Lenses

The purpose of the experiment is to ultimately verify the relationship between the focal length f, image distance D-i, and object distance D-o by exploring converging lenses.

To begin, one had to measure the focal length of the lense and this was accomplished by using an infinite light source--the sun.  The focal length was distance between the lense and the sharp point on the surface where all the sun rays collected.  The focal length was measured to be 20 +/-1 cm.

Once that was accomplished, the lense was placed four focal lengths--D-o equals 80 +/- .5cm--away from an object--a filament--that had a height of 9 +/-.5 cm ( one should keep in mind that there is a light source emanating from the object. See picture below). 
     

The height of the image H-i was measured to be 3 +/- .5 cm and the image distance D-i equals to 25 +/- .5 cm.   It is very important to note that image being projected is real and inverted.  Nonetheless, the lense was flipped around so the light of the object enters the other side.  This change did not produce any new data that was not already known.  That is to say that the image was still real and inverted. The image distance and height were remained the same as well.  The magnification was .49 +/-.091.

The lense was then moved to 2 focal lengths:
D-o = 40 +/- .5 cm H-o = 9 +/- .5 cm
D-i = 36 +/- .5cm   H-i = 8.5+/- .05 cm
M = .94 +/- .058

*After flipping the lense again, nothing was changed--all numbers are the same and the image was still real and inverted.

The lense was then moved to 1.5 focal lengths:
D-o = 30 +/- .5 cm H-o = 9 +/- .5 cm
D -i = 52 +/- .5 cm H-i = 16 =/- .5 cm
M = 1.78 +/- .153
*Once again the image was real and inverted and numbers did not change after flipping the lense.


The next part of the experiment consisted of applying the same technique of moving the lense to various distances from the object. The object was no longer the fillament but a small key chain that had the form of a bear.  The following data was obtained.

 

Object distance (cm)		Image distance (cm)		object height (cm)	image height (cm)	M	Type of image
5f		23 +/- .5		5.1 +/- .05	1.7 +/- .05	0.333 +/- .0131	real,inverted
4f		24.5 +/- .5		5.1 +/- .05	2 +/- .05	0.392 +/- .0136	real, inverted
3f		28 +/- .5		5.1 +/- .05	2.5 +/- .05	0.49 +/- .0057	real, inverted
2f		32 +/- .5		5.1+/- .05	3.2 +/- .05	0.627 +/- .0159	real, inverted

 

The image is real and inverted.

The graph above is one over the image distance versus negative one over the object distance.  The y-intercept represents one over the focal length 1/f.  Initially the focal lenth was measured to be 20 +/- 1 cm.  However with respect to the graph, the focal length is 19.69 cm.  This yields a percent difference 1.5 percent which is within error range.  More importantly the lab supports the idea that 1/D-i + 1/D-o = 1/f.