Lenses

Purpose:

            The purpose of this lab experiment is to observe a few characteristics of a converging lens then an object is placed on one side of the lens and the real, inverted image is placed on the other side of the lens.

Procedure:

1.      A lens was picked out as well as a light source, meter stick, and a V-shaped holding stand for to place the stick in as well as a lens holder.

2.      The converging lens was taken outside to have its focal length measured.

3.      The lens was brought back inside and the apparatus for which it will be held on was set up. 

4.      Once this was set up, the lens was then moved further and closer from the light source and the image was measured and compared to the original object, the light source. The light source was measured and determined to be used as the object height. First, we stared by moving the image a distance of 4 times the foal length found from the object, the object distance. This image was then shown by holding a notebook on the back side of the lens and determining when the object was at most focus. This was then measured with a ruler and the distance from the lens was recorded from the meter stick. These values would become the image height and image distance. 

5.      Once all of these values were recorded, the magnification (M) of the lens was then determined by using the formula, M = h_i/h_o. That is, the height of the image over the height of the original object.

6.      Next, the lens was taken out of the holding fixture and flipped to determine if the image properties differed. For this specific lens, the image remained unchanged since it was a converging lens with equal radius curvatures. It should be noted that the image was inverted, as some of the pictures will point out.

7.      The steps of 4 and 5 were repeated with the following object distances: 5f, 3f, 2f, 1.5f.

8.      For the next part, we covered half of the lens with a ruler to determine how that would affect the image projected. 

9.      Lastly, we took the lens and moved it a distance of half its focal length to see what would happen.

Data Analysis:

             Listed below is a table of all of the recorded values for the various object distances used as described in step 7. 

Object distance do­ cm	Image distance di cm	Object height ho cm	Image height hi cm	M	Type of image
5f = 91	23.6	8.6	1.8	.21	Real
4f = 73	25.7	8.6	3.1	.36	Real
3f = 54.6	29	8.6	4.6	.53	Real
2f = 36.5	39	8.6	9.5	1.1	Real
1.5f = 27	63	8.6	20.3	2.4	Real

The data  suggest that as the lens is moved closer to the focal point, the height of the image increases, along with the magnification. This is confirmed with our experiment as we saw the image getting gradually bigger as we moved towards the focal point. 

As step 8 indicates, we used a ruler to cover up half of the lens. Our initial guess was that only half of the image would be projected onto the page. This conclusion was wrong however. As the image from step 8 shows, the entire image is still present at the same height as it would be without the ruler. The only thing affected by the ruler is the intensity of the light that was viewed. As the ruler covered more of the lens, the image got dimmer. This is because the ruler only blocked some of the light from entering. Less light going through meant that the brightness of the picture will be less as well.

For the next step, step 9, we moved the lens inside of its focal point. When this was done, no matter how close we got to the lens or further away, we could not see the image. Once the lens was viewed directly, as the image shows, we were able to see the image. This image changed from the original image in that it is now erect and no longer real but virtual. 

After all the data was collected, the relationship of image distance versus object distance was then graphed and compared. 

As the picture shows, this relationship is an inverse one. This suggests that when an object is placed a certain distance from the lens, the image distance goes to infinity (much like how telescopes work!).

Next, a graph of inverse image distance vs. negative inverse object distance was plotted. This graph is shown below. 

This line suggests a linear relationship. The slop of this line was found to be .9965 and the y intercept was -.05283. This graphs shows a linear relationship of their reciprocals. This leads us to the conclusion that this is the basis for the 1/p + 1/q = 1/f equation.

Summary:

            Through this experiment, a number of results and characteristics of lenses were able to be observed. It was found that a when the image of a converging lens is real, the image is always inverted and goes through either magnification or demagnification. Once the image is placed within the focal point however, the image changed to become erect and virtual. It is also shown that the distance of the object and the distance of the image share an inverse relationship to one another and at some point the image distance will go to infinity.