Working with Lenses Lab Report: Katelynn Smith and Aubrey Hormel

Working with Lenses

Katelynn and Aubrey

Abstract

          Students learned about the nature of convex and concave lenses and mirrors, and used this knowledge to construct their own amateur telescope. First, students explored the focal lengths and images produced by several convex lenses, a concave lens, and a concave mirror. They were then required to integrate this knowledge in the construction of a telescope, and, by switching the lenses used for the eyepiece, were able to observe the affects each lens has on the image received by your eye.

Introduction

          Until Galileo invented the refracting telescope, humans were confined to a limited view of the Universe. Stars and planets were tiny, mysterious points of light. A refracting telescope uses the physical nature of lenses to focus light rays from an infinitely distant light source to a single point of convergence, then uses another lens to magnify this converging light into an image viewed through the eyepiece. To elaborate, every lens has an associated focal length, and when two lenses are positioned at a distant equal to the sum of their focal lengths, we have a telescope. As well as the apparent size of the image, lenses can also change the orientation of the image, making it reversed or up-side-down (inverted).

Materials: 

Distant light source, meter stick, meter stick stands, lens clamp, lens kit, telescope kit, paper

Procedure:

A. Students will find a partner, then set up the meter stick with the stands, attach the lens clamp, and align the meter stick with a distant light source. Partners acquire a lens kit and a telescope kit.

B. Students record the number of their lens kit, separate the items, and note distinguishing characteristics of each lens or mirror: convex/concave, diameter, relative brightness, and how their shape compares with those lenses of the same type.

Next, students place each lens in the lens clamp and determine the focal length by moving a piece of paper along the meter stick. When the image comes into focus, students note the distance between the paper and the lens clamp, as well as the orientation of the image produced. For the concave lens, a focal length cannot be determined in this way, but students still recorded the orientation of the image. The technique had to be altered to determine the focal length of the concave mirror. Students angled the mirror so the light converged on piece of paper below.

Students once again produced an image on a piece of paper behind a lens, then covered half of the lens with a piece of paper and observed how this affected the image.

C.  Students used the lenses in their kit to construct a telescope. The convex lens with the largest focal length is used for the objective lens, and students use each of the other lenses as eyepieces at different times.

Once the lenses are mounted, students must slide the cardboard tubes so that the focal lengths of the two lenses are aligned; this focuses the telescope, and follows the equation  D = fO + fE, , where  fO is the focal length of the objective lens and fE is the focal length of the eyepiece. When the telescope is focused, students record the orientation and approximate magnification of the images produced. After estimating the magnification, students calculate the true magnification of each lens combination using the formula M = fO/fE.

D. In this part, students created a Galilean refractor by using the same objective lens and a concave lens for the eyepiece. Students note characteristics of this kind of telescope, as well as the orientation of the image produced.

Results and Discussion:

B.) Our lens kit number was 6. Using this lens kit, we identified the individual lenses and numbered them for ease of organization.

#	Type	Diameter (cm)	Other description
1	Convex lens	4.5	Almost flat face
2	Convex lens	3.5	Thicker lens
3	Convex lens	3.5	Thinner lens
4	Concave lens	3.4
5	Concave mirror	5

We then used the now numbered lenses to make further observations concerning the general mechanics of a telescope and lenses. Our observations on focal length, image size, and image orientation resulting from the use of the lenses and mirror are as follows:

#	Focal length (cm)	Image size (mm)	Orientation	Brightness
1	50	5	Inverted	Brightest
2	3.5	1	Inverted	Brighter
3	6	1	Inverted	Bright
4	?		Upright	Bright
5	?		Inverted

The properties of the concave mirror most resembled the properties of the convex lenses. Most notably, the resulting image was inverted like it would be with a convex lens.

To better understand the light gathering properties of the lenses, we put the convex lens with the longest focal point (#1) into the lens clamp. We half covered the lens with a piece of thick paper and noticed that the resulting image was not noticeably dimmer than the image left with a fully lit lens. We proceeded to cover more of the lens to notice that the image becomes seemingly exponentially dimmer and fuzzier as the light source is blocked. The image did not disappear until almost the entire light source was blocked from the lens.

C.) After observing the lenses individually, we created an astronomical refractor from combinations of two concave lenses. The distances they had to be separated from each other can be calculated with the equation fO + fE, with fO being the focal length of the objective and fE being the focal length of the eyepiece. The magnification resulting from the combination of lenses can be calculated using the formula M=fO/fE.

AR #	(#) fO	(#) fE	Distance Apart	Est. magnification	Act. magnification
1	(1) 50 cm	(2) 3.5 cm	53.5 cm	10x	14.3x
2	(1) 50 cm	(3) 6 cm	56 cm	5x	8.3x

Our actual calculations regarding the magnification of the images were relatively close to the estimates when using the telescopes.

The following is a diagram representing the required distance (fO + fE) to create a focused image in the eyepiece of a telescope:

D. After making the astronomical refractor, we put a Galilean refractor together with the concave lens as the eyepiece. The focus was much closer than it was with the astronomical refractor. We estimated that objects were about 5 times their original size when using this telescope. The images were upright and normally oriented. This is different from the astronomical refractor because the images were not inverted or changed aside from their magnification.

Conclusion

          This lab allowed students to develop skill in producing images of a light source using lenses, determining their focal lengths, and applying this knowledge in constructing an amateur telescope. It also solidified understanding of physics as applied to light, matter, and telescopes, because we performed experiments that showed how lenses cause light to converge or diverge. We were able to measure focal lengths and check that the formula for the distance required between two lenses in order to create a telescope, D = fO + fE, is accurate.