Experiment 9: Lenses

Purpose:

        The purpose of this lab is to analyze the characteristic of a biconvex lens and verify the relationship between the image distance, object distance, and focal length.

Experiment:

The focal length of the lens can be found by measuring when the parallel ray from the sun passing through the lens form a single bright dot.

The following apparatus is then set up

We can then measure the image distance and image height when the image is focused on a screen and the object distance is equal to 1.5f, 2f, 3f, 4f, and 5f

The image focused on a whiteboard

Measuring image distance and image height

Data and Data Analysis:

Focal Length (f) = 4.8 ± 0.5cm

d0(cm)	di(cm)	h0(cm)	hi(cm)	M	Type of image
25	7.4	8.8	2.3	0.26	Real, inverted
20	8.4	8.8	3.4	0.39	Real, inverted
15	8.9	4.0	2.6	0.65	Real, inverted
10	11.8	4.0	4.5	1.12	Real, inverted
7.5	18.3	1.1	2.8	2.55	Real, inverted

When the object distance is changed to 0.5f, the image no longer shows up on the board, however, when looked through the lens, the image is upright. This means that the image is virtual.

Graph of d_i vs d₀

Inverse d_i vs d₀

d0(cm)	Inverse di(1/cm)
25	0.135
20	0.119
15	0.112
10	0.085
7.5	0.055

Inverse d_i vs negative inverse d₀

Inverse di(1/cm)	Negative inverse d0(1/cm)
0.135	-0.04
0.119	-0.05
0.112	-0.067
0.085	-0.1
0.055	-0.13

The lens equation shows that:

which implies that the slope of the graph above should be 1 and the y-intercept is 1/f.

We can then conclude that, according to the graph, the focal length should be:

f = 1/0.1653 = 6.0cm

From the regression line of the graph we can then conclude that:

Error Analysis:

The error on this experiment can be mostly contributed to measurement error. We can contribute an error of about ±3cm on all measurement due to the increments of the ruler used, ruler that is not perfectly perpendicular with the paper and the light source, and the image that may not be completely focused on the screen.

Summary:

From this experiment, we can conclude that the image created by a biconvex lens is real and inverted. The magnification of this lens vary with the object distance. As the object distance gets smaller, the magnification becomes larger. We can also conclude that if the object distance is smaller than the focal length, then the image produced by this lens become virtual and upright.