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Geometric optics explains how optical devices (such as lenses and mirrors) create images by considering that light travels in rays, which are straight lines emanating from a light source or reflected from an object. A ray diagram is a useful tool in geometric optics; it describes images formed by lenses or mirrors. A ray diagram can help:
In the design of optical devices such as microscopes, telescopes, or movie projectors
Explain how the human eye creates an image formed on the retina, which our brains interpret for us as sight
Determine how to correct our sight when an abnormality in our eyes blurs our vision
Consider the ray diagram in Fig. 2, which is for a double convex lens. The left arrow represents an object such as a building or a tree. A few simple rules describe how rays of light refract when they pass through a thin lens like the one in this diagram or the ones in our eyes. Rays traveling parallel to the center axis (perpendicular to the center of the lens) refract so that they pass through the focal point on the other side of the lens. The place where the rays converge shows where the top of the arrow would be in the image formed by the lens. Different lenses and mirrors require slightly different rules when you draw their ray diagrams, but the ray diagram in Fig. 2 is similar to how the eye makes an image.
Fig. 3 shows a ray diagram that describes the image formed on the retina of a human eye. The eye, using tissue instead of glass, works like any other optical device such as a telescope or a camera. This means that the same ray diagrams used to describe those devices can be used to describe the images formed by the tissues in the eye, as well as to design devices such as eye glasses to correct our vision when needed.
This simple model of an eye shows how geometric optics applies to the formation of images in the human eye.
Next Generation Science Standards®
Disciplinary Core Ideas:
PS4: Waves and their Applications in Technologies for Information Transfer (wave properties of light and electromagnetic radiation)
ETS1: Engineering Design (corrective lenses, microscopes, telescopes, projectors)
LS1.A: Structure and Function: Multicellular organism have a hierarchical structural organization, in which any one system is made up of numerous parts and is itself a component of the next level.
Crosscutting Concepts: Structure and Function (anatomy of the human eye)
Double Convex Lens
3 Ring Stands
2 Universal Joints
Follow all established safety protocols for laboratory activities. Do not use lenses to focus light from the sun. Do not look directly into the sun or light sources. If you are substituting a strong light source that produces heat, do not touch the light source or place the light source near flammable materials.
Take 1 standard balloon (a 9” white balloon works well) and partially inflate it. It should be inflated enough that the surface of the balloon is smooth with no bumps but not inflated so much that it pops when squeezed.
Twist the balloon at the neck to pinch off the air.
Stretch the mouth of the balloon over and around the double convex lens so that the lens is held in place in front of the balloon and light can pass through the lens. When you untwist the neck of the balloon, the lens should remain in place and no air should escape. See Fig. 4. (Some air may escape as you fit the lens into the neck. Start with slightly more air in the balloon than you want to end up with.
Safety tip: Do not try to insert the lens then inflate the balloon. This could be a choking hazard.)
Teacher tip: This step is a little difficult. We recommend:
Practice setting up the lens yourself before performing this activity in class.
Students should work with a partner to set up the lens.
Use plastic lenses instead of glass, in case the lenses are dropped.
Have extra balloons on hand when performing this activity in class; it is easy to rip the neck.
If setting up the lens in the balloon is too difficult or time consuming, an alternate method is to hold the double convex lens in front of a window. Hold up an index card or sheet of white paper so that the lens is between the paper and the window. Move the card until you can see a clear image projected on the paper. The clearest image will form when the distance between the lens and the paper is the focal length of the lens.
4. Use the permanent marker to draw an “object” on the lens of the flashlight. The “object” is typically an arrow, but it can be a face or any simple design with a definite top and bottom.
5. Use a pair of ring stands to hold the balloon in place; use the third ring stand with a burette clamp to hold the flashlight. Position the ring stands so that an image forms on the back of the balloon, simulating an image forming on the retina of an eye. See Fig. 5.
6. Squeeze the balloon from the sides. The balloon will become longer, simulating nearsightedness. Then squeeze the balloon from the front and back by moving the ring stands. This will cause the balloon to become shorter, simulating farsightedness.
As light rays reflect off of an object such as a tree, some of the rays travel to the eye. Rays of light enter the eye through an aperture called the pupil, the dark spot in the center of the eye. Surrounding the pupil is a colored ring called the iris, which opens and closes, controlling the size of the pupil and thereby the amount of light that enters the eye. Covering the pupil is a layer of transparent tissue called the cornea, and behind the pupil is another transparent tissue called the lens. Together the cornea and the lens focus the light entering the eye by bending, or refracting, the rays of light entering the eye. Muscles surrounding the eye change the shape of the eye slightly to focus the eye, similar to the way a telescope works. When everything works properly, an image forms on the tissue of the back inner wall of the eye. This tissue is known as the retina, and it contains light-sensitive cells known as rods and cones. The rods and cones process the light from the image projected on the retina into a signal that is carried by the optic nerve to the back of the skull, where the visual center of the brain turns that information into the images we perceive as sight.
Sometimes small deformities in a person’s eye can interfere with the eye’s ability to focus light correctly on the retina. Corrective lenses can sometimes help people with vision problems see more clearly. A positive lens may be used.
Figure 8. Corrected nearsightedness.
If you have access to different lenses, try these additional exercises.
Corrective Lenses: Corrective lenses can be used to compensate for nearsightedness and farsightedness. Position the balloon and flashlight on a table so that a clear image forms on the back of the balloon. Use a stack of books on either side of the balloon and flashlight to hold them in place. Move the books so they squeeze the balloon and the image becomes blurry. Try placing different lenses (convex, double convex, concave, double concave) between the balloon and the flashlight, varying the lens distance from the balloon. Try to find a lens and a distance that correct the image formed on the back of the balloon so it appears clear. The eye of a person who is nearsighted is slightly too long. The retina is slightly behind the point where the eye forms a focused image, causing the image formed on the retina to be blurry. A diverging lens placed in front of the eye causes the rays entering the eye to spread out so that the cornea and the lens focus the light correctly and form a clear image on the retina. The eye of a person who is farsighted is slightly shorter than normal. The retina is located ahead of the point where the lens and cornea produce a focused image. A converging lens adds focusing power to the lens and cornea, refracting the light more and moving the focused image to the retina.
Telescope: Ray diagrams also can be used to design optical devices for a number of purposes. The diagrams below show just 2 types of telescope—one using converging lenses, the other using a combination of converging and diverging lenses. Some telescopes use a combination of lenses and mirrors for even greater magnification. The correct combination of lenses or of lenses and mirrors can be used to build telescopes, microscopes, or even projectors. Interested students can research how to draw ray diagrams for more complex optical systems or experiment to find out what types of images are generated with the different combinations of lenses and mirrors.