Working With Lenses - Gates Bartz and Caleb Skocy

Purpose:

In this exercise you will become familiar with the properties of lenses, and will use the lenses in various combinations to build a simple telescope.

Introduction:

Telescopes have been used by astronomers to study the Universe for over 400 years. Telescopes are divided into two basic types; the refractor and the reflector. The main optical component in the refractor is a lens, while a mirror is in the heart of a reflector.

The main lens in a refractor is always convex in shape, that is, it is thicker in the center than at the edge. The main lens is called the “objective” of the telescope because light from the object being viewed strikes the lens first. The lens used near the eye to view the image of the object is called the eyepiece, and can be either a convex or a concave lens. A concave lens is thinner in the center than at the edge.

A refracting telescope that uses a convex lens for its eyepiece is called an astronomical refractor. The other, which uses a concave lens for its eyepiece is called a Galilean refractor because Galileo’s telescope was of this type. Convex lenses can produce real images of an object by bringing the light from that object to a focus behind the lens.

In order to build a refracting telescope, you must decide on the proper choice of lenses. The objective lens must have a long focal length, and the eyepiece lens must have a short focal length. The focal length is the distance from the lens to the image of an object that is infinitely far away.

The three important properties that a telescope must have to be useful in studying distant objects are: 1) magnification, the ability to make objects look bigger; 2) light-gathering power, the capability of detecting dim objects; and 3) resolving power, the ability to distinguish between closely spaced features, that is, the ability to see detail.

The image orientation must be described using a pair of words, right-side-up or inverted, AND normal or reversed.

The field of view is the circular portion of a scene that is visible through a lens, mirror, or telescope.

General Procedure (Read Carefully):

1.     You will be given a packet of lenses and mirrors. Open this packet only when it is sitting safely on the lab table, preferably near the center. The lenses and mirrors in the packet are made of glass. They will break if you drop them on the floor. Be careful!

2.     It is important to number the lenses and mirrors you use. Return each lens and mirror to its packet after every use.

3.     You should make all measurements of focal length in centimeters and image size in millimeters, and be certain to say what units you are using for every number you record.

4.     Record your measurements in the lab writeup. Be clear and complete with your answers. For example, always clearly state which lenses you are referring to, and if necessary, show your work and/or explain your reasoning.

Results:

A)   Setting up the equipment, getting the optics and light source.  You will be issued a meter stick, and a packet containing fragile lenses and a mirror. A light source will be set up across the room.

B)   Finding Focal Lengths: THIS WILL REQUIRE WORKING WITH A PARTNER

·       In this lab, Caleb Skocy worked together with Gates Bartz.

a.     First, record your lens kit #.  Next, separate the concave lens from the convex lenses.  Determine what type of lenses and mirror you have in your set and describe them in your writeup.  As a LAST RESORT, feel the shapes of the lenses with your fingers.

·       We used lab kit #11. We ordered our lenses and mirrors 1-6. Numbers 1-3 were convex lenses of varying sizes. Number 4 was a concave lens. Number 5 was a convex mirror, and number 6 was a concave mirror.

b.     You can best measure the focal length of a convex lens by forming the image of an infinitely distant object and simply measuring the distance between the lens and the image.  However, in the confines of a classroom, you must settle for an object as far away as practical, that is, on the other side of the room.

c.     Use the light source as a distant object.  With the largest diameter convex lens, form a sharp image of the object on a white surface (a piece of stiff paper preferably).  Measure the lens-to-image distance in centimeters, and record it in your lab writeup as the focal length for this lens.  Record the size AND the orientation of the image.  To determine orientation: face the light source, then turn and face the image on the white surface, and compare.  Make a note of the relative brightness of the image compared to that of the other lenses.  Use terms “bright, brighter, and brightest”, etc.

d.     Repeat the above for the rest of the convex lenses in your set.  Note the focal length of the concave lens CANNOT be determined this way.

·       We measured the focal length (in cm), varying brightness, orientation, and image size (in mm) of the projected image for each of the convex lenses.

Lenses	#1 (Convex)	#2 (Convex)	#3 (Convex)
Focal Length (cm)	44	6	3
Image Size (mm)	5	1.5	0.5
Orientation	INV	INV	INV
Brightness	Brightest	Brighter	Bright

e.     Determine and record the focal length, image size and brightness of the image of the mirror.  You may have to vary your technique to succeed at this.  Which lens does its properties most resemble?

·       We measured the focal length (in cm), varying brightness, orientation, and image size (in mm) of the projected image for each of the mirrors (convex and concave).

Mirrors	#5 (convex)	#6 (concave)
Focal Length (cm)	68	6
Image Size (mm)	8	1.5
Orientation	INV	INV
Brightness	Brightest	Bright

·       To determine the focal length of this lens, we had to resolve the image reflected off the front of the mirror, rather than behind as we did when seeing light refracted through the lens. Both of these mirrors are comparable to the convex lenses we looked through earlier. Lens #5 corresponds with lens #1, and lens #6 is similar to lens #2.

f.      With the convex lens with the longest focal length set up to produce a sharp image on the white surface:  Half-cover the lens with an index card or similar, and note what happens to the image.  Do you still see the entire image of the light bulb?  How does the brightness and clarity of the image change as you cover the lens?

·       When you slowly cover the lens with your hand the image clarity remains the same, and you can still see the entire image. However, the brightness slowly decreases until the lens is fully covered and the image disappears completely.

C)   Assembling the telescope (CAREFUL--always assemble and disassemble over the table).

a.     Astronomical Refractor: In a refractor, an image is formed by the objective lens at a distance of one focal length behind it.  Call this distance fO.  This image is viewed through the eyepiece lens by placing the eyepiece lens at a distance equal to the focal length of the eyepiece, fE, BEYOND the image formed by the objective.  The total separation of the two lenses is therefore fO+fE.  In order to maintain this separation and keep out stray light, the lenses are mounted in a tube.  Mount the convex lens which had the longest focal length at the front of the tube as the objective.  Mount one of the other convex lenses as the eyepiece and slide the tubes open to roughly the proper separation for focusing on very distant objects which are as far away as possible.  Record the orientation of the images seen through the telescope and estimate how many times bigger things look through your telescope.

b.     Repeat Part a by changing the eyepiece (over the table!) to the other convex lenses.  Record any similarities and differences.

c.     The magnification of a telescope is given by the formula: M=fO/fE.  Calculate the magnification of your telescope from parts a and b.  Compare these results with your estimates of how many times bigger objects looked in each case.

·       We used the convex lens with the longest focal length for the objective lens of the telescope. We used (one at a time) the other two convex lenses as the eyepieces for our telescopes. Then we recorded the orientation of the observed image, and estimated the magnification of the image.

Objective Lens	Eyepiece Lens	fO	fE	Orientation	Estimated Magnification	Actual Magnification
#1	#2	44cm	6cm	INV	10	7.3
#1	#3	44cm	3cm	INV	15	14.6

·       The estimated magnification actually turned out to be very close to the actual magnification that we calculated.

D)   Galilean refractor:

a.     Use the concave lens as the eyepiece in your telescope with the same lens as before for the objective lens.  You will find a focus at a much closer separation of the lens.

b.     Observe objects around the room.  Record the orientation and estimate the magnification of this telescope.  Record any similarities and differences compared to the astronomical refractor.

·       In this section, we replaced the convex eyepiece lens with the concave lens. We also recorded the orientation and estimated the magnification for this pair of lenses. Unfortunately, we could not calculate the actual magnification accurately, as we do not know the focal length of this lens. We can, however, estimate the approximate focal length of the lens based on our estimate of the lens magnification.

Objective Lens	Eyepiece Lens	fO	fE	Orientation	Estimated magnification
#1	#4	44cm	~2.2cm	Correct	20

·       The main difference between the two lens alignments was that the concave lens caused the image to correct its orientation. It also magnified the distant object much more than the other lenses.

Conclusion:

In this lab we learned about how exactly to determine the focal length of a lens, how to build a basic refracting telescope, why it needs to be focused, how focal length contributes to magnification of objects, how to calculate the magnification power of a telescope using the focal lengths of the lenses, and we learned that different types of lenses refract in different ways to resolve an image either upside down or right side up. We also learned that, in a refracting telescope, the ideal lenses for maximum magnification is a combination of an objective lens with the largest possible focal length and an eyepiece lens with the shortest possible focal length.