University of South Carolina

PHYSICS AND THE VISUAL ARTS
Notes on Lesson 4


Things to remember from the lesson and demonstrations, from reading, and the lab exercise.

Refraction is the bending of a light ray as it passes from one medium to another. A light ray passing from an optically less dense medium to a more dense medium is bent toward the normal. (More dense means larger index of refraction n.) Similarly, a light ray passing from a more dense medium into a less dense medium is bent away from the normal. The index of refraction is the ratio of the speed of light in the vacuum to the speed of light in a medium: n = c/v. You should know the law of refraction (also known as Snell's law). What's more, you should be able to use it.

Can you explain the demonstration regarding the CocaColaTM bottle in and out of the water in terms of the law of refraction?

Here is a demonstration that you can do for yourself. Take two small cups or tumblers. Fill one about 3/4 full with water and leave the other one empty. Place a small coin on the bottom in each cup and position it near the center. Can you explain in words or by diagram with words why the coin at the bottom of the glass containing water appears closer to you than does the coin in the glass that contains no water? How does the water affect the angle at which you can see the coin when peering over the edge of the glass?

When the light is incident on an interface from within the more dense medium, the emerging light rays are bent away from the normal. As the angle of incidence is increased, the angle of transmission is increased until it reaches 90ƒ. The incident angle corresponding to the 90ƒ emergent angle is called the critical angle. For incident angles greater than the critical angle, no light passes into the second medium, instead it is totally internally reflected. For angles less than the critical angle some light is partially transmitted and partially reflected.

Total internal reflection occurs only for light passing from a more dense medium to a less dense medium (i.e. from a high index to low index of refraction). An example is light passing from glass into air. The total internal reflection occurs only when the angle of incidence is greater than a particular angle called the critical angle. For incident light at incidence angles less than the critical angle there is no total reflection. For light incident at greater than the critical angle the light is totally reflected. Note that there is no total reflection for light incident from low index to high index regardless of the angle of incidence.

Total internal reflection allows light to pass through optical fibers without leaking out the side. If the fiber is clear enough the light passes from one end to the other with mimimal loss. Can you explain the difference between a coherent bundle of fibers and an incoherent bundle. One is an image conduit and the other is just a light guide. The fiber bundle shown in the figure at the right is an image conduit. Look closely and you can see that the words from the printed page appear at the upper end of the bundle.

What is a Fresnel lens? Where does it get its name?


Be sure to study the ray tracing rules for both mirrors and lenses. I will not expect you to perform ray tracing on a test. But, it is easy, and it will help you locate images. You should practice doing ray tracing or you will likely not be able to do it.

Do you remember what causes a rainbow?

In class you saw real images and virtual images. Can you remember what they were and how they were made? What is a virtual object?

Lenses and mirrors behave similarly. A converging (positive) lens acts similar to a concave (converging) mirror. A diverging (negative) lens acts similar to a convex (diverging) mirror.

Your text does not give you the mathematical relationship that lets you compute the image position if you know the focal length of the lens and the position of the object. The relationship is known as the thin lens equation. It relates the object distance o to the image distance i and the focal length f of the lens. If you know any two of the quantities, the third is uniquely given by the thin lens equation. The equation is
1/o + 1/i = 1/f.

You will not be required to use the thin lens equation, but if you are mathematically inclined you may find it very useful.

The linear or transverse magnification of an image is the ratio of the image height to the object height. We can express the magnification in terms of i and o as
m = -i/o.

The power of a lens is 1/f. When f is in meters, the power is in diopters.

The Eye

The eye is a nearly spherical ball with an aperture that lets light reach the inner wall called the retina. You need to know the main parts of the eye and their functions. They are:

Can you identify these parts on a diagram of the eye?

How did we demonstrate the existance of the blind spot?

Accomodation is the changing of the lens shape to focus at different distances.

You should also remember the effects of pupil size, the corrections needed for myopia (near-sightedness) and hyperyopia (far-sightedness). What is presbyopia? What is astigmatism and how to correct for it?

What are the near point and the far point? What are they for the "normal" eye? (Give a number and units.)
What is myopia and what is hyperopia?
What kind of lens is needed to correct for hyperopia and what kind is needed for correcting myopia?

What is presbyopia?
What is astigmatism and how do we correct for it?

The simple magnifier or magnifying glass. A positive lens held close to the eye is a magnifier. The importance of the magnifier is that it allows the image to cover a much larger part of the retina. Usually, we define that kind magnification in terms of the angular increase in the image (as seen by the increased size on the retina). When an object is brought to the focal point of the magnifier lens, the eye sees an erect virtual image at infinity. For this situation we showed that the angular magnification is

angular magnification (magnifying power) M = 25 cm/f,

where f is the focal length of the lens. The 25 cm corresponds to the near point of a "normal" eye. The far point is taken as infinity.

The astronomical telescope is made from two positive lenses, one used as the objective and one used as an eyepiece. We showed that the (angular) magnification of the telescope is

telescope magnification M = -f(objective)/f(eyepiece)

where f(objective) and f(eyepiece)are the focal lengths of the objective and eye lens, respectively. The image in an astronomical telescope is inverted. A third lens may be used to erect the image.

If a negative (diverging) lens is used for the eyepiece, we have a Galilean telescope or opera glass. The image in a Galilean telescope is erect. Also the Galilean scope is shorter because the lens is placed closer to the objective than the focal distance. In the astronomical scope the two lenses are placed apart a distance equal to the sum of the focal lengths for imaging and object at infinity. For a closer object the lenses are moved farther apart.


What are binoculars and what are opera glasses?

Finally, the objective lens in a telescope can be replaced with a mirror though we did not talk about that in class.

Link to the home page for the Hubble Space Telescope .


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Last Modified: 09/12/04
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