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Submitting Assignment: Initial Activities with Waves and Optics, Part 2

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For the first part of this lab you will again use the cylindrical lens and candle flame, with a book for your screen.

Typically when the position of the candle flame remains fixed, and you then move the screen behind the lens back and forth, closer to and further from the water-filled cylinder (recall that you used your physics book as a screen in Part 1 of this experiment),  the image (i.e., the vertical bright band) on the screen will get wider or narrower.  There will be one particular distance at which the band will have its minimum width and sharpest focus.

• At that distance the image of the flame will be regarded as 'in focus'.
• That distance will be called the 'focused position' for the system.
• For different distances of the candle flame from the cylindrical lens, the focused positions will also differ.

However if the source gets too close to the lens (i.e., to the cylinder--the cylinder is acting here as a lens), it is no longer possible to form a sharply focused band.

• How close does the source have to get to the lens before this occurs? Specifically what is the maximum distance from the lens at which it is not possible to form a reasonably sharp image on the screen?
• If the source is at this position, what happens to the width of the 'unfocused image' as you move the screen further and further back from the lens?

Answer below.  Explain what your answer means, and how you drew your conclusions.

Your answer (start in the next line):

closeness of source when sharp image no longer achievable:

behavior of 'unfocused image' as screen moves back:

With the source at a certain specific distance in front of the cylindrical lens, the image on the screen remains about the same width as you move the screen further and further back from the lens.  As best you can, determine the distance of the source from the lens at which this occurs.

Your answer (start in the next line):

distance at which image doesn't significantly change width as screen is moved back:

Now you will need two light sources (e.g., two candle flames). 

Recall that the sharpest image you can make of a candle flame is a thin vertical strip on the screen.

If you place the candles so the two flames are side by side, separated by a few centimeters, both about 20 or 30 cm in front of the cylinder, you will be able to form two separate images--i.e., two distinct thin vertical strips of light on the screen.  Do this and measure how far the light sources are from the front of the lens, the distance of the images from the back of the lens, the separation of the two sources (i.e., how far apart the two sources are), and the separation between the centers of the two image lines.  Measure also widths of the two image lines. 

• In the first line below, report the diameter of the lens, the distance from the light sources to the front of the lens and the distance of the image from the back of the lens, using comma-delimited format. 
• In the second comma-delimited line report the separation of the two light sources and the separation between the centers of the two images. 
• In the third line report the widths of the two image lines. 
• Starting in the fourth line, give a brief synopsis of what your results mean and how they were obtained.  Also describe the images, indicating the sharpness of the images (i.e., how easy was it to determine just where the edges of these lines were, how much uncertainty there would be in your determination of the image widths).  In addition report any other characteristics you might have observed related to the way the light from the sources falls on the screen. 

Your answers:

diameter, source position, image position:
separation of sources, separation of images:
widths of individual image lines:
synopsis of meanings:

Keeping the light sources at a constant separation, move them further from the lens and adjust the screen to for the sharpest possible image.  Does the separation of the images increase or decrease as you move the sources further away?  Answer in a complete, self-contained sentence:

Your answer:

does image separation increase or decrease with increasing source distance:

A cylindrical lens is of limited precision, and for most optical applications is not particularly useful.  One limit to its precision is its thickness--light traveling through the center travels much further through the distance than light that travels through its edges, and since the direction of a ray of light changes at the front and again at the back of the lens, the effects of these direction changes depend significantly on where between center and edge the ray first encounters the lens.  Another limit is that light is focused in only one direction, so that a small source of light like a candle flame is focused onto a vertical strip rather than a point. 

A cylinder curves only in one direction.  If we imagine slicing a vertical cylinder into thin slices, we see that we would get circular disks if it is sliced in a horizontal plane, i.e., in a plane perpendicular to its central axis.  However if we make vertical slices, the slices will be rectangular.  The result is that cylinders focus light only in one direction. 

By contrast a sphere curves in all directions--no matter how we slice it, thin slices of a sphere will always be circular.  A spherical lens would focus light in all directions.  So the image of a point source would be a point.  However a sphere is still too thick to form a useful lens.

... the cylinder is rounded in just one direction; in that direction it is rounded on two sides ...

Eyeglasses, camera lenses, and most other practical lenses are rounded in two directions, like spheres, rather than in one direction like a cylinder.  So a well-shaped lens can focus light not just in one direction, but two.  So an ideal lens would focus a point of light onto a single image point, not onto an entire straight line (like the vertical images you have observed with cylindrical lenses).

... there is no such thing as a point source, and no such thing as a perfect image ...

As you have seen, the cylindrical lens is ultimately limited in its ability to form distinct images from distinct sources.  We say that the lens has limited 'resolving power', limited ability to 'resolve', or form distinct images, of distinct objects.  As mentioned, these limits are primary the result of the thickness of the lens, but the circular shape isn't quite perfect for this purpose either. 

Like the cylindrical lens, any real lens has limits to how well it can resolve images.

Your lab materials include some lenses of reasonably good quality, and one mirror.  When you handle a lens or mirror, never touch the surface--handle only by its edges.  Keep the lenses clean, but use only lens tissue to clean them.

Using the candles, one of the lenses and your book as a screen, quickly repeat the preceding experiment.  Place the lens about 20 or 30 cm from the light sources, and move the book closer or further from the lens to form images of the two candles.  You can improvise something (maybe a stick of chewing gum, a dab of peanut butter, and piece of clay) to hold the lens in place (however if you do mess up part of the lens, clean in carefully, handling the lens by the edges and cleaning only the affected part, preferably using a piece of lens tissue).  This time measure distances from the sources to the center of the lens, and from the center of the lens to the images.

• In the first line, report the distance from the light sources to the center of the lens and the distance of the image from the center of the lens, using comma-delimited format. 
• In the second comma-delimited line report the separation of the two light sources and the separation between the centers of the two images. 
• Starting in the third line, give a brief synopsis of what your results mean and how they were obtained.  Also describe the images, indicating the sharpness of the images (i.e., just how clear were the images, how accurately would it be possible to measure the distance between their centers).

Your answers:

(thin lens) source position, image position:
separation of sources, separation of images:
synopsis:

See how far away you have to be before the lens fails to resolve the two sources into two images.  Depending on the space in which you are working, it might well be impossible to do so.  In this case take measurements as before, at the maximum distance you were able to achieve, and report your results below.  Whichever situation you report, use complete self-contained sentences to give your results.

Your answers:

how far until two images can't be distinguished:

By moving the sources closer to the lens, see the maximum separation you can get between the centers of the two images.  At this distance:

• In the first line, report the distance from the light sources to the center of the lens and the distance of the image from the center of the lens, using comma-delimited format. 
• In the second comma-delimited line report the separation of the two light sources and the separation between the centers of the two images. 
• Starting in the third line, give a brief synopsis of what your results mean and how they were obtained.  Also describe the images, indicating the sharpness of the images (i.e., just how clear were the images, how accurately would it be possible to measure the distance between their centers).   Be sure to describe the sharpness of the images of the individual candle flames.

Your answers:

(maximum separation of images) source distance, image distance:
separation of sources, separation of images:
synopsis:

You may include final comments below:

Your instructor is trying to gauge the typical time spent by students on these experiments.  Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades: 

• Approximately how long did it take you to complete this experiment?