REFRACTI0N FR0M A SPHERICAL SURFACE:THIN LENS
Amof Paul, Phy13L/B5
This experiment determines the focal length, the point of focus, and the magnification of images, in which the light rays converges or diverges through the use of thin spherical surfaces (convex and concave lenses). Apart from the thin lens, we also use the image screen, light source and the 0ptical bench to conduct this experiment. There were three parts to it, in which all results were recorded in order to calculate the focal length and its focal point with respect to the differences between image and the object and the form of projection in which either of the two produce as a result of Refraction of lights
Key Words: Concave, Convex, Spherical surfaces, Refraction
The above explained experiment was simple yet very reliable since focal point can be determined even if the object is observed from a finite distance or vise-versa with the image distance: according to a theory which states: As further the object passes through a spherical surface, the light changes its part and change direction and the angle decrease to a smaller angle, as a result approximations are made with respect to the decreasing angle. Therefore by using the equations used earlier in the previous equations such as 1f=1s’+1s we were able to calculate the focal point and using the image distance measured. With those results, images are then described according to the values calculated, whether if the image is real, virtual, and erect or it is inverted depending on the direction and the position with respect to the differences in distances affected the magnification of the objects figure.
Spherical Mirrors are very useful apart from the plane mirrors because of its own properties. Discussed below are the methods used on this experiment, the actual images captured during the experiment, and with each parts to it, are the descriptions on how it was done to archive the objective of the experiment. As shown in figure 1 was the actual image and the set-up of the experiment.
7620026289000Fig 1: Shows the equipment’s used during the experiment
For the first part of the experiment, the light source was used with the image taken from infinity to determine the focal length of the lens using an object at infinity. The window from the lab was taken as the distant object for the experiment while that object was projected on the screen from the lenses to compute for the focal length. Since the object is at infinity, the focal length was only taken with respect to the image distance. It is because any number is divided by infinity is zero, therefore the focal distance is only taken from the image distance.
-952528257500Fig 2: Shows the Image taken at an infinite distance
In Part 2: Placing the light source, one meters away from the screen, and by moving the convex lens we were then able to make a sharp image of the object on the screen to compute for the focal length and its percentage error. As experimented and as shown on the figure, the object distance and the image distance pairs are the inverse of each other. That means that the object and image distance are interchangeable.
Fig 3: Shows the Focal length using an object at an Infinite Distance
And finally, for the last part of the experiment is the magnification of the object size and the image size using the spherical mirrors. As we have observed, the magnification of their sizes depend on which lenses they are used, however most importantly is also because of the distances in which they are being magnified which affects their sizes produced on the image screen. Here is an example on how it was seen when the focus was magnified during the experiment.
Fig 4: Shows the Magnification of the image size to determine the Focal length.
Results and Discussions
Since lights passes through the spherical mirrors and bends, we tend to describe as diverging and converging, their images produced are then affected because of its properties. As for these tabulated results are experimented values done on the two spherical mirrors, the convex lens and the concave lens.
In our experimental findings, we observed that the image distance and the focal length are equal regardless of they are taken.. This is because of the property at infinity which states that, any object divided by infinity is zero. By this formula 1f=1s’+1s ; we able to calculate the focal length.( s’ is the object distance and s is the image distance)
Table 1 Shows the Determination of Focal Length using a 0bject at Infinity
LENS 1 LENS 2
Trial Object Distance Image Distance Focal Length Trial Object Distance Image Distance Focal Length
1 ?1O cm 1O cm 1 ?2O cm 20.00 cm
2 ?9.9O cm 9.90 cm 2 ?19.90 cm 19.90 cm
Focal Length (Average) 9.95 cm Focal Length (Average) 19.95 cm
Focal Length (Actual) 1Ocm Focal Length (Actual) 2O cm
Percent Error O.25 % Percent Error O.25 %
Shown below on Table 2 is the second part of the experiment about determining the Focal length using an Object at an infinite distance? In comparison with tabulated results on Table 1 it was observed that, since both distance can be measured, the focal length was also easily calculated using the same formula of 1f=1s’+1s. Even the object is at infinite distance, its focal length was easily calculated because what we need is the distance of the object and image distance as refracted when using the spherical lens without considering the actual object at its finite distance.
Table 2 Is the Determination of Focal Length using a 0bject at a Finite Distance
Distance between Screen and Light Source is 1OO cm LENS 1 LENS 2
Position 1 Position 2 Position 1 Position 2
0bject Distance, s 11.10 cm 88.90 cm 26.80 cm 73.O0 cm
Image Distance, s’ 88.9O cm 11.1O cm 73.2O cm 27.0O cm
Focal Length, f 9.8679 cm 9.8679 cm 19.6176 cm 19.71 cm
Focal Length (Av) 9.8679 cm 19.4438 cm
Focal Length (Act) 1O cm 2O cm
Percentage Error 1.321 % 1.681 %
Graphical methods also are very useful in determining the focal length of the position of the objects. As tabulated below are the positions of the objects which was measured and so the results were tabulated. After collecting the results, the values were then drawn graphically in order that the focal length was identified as shown below.
Table 3 Shows the determination of focal length and radius
Object Size, ho = 4.2 cm
Gap between the Screen and Light Source Position 1 Position 2
ss’hiss’hi1O0 cm 11.1 cm 88.9 cm 35.6 cm 88.9 cm 11.1 cm O.5 cm
95 cm 11.3 cm 83.7 cm 33.6 cm 84.Ocm 11.O cm O.6 cm
90 cm 11.4 cm 78.6 cm 30.8 cm 78.9 cm 11.1 cm O.6 cm
Gap between the Screen and Light Source Position 1 Position 2
1s1s’1s1s’100 cm O.09 cm-1 O.0112 cm-1 0.O112 cm-1 O.09 cm-1
95 cm O.0855 cm-1 0.O119 cm-1 O.0119 cm-1 O.09 cm-1
90 cm 0.O877 cm-1 O.0126 cm-1 0.O127 cm-1 0.O9 cm-1
x–intercept 0.1O014 cm-1 Focal Length 9.986 cm
y-intercept O.10143 cm-1 Focal Length 9.859 cm
Focal Length (Av) 9.9225 cm
Focal Length (Act) 1O cm
Percentage Error 0.14O5 %
Position Magnification, mPercentage Difference
m=s’sm=hihoPosition 1 8.OO9 8.86 8.O41 %
7.4O7 8.195 9.27 %
6.982 7.51 7.29 %
Position 2 O.125 O.122 2.43 %
O.31 O.146 1O.83 %
O.141 O.146 3.48 %
In conclusion of this experiment, we were able to achieve our objective by computing for the focal point and focal length with respect to the object distance and the image distance. Since objects are taken from infinity, we observed that, both distance are equal. As a result we only got O.25% as our percentage error. For the next part vice versa when the image distance was greater, we were then able to calculate the focal point and its length, as result, the percentage error was only 1.68%. And finally by using graphical method, we were able to identify the focal point using the graph in which by using the same result we were able to identify the images position and the difference in sizes. Of which they can be described as enlarged, inverted or of the same sizes. More over the experiment was a success and the objectives were achieved.
(1) Young ; Freedman University Physics 13th (2012)