Physics lab assignments

macaulay.cuny.edu

Kent State University

Act IV Lab 12

Exploring refraction in lenses

The idea: Light is the fastest-moving phenomenon in the universe, but ordinary stuff – air, water, glass – slows it down appreciably. If light moves from one medium to another ‘head-on,’ so to speak, it slows down but it continues in the same direction. But if light enters a new medium at an angle, its direction of motion changes along with its speed. That fact, alone, makes possible our ability to bring light to a focus, to use and control beams of light for practical purposes and for entertainment, and to see! The great gift of eyesight depends completely on light slowing and bending in denser media.

But how does light ‘know’ how much to bend? Think about three light rays, as in the simple diagram at the left, scattering off the tip of the object, an arrow standing upright. (Why do physics books always use arrows as objects? How often do you take a picture of an arrow standing on its tail?) Of course there are uncountable numbers of rays coming from the arrow tip, and every other point along it – as well as everything else! How does a simple, inanimate curved piece of glass sort them all out into an image? How does your eye do it?

But back to those three rays. What happens to them, happens to all. One explanation of why they come to a focus is that the farther the ray strikes the lens from the center, the more obliquely it hits the surface, and the more strongly it bends. The red ray hits the surface at a pretty large angle, but it comes out at the exact same angle, and so the effects cancel for it and it passes straight through. The blue ray makes a smaller angle with the surface coming in, but a larger one going out, and so it is bent downward quite a bit. The purple ray makes the most glancing impact of all with the lens surface, so it bends the most. In short, rays that hit the lens farthest from the center bend the most, and they ‘need’ to bend the most to come together.

A deeper explanation came from French mathematician Pierre Fermat. In 1662 he suggested that light always takes the least time – not the shortest path, but the quickest! The red ray takes the most direct route of the three, but it goes through the thickest part of the lens and slows down the most. The purple ray obviously takes the most roundabout path, but it passes through the least amount of glass and so is ‘penalized’ the least. The trouble is, Fermat’s Principle of least time seems to suggest that light ‘knows’ ahead of time where it will end up, and then calculates, somehow, the quickest path.

The best explanation comes from redefining distance. If we measure the path length of those three rays in human terms, using millimeters or inches, then the paths are of different length. But how does light measure distance? In terms of wavelengths! Because the frequency of light (its color) does not change in refraction, but the speed does change, the wavelength of light changes. All three rays in the diagram travel the same number of wavelengths, so the rays interfere constructively only at exactly one point. The red ray travels through the most glass, so its wavelength stays shorter for more cycles. The purple ray travels through the least glass, so it has relatively few short waves. The point where all the rays meet is the only point where all three rays arrive in step, in the same phase relationship as when they left the arrow tip. They all left together; they must all arrive together if they are to form an image!

The same wonder is at work when you read these letters. Light streaming off your computer monitor, or bouncing off these letters on a page, go off at the same instant, and almost as if the waves are holding hands, they arrive together at a point inside your eye. Try to keep that sense of wonder about everything you ever see! – even the mundane images in this experiment.

What you’ll learn: By the end of this lab, you will understand how to 1) measure the focal length of a convex or converging lens, 2) predict where images form when refracted by a convex lens, and 3) explain why object distance and image distance are inversely related.

What you’ll need: Lens from any reading glasses Yard stick or tape measure from your lab packet Scissors Transparent tape

Index card from your lab packet Computer monitor to act as a light source Dark room Willing assistant

What you’ll do: 1) Acquire a pair of simple, non-prescription reading glasses. Since you won’t be harming them, you could just borrow a pair from most any older person you know. Or you could buy an inexpensive pair from a drug store or discount store. You might do especially well at dollar stores, or Goodwill. If you get a new pair with the power marked in diopters (such as +2.0) so much the better.

2) Next, make your own meter stick by cutting apart the strips printed on the card stock in your lab packet. Lay them accurately end to end and tape them together to make a flexible and temporary but accurate way to measure. You have enough strips to make a second one, as well, if you need it.

3) Now, measure the focal length of the lens. As illustrated in the introductory video, use a room that can be darkened well by closing doors and pulling shades. You may have to do the lab at night with the lights off, if you can’t darken the room enough by day. Bring along your assistant and your laptop to use as a light source.

(If you use a desktop computer in a room that can’t be darkened well, as I do, then choose some other small light source – a flashlight, a candle, a small desk lamp – anything that is bright if you look at it, but that does not pour a lot of light all over the room.)

Turn up the brightness of your laptop as high as you can and get a large, high contrast image in your screen. In the introductory video I down- loaded a fat red arrow and enlarged it so it nearly filled the screen on a bright white background. Or, you could open a blank white word processor screen and type I LOVE PHYSICS, or maybe something else, in giant bold letters.

Set the laptop on one end of a long table or counter, if you have one. If not, use the floor! Put your hand over one lens of the glasses, so that only one lens is clear and available for use. Hold the lens several feet away from the laptop screen; the biggest problem in this lab is starting with the lens too close to the laptop! Have your assistant hold the card several feet beyond the lens, as I demonstrated in the introductory video. Then slowly move the lens toward or away from the card until you can see an image of the laptop on the card. It won’t be a perfect photographic image, but it still should be pretty clear and recognizable. What kind of image is it, virtual or real? How do you know? Record your answers on the Report Sheet.

4) With the lens in place and the image in focus on the card, have your trusty assistant measure, as accurately as possible, the distances from both sides of the lens, in centimeters. The distance from the lens to the laptop is the object distance, do. On the other side of the lens, the distance from the lens to the card is the image distance, di. Record both distances on the Report Sheet.

5) While you have everything more or less in place, repeat the process twice more. Have your assistant move the card farther away from the laptop or closer to it – but not very close! – and again move the lens back and forth until you see a reasonably clear image. Again, measure do and di for each of the two new trials and record them on the Report Sheet.

6) You can get up off the floor and turn the lights back on! Next, use the lens equation to solve for f, the focal length of the lens, from each of the three pairs of distances. That equation is:

1/f = 1/do + 1/di

All three variables of interest are in the denominator; this is not the same as f = do + di!

You can use the equation as written, but here it is, solved for f:

f = (do di) / (do + di)

That is, the focal length of lens equals the product of the two distances divided by their sum.

Calculate the focal length of the lens from each pair of numbers and round them to whole numbers. Record your results in the third column on the Report Sheet.

7) Zoom lenses on cameras can change their focal length, but one solid piece of glass or plastic, as you had in your hands, has one fixed focal length, so all of the focal length values should be more or less the same. (If so, good for you! If not, back into the dark to do them over!) Average out the three values of the focal length and again round it to a whole number.

8) The shorter the focal length of a lens, the more strongly it will magnify an image if you hold it close to, say, small print on paper. That’s seems backwards, in a way, that a smaller focal length would have a higher magnifying power, so opticians and reading glass makers

invented the diopter scale. By definition, the power of a lens in diopters is the reciprocal of its focal length, in meters. So, a +2.0 lens would have a focal length of 1/2.0 or ½ m. Since we are working in centimeters, we can say that the diopter power is 100 cm divided by the focal length in cm. Using the value from step 7, calculate the diopter power of your lens. Round it to the nearest 0.25. How does that compare with the manufacturer’s stated diopter value, if known?

As a brief aside, why is the image not perfectly clear, when these are reading glasses, after all? It’s because when you are reading through them, you are using only the tiny part of the lens directly between your eye and the letters you are trying to read at any one time. But in this experiment, you are using the entire lens, all at once. It’s easy to make a lens that is accurate over a small portion of its surface, and much harder – and so, much more expensive – to make it accurate over the entire surface. That’s why inexpensive, one-time use cameras, like those left on the table for you at wedding receptions, always have small lenses and must use flash for most pictures. Expensive cameras have large diameter lenses which often cost more than the camera itself!

Web extension

The f/ ratio or f/ number for camera lenses is defined as the focal length of the lens divided by its aperture, or diameter. What are some of the more-or-less standard values of f/ ratios? With each increase in f/ number, what happens to the brightness of light passing through the lens?

Be sure to include the web address of your sources.