper) are all parallel to each other, but they aren't parallel to rays coming from other single points (say, the bottom of a different skyscraper). The rays will all converge onto the focal plane, but only the rays parallel to the optic axis will converge to the focal point.

Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy


Hi Alexandra,

The ray tracings are reasonable. The statement of your physics instructor that "there are rays coming in to form an image that are not parallel to the optical axis" is the key here.

Consider the ultimate in parallel light rays coming to your eye, the night sky. Any light rays from an individual star to your eye can be considered parallel (i.e., the star is a point source). But the image you see is of several different stars and the light rays from separate stars are not parallel to each other so they focus at different points on your retina.

The same happens with the skyline. Each source point from the skyline has parallel rays of light coming to your eye but any two points don't produce parallel light rays.

Another way to envision this is to think of the center of the lens as a fulcrum. The beam will represent the light rays coming from the skyline to the lens of the eye to the focus point on the retina. Trace the skyline with your mile long beam and it will "draw" the inverted version of the skyline on the retina.

Also, note that the "fovea" is not the focal point for these incoming parallel rays. The fovea is a region of the retina with the most acute vision and light near the optical axis of the eye will be focused there. The parallel rays for objects (stars in my example) near the periphery of your vision will be focused on the portion of the retina far to the side of the eyeball.

Regards, Greg Bradburn


I think I understand your confusion. You do indeed need to find a better-explaining figure. The proper figure has at least 6 ray-lines: for at least 2 distinct points in the object & retina-image (such as: base-of-building, top-of-building),

3 rays: straight line though center of lens, ray diverging to top of lens & bent back down, ray diverging to bottom of lens and bent up.

The figure you cited is a bit oversimplified for understanding the optical situation.

http://www.internal.schools.net.au/edu/lesson_ideas/optics/
images/eye_focus.gif

It only shows 2 rays, not 6. I think it's mostly for anatomy, with just a cursory two rays to show that "optics happens in this part".

A better figure is at Wikipedia in the article "real image" http://en.wikipedia.org/wiki/Real_image you'll find this figure: http://en.wikipedia.org/wiki/File:Realimageondetector.svg In the caption it says: "Each region of the detector or retina indicates the light produced by a corresponding region of the object. " (It shows 9 rays, so it must be really good...;>)

There must be many other such images on the web. An old classic includes a candle as the object being viewed. The question is what keywords to use for the search. "lens imaging ray diagram" gets you started. I found http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html that way.

The lens does a "transform" of the image which may be described as: - all rays going through center of lens go straight, are not bent. - all rays from one point of the object are directed to one point on the retina (focusing action, convergence of rays) - rays from different points on the object are directed to different points in the retina (imaging action, like a lever with fulcrum at center of lens).

The bi-conical ray-focusing-figure for one point of the image pivots around the center point of the lens, painting an image on the retina from various points of the object. This is true regardless of distance. For distances shorter than infinity, the lens is changed to be a little stronger-converging, so focus is maintained, and the same focusing and imaging still happens.

Jim Swenson


This is a great question that describes the confusion commonly encountered when viewing ray diagrams in geometric optics. Most ray diagrams illustrate how a single object point is refracted to form a single image point on the retina or film plane. This point-to-point correspondence (or conjugacy) is a fundamental principle of geometric optics. However, most objects do not consist of a single point as Alexandra correctly noted. A real object is composed of an infinite number of individual object points, and each object point is refracted and imaged to a unique image point. The inverted real image formed on the retina (or film plane) by convergent light rays is comprised of all the individual image points taken together.

Here are several web sites from a Google search (“ray tracing converging lens”) that illustrate how the eye (or any converging lens) forms a real inverted image:

http://www.batesville.k12.in.us/physics/PhyNet/Optics/Lenses/
Ray_Tracing.html

http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=38

http://whs.wsd.wednet.edu/Faculty/Busse/MathHomePage/busseclasses/
apphysics/studyguides/chapter18_2008/Chapter18StudyGuide2008.html

http://courses.durhamtech.edu/opticianry/oph142/NFOS-12/
Geometric_Optics_files/thin_lens_ray_tracing.html

http://cnx.org/content/m32832/latest/

http://www.pa.msu.edu/courses/2000spring/phy232/lectures/lenses/
images.html

I would encourage you to pursue your interest in eye care, and to consider a career in optometry. I am an optometrist and faculty member at the University of Alabama at Birmingham (UAB) School of Optometry. Please feel free to contact me if you have any questions.

Adam Gordon

Adam Gordon, OD, MPH
Director, Cornea and Contact Lens Clinic
UAB School of Optometry


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