Lens Lab

  In this lab, we investigated the properties of lenses, finding their focal lengths and their magnifications, and ultimately constructing simple telescopes.

  We worked with four different lenses.  We identified them by their total apparent size, with (1) being the biggest and (4) being the smallest.

  To measure the focal lengths of the lenses, we set up a light bulb on one end of a long table, and a white, flat surface on the other end.

  We then measured the distance from the light to the lens (F₁) and the distance from the lens to the focused point of light (F₂).  Here is a chart of our measurements:

Lens	(1)	(2)	(3)	(4)
F1	2.832m	2.948m	2.952m	2.968m
F2	0.168m	0.052m	0.048m	0.032m

  The next step was to determine the magnification of the lenses.  We did this by moving the lenses from the previous step until we got a focused, inverted image of the light bulb.  We then measured the new distance from the light to the lens (D_o), and from the lens to the focused image (D_i).  We also measured the size of the filament in the focused image to the size of the real filament (0.063m).  We then applied two equations that we were given, Magnification = (Image Size)/(Real Object Size), and 1/F₂ = 1/D_o + 1/D_i, to test and analyze our data.  Here is a chart of these measurements and calculations:

Lens	(1)	(2)	(3)	(4)
Do	0.905m	0.057m	0.052m	0.037m
Di	0.195m	1.043m	1.048m	0.973m
Image Filament Size	0.010m	0.002m	0.003m	0.004m
1/F2	5.952	19.23	20.83	31.25
1/Do + 1/Di	6.233	18.50	20.18	28.05

  We then set up two lenses in serial, to try to make a simple telescope.  We determined the rough magnifications of the telescope by pointing it at a cinderblock wall and seeing how many cinderblocks in the real wall fit in the image of one cinderblock in the magnified image from the telescope.

Lenses:	Distance between lenses when focused:
(2), (4)	0.422 m
(1), (3)	0.409 m
(1), (4)	0.419 m
(2), (3)	0.418 m

  This distance is not the same when viewing closer objects; it increases when viewing more distant objects.  This is the purpose of 'focusing'; a telescope is focused by moving the lenses so that they are the correct distances away from each other to make the image showing through the telescope appear focused.

  The inverting of the image is a somewhat complex process; it is best explained through modifying a picture from the lab:

  The light that starts off on top ends up on the bottom, and vice versa.  The light comes to a point and then expands outwards.  It's like a pair of scissors, although it's a slightly obscure analogy; they cross in the middle, and the handle on the bottom is connected to the top blade.

  We had a very hard time determining the magnification of some of our sets of lenses; many of them were too spherical, and provided a distorted image.  We did manage to focus some of them, however, and we took a picture of this focused image.  Here are some pictures, both of ours and of the class in general (it's hard to tell the difference between ours and others, so these are just all of the pictures that came out well) that demonstrate magnifications:

Maybe 1.5x	Probably also 1.5x	Maybe 1.25x

  Now, in answer to the 'Questions to Consider' at the back of this lab sheet:

1) Why do telescopes need to have adjustable focus knobs?  These knobs change the distance between the two lenses.  Why isn't this distance fixed?  Do you need to change focus when switching from viewing Saturn to viewing Jupiter?
  The distance between the two lenses needed to focus an image is not fixed; it varies with the distance from the object on which one is focusing.  Therefore, to view objects at different distances, one needs to be able to adjust the distance between the two lenses in a telescope.  Also, the mechanism that allows the distance between lenses to be adjusted also generally lets one switch eyepieces, which is desirable because switching eyepieces is the easiest way to change magnification.  Technically, you do need to change focus when switching from viewing Saturn to viewing Jupiter, but focus varies nonlinearly with distance, so because both Jupiter and Saturn are extremely far away, the adjustment necesary in focus is extremely tiny.  It is likely well below the accuracy permitted by Earth's atmosphere; in any case, it is negligible, and usually ignored.

2) If you were to buy a telescope, why is is useful to buy lots of different eyepieces?  Given that our telescope has a focal length of approximately 120 inches, and we have eyepieces ranging in focal length from 4.5mm to 32mm, what kinds of power/magnification can we achieve?  When is it better to use the 32mm eyepiece?, the 4.5mm eyepiece?
  Eyepieces determine the amount of magnification that you can get out of your telescope, so buying many different eyepieces ensures that you have many different varying amounts of magnification.  Magnification is equal to the main lens focal length over the eyepiece focal length, so the 4.5mm lens would give (120in * 2.54cm/in)/0.45cm = 677.3x magnification, and the 32mm lens would give (120in * 2.54cm/in)/3.2 = 95.25x.  The 32mm eyepiece is more useful for viewing larger objects in the sky, whereas the 4.5mm eyepiece is good for looking at very small or very distant objects.  It is hard to look through the 4.5mm lens, though, because it is so tiny; in any case, the theoretical accuracy that it provides is limited by the atmosphere, which distorts light and drastically lowers the maximum potential accuracy of an earth-based telescope, is such that it really isn't worth using the 4.5mm eyepiece in most cases.

3) Why is it that when you look through the small fat lens you tend to get a rainbow halo around the image? (think about prisms)  Why does this happen more dramatically with the thick lens?  Why is this a big problem for astronomers?  How do you think it can be corrected?
  The rainbow halo is caused by the fact that different colors, or frequencies, of light travel through substances at different rates.  Because of this, the colors spread out and make a rainbow halo.  Fatter lenses have more glass for the light to travel through, so the light spreads out for more time and disperses at a greater angle.  This is a major problem for astronomers because this same effect occurs when viewing astronomical bodies; bizarre color spectrums can appear around stars and planets, making it far more difficult to get an accurate image of them.  Mirror-based telescopes do not have this effect, so using them avoids it altogether; also, special kinds of glass exist that cause the light to not spread out into its individual frequencies; use of this glass would also remedy the problem, but it also makes the telescope cost far more than it would otherwise.