Experiment 10: Lenses

Introduction

The purpose of this experiment was to observe how the image changes based on the object distance. In this experiment, a meter stick, a converging lens, and a socket lamp with filament, a lens holder, and a cardboard. First, the focal length of the lens was determined by measuring the distance between the lens and the focus of the sun rays. Then the object distances varying from 1.5f to 5f were computed using the focal length. These computed distances were used to position the lens distance from the filament. The set up of the apparatus was shown in figure 2. The height of the filament was also measured. After turning the power on to let the light shine through the filament, the cardboard distance from the lens was adjusted till a sharp image was obtained. This image distance and its height were also measured. After recording all these data, the magnification of the lens was computed, and two graphs were constructed to observe the relationship between the image and object distance, and the focal length.  

 Figure 1: Measuring the focal length of the converging lens

Figure 2: Experimental set-up

Figure 3: Image forming through the converging lens

Data and Analysis

Focal length (f) = 9.5 ± 0.25 cm

Table 1: Recorded data of the object and image distances and heights

Object distance as a multiple of f(cm)	Object distance(cm)	Image distance(cm)	Object height(cm)	Image height(cm)	Type of image
5f	47.5 ± 1.25	16.50 ± 0.25	8.80 ± 0.25	3.30 ± 0.25	Inverted, real
4f	38.0 ± 1.00	17.00 ± 0.25		4.40 ± 0.25	Inverted, real
3f	28.5 ± 0.75	18.00 ± 0.25		6.60 ± 0.25	Inverted, real
2f	19.0 ± 0.50	25.50 ± 0.25		14.30 ± 0.25	Inverted, real
1.5f	14.3 ± 0.38	23.25 ± 0.25		16.50 ± 0.25	Inverted, real

Table 2: Comparison of magnification from distance ratios and height ratios

Object distance as a multiple of f(cm)	Md (di/d0)	Mh (hi/h0)	% difference between Md and Mh (%)
5f	0.347 ± 0.011	0.375 ± 0.030	5.10
4f	0.447 ± 0.013	0.500 ± 0.032	7.33
3f	0.632 ± 0.019	0.750 ± 0.036	11.1
2f	1.34 ± 0.04	1.63 ± 0.05	12.6
1.5f	1.63 ± 0.05	1.88 ± 0.06	9.28

Graph 1: Object distance vs. Image distance

Graph 2: Inverse image distance vs. Negative inverse object distance

Conclusion

According to table 1 and graph 1, as the object distance decreased, the image distance increased. Therefore, the image and object distance had inverse relationship as shown in graph 1. However, at 1.5f, even though the object distance decreased, the image distance decreased. This was because the image became dimmer and unclearer as the object distance decreased. Hence, uncertainty became greater since it became harder to see the actual height of the image. Another relationship observed in this experiment was that the image height increased as the object distance decreased. This was because the image distance got smaller. Besides, the image observed was always inverted. Since the image formed by the converging lens was inverted, the image was real. This idea was explained in experiment 9. As shown in table 2, the magnification obtained from distance ratio and height ratio increased as the object distance decreased. This agreed with the observation since the image got larger as the object was nearer to the lens. However, most of these values were not within the uncertainties of each other. This was possibly because the focus was not as accurate as it should have been. Unclear images at small object distances also contributed to this error.

According to graph 2, the inverse image distance and inverse object distance had linear relationship. This relationship actually described the relationship between the image distance, object distance, and the focal length, which was 1/d₀ + 1/d_i = 1/f. The y-intercept 0.08178cm^-1, obtained from the graph was the inverse of the focal length of the lens. By taking the reciprocal of the y-intercept, the graphical focal length was computed to be 12.23cm. However, the measured focal length was 9.5cm. This large difference in focal length was contributed by the image distance at 1.5f. As mentioned earlier, this was the only data set that deviated from the image-object distance relationship. This smaller image distance with larger inverse value lower the slope, hence, smaller y-intercept and larger focal length.
When half of the lens was covered, the image became dimmer since the light passed through the lens was decreased by a factor of 2 due to halved-lens. Besides, as the object distance became closer to the lens, the image size and distance became larger. At 0.5f, there was no image because the image was between the vertex and the focus; hence, the image became virtual.