Experiment 9: Lenses

PURPOSE: To observe and verify the relationship between the object distance and the image distance through a mathematical relationship.

PROCEDURE:

Convex lens used in the apparatus for the experiment 

Setup of the apparatus with convex lens between the object and the image projection.

Image of the object displayed at some distance from the lens

image displayed inside the lens when object is 0.5f  from the lens.

DATA & ANALYSIS:

Focal point was determined to being 5.3 cm for the lens.

Focal distance	Object Distance cm	Image Distance cm	Object Height cm	Image Height cm	Magnification	Type of Image
5f	26.5 ± 0.3	7 ± 0.3	8.8 ± 0.1	2.3 ± 0.05	0.261363636	Diminished;Inverted; real
4f	21.2 ± 0.3	7.7 ± 0.3	8.8 ± 0.1	2.9 ± 0.05	0.329545455	Diminished;Inverted; real
3f	15.9 ± 0.3	8.4 ± 0.3	8.8 ± 0.1	4.6 ± 0.05	0.522727273	Diminished;Inverted; real
2f	10.6 ± 0.3	11.5 ± 0.3	8.8 ± 0.1	9.1 ± 0.05	1.034090909	Same; Inverted; real
1.5f	7.95 ± 0.3	15.95 ± 0.3	8.8 ± 0.1	16 ± 0.05	1.818181818	Magnified;Inverted; real

If the object distance was set to 0.5f the image no longer appears on the screen and instead is displayed on the lens itself and is also no longer inverted and instead erect. The image is therefore considered virtual since it is displayed on the object side.

With the best fit line an equation, y= mx+b is found with a slope of .9038 and a y-intercept 0.1748. The y intercept is the inverse of the focal length.

Measured focal length	Y-intercept focal length
5.3 cm ± 0.5	5.72 cm

CONCLUSION:

The magnification had increased as the focal distance decreased until the object was less than the focal distance which created a a virtual image and thus did not show up as a projection on the piece of paper.          
The lens used was a converging lens inverting the image onto the piece of paper creating a real image of the object. However, again the image was erect in the lens when the object distance was .5f, creating a virtual image. Graph 1 shows the relationship between the image and the object distance verifying that there was an inverse relationship. Graph 2 represented a different approach to view the relationship between the object distance and the image distance. A negative inverse and and inverse image distance was graphed and the y-intercept that was found from the linear graph equaled to the inverse of the focus length. The measured focal length that was used by the suns ray was about 5.3 with an uncertainty of about ± 0.5. With this uncertainty the y-intercept or focal length is within the value of uncertainty indicating that the relationship between the image distance and object distance is verified with the following equation