Light and optics/Vision and lenses
Here we will use human vision and its corrections to understand how a lens works. The focus will be on schematic drawings that are very easy to sketch, but will not represent actual relative lengths. Nor will these drawings depict the human eye very accurately. The goal is simplicity and clarity regarding the nature of the objects and images involved.
This page is formatted so that instructors may lecture from it directly from the internet. In such a lecture, it is customary to avoid discussion of a number of important approximations. They are (1) the paraxial approximation and (2) the thin lens approximation. The latter approximation allows us to avoid spherical and other aberrations.
In this lesson, we shall use vision and the human eye to introduce ray diagrams and the thin lens equation.
Sketches of the eye and a simple ray diagram
Wrong!!! This is one of many misleading images that can be found on the internet.
The eye is a complicated device involving two lenses adjacent to each other. To simplify the discussion we shall assume that only one lens exists, which is permissible because one lens is often an acceptable approximation to two adjacent lenses.
Though not correct from a biological standpoint, this diagram accurately depicts how muscles control the shape of the lens, as well as the fact that the cornea is the stronger of the two lenses.
This schematic diagram correctly captures the "physics" of an eye looking at the red dot in the center of the yellow star. This resource does not cover the paraxial and thin lens approximations, but as will be discussed later, both approximations are violated by this schematic sketch.
Thin lens equation if p, q, and f are all positive
Here we introduce the thin lens equation:
is called the focal point and is a property of the lens. A strong lens has a short focal length.
The image distance is p, the object distance is q, and the focal length is f. Since everything is positive, this is the diagram you want to learn first. In this case .
We shall later see what it means for f, p, or q to be negative. But for now, we note that if all three are positive, and increase in p implies a decrease in q, and vice-versa, if all three parameters are positive. According to the thin lens formula, if p is made very large, then q approaches f. This is depicted in the figure below, where the lens has the same focal length as the lens in the figure above.
The focal length is defined to be the distance from the lens to the object if the incoming rays are parallel. Parallel rays come from an object that is far away. This is often stated as parallel rays meet at infinity", or "the object is at infinity".
Beware the focal point
The rays meet at the focal point only if the incoming rays are parallel, and the distance from the lens to the image is not the focal length unless the object is at infinity. Don't call the image a "focal point" unless it really is the focal point. If an image on a screen seems out of focus, don't say you are trying to find the "focal point". Say you are trying to find the location of the image; if the image is out of focus, the screen is probably not at the location of the image.
The quiz for this page has been moved to Physics equations/25-Geometric Optics/Q:vision
This lab does not require special equipment
This lab requires only pencil, paper, and a ruler. Copy these images and paste into a word processor, ask students to determine the focal length of each image.
Other lab projects
- See File:Editable ray diagram of eye v0.svg and note that the rays are not shown as bent at the "eye lens". Correct this error. This is a great opportunity to learn about Inkscape , and the concept of "layers" in illustration software.
- For biology students:
- Dissect the eye of a large animal (e.g. sheep), take careful measurements and modify the image at File:Editable ray diagram of eye v0.svg accordingly. Post as a new image on commons for everybody to use.
- Research the dimensions of the human eye and post a scale on File:Editable ray diagram of eye v0.svg
- If you don't want to edit the images, post your measurements here and someone else will edit the svg files.
- For anyone: Compare different ways to create an image for use in the classroom. Methods include:
- Shining a bright light on a printed photograph or drawing.
- Using an image projected on a screen by an overhead projector.
- Using a candle
- Using a the filament of a bare lightbulb (15W and 45W are often available as refrigerator bulbs -- There is a reason why such bulbs are "bare"--can you think of it?
- Using equipment purchased specifically for use in a classroom optics lab
References and footnotes
- "The image ... is formed by two lenses – the cornea (with fixed focal length), and the eye-lens (whose focal length can be varied by changing its shape) The focal length of the combination ... is typically about 20 mm. The optical strength of the cornea is much greater than the strength of the eye-lens" http://www.colorado.edu/physics/phys1230/phys1230_fa01/topic36.html These assertions need to be verified and quantified, and then put into an image.
- Illustration by w:John Tenniel. From w:Through the Looking-Glass, by w:Lewis Carroll, who was a mathematician. Was w:Humpty Dumpty a professor?