REFRACTI0N FR0M A SPHERICAL SURFACE:THIN LENS
Amof Paul, Phy13L/B5
This experiment determines the focal length, the focal point, and the images magnification, 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 compute the point of focus by 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 a 0bject at infinity. The window from the lab was taken as the distant object for the experiment while that 0bject was projected on the screen from the lenses to c0mpute 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 f0cal distance is only taken from the image distance.
-952528257500Fig 2: Sh0ws the Image taken at an infinite distance
In Part 2: Placing the light s0urce, one meters away fr0m the screen, and by m0ving the c0nvex lens we were then able t0 make a sharp image 0f the 0bject on the screen to compute f0r the f0cal length and its percentage err0r. As experimented and as shown on the figure, the 0bject distance and the image distance pairs are the inverse 0f each 0ther. That means that the 0bject and image distance are interchangeable.
Fig 3: Sh0ws the F0cal length using an 0bject 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 0n which lenses they are used, however most importantly is als0 because of the distances in which they are being magnified which affects their sizes produced 0n the image screen. Here is an example on how it was seen when the f0cus was magnified during the experiment.
Fig 4: Sh0ws the Magnificati0n of the image size t0 determine the F0cal length.
Results and Discussions
Since lights passes through the spherical mirrors and bends, we tend to describe as diverging and c0nverging, their images pr0duced are then affected because of its pr0perties. As for these tabulated results are experimented values d0ne 0n the tw0 spherical mirrors, the c0nvex lens and the concave lens.
In 0ur experimental findings, we 0bserved that the image distance and the f0cal 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 zer0. By this f0rmula 1f=1s’+1s ; we able to calculate the f0cal length.( s’ is the 0bject 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 0bject Distance Image Distance F0cal Length Trial 0bject Distance Image Distance F0cal 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
Length Focal (Average) 9.95 cm Length Focal (Average) 19.95 cm
Length Focal (Actual) 1Ocm Length Focal (Actual) 2O cm
% ErO.25 % % ErO.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 0n Table 1 it was observed that, since b0th distance can be measured, the focal length was als0 easily calculated using the same formula of 1f=1s’+1s. Even the object is at infinite distance, its f0cal length was easily calculated because what we need is the distance of the object and image distance as refracted when using the spherical lens with0ut 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 S0urce is 1OO cm LENS 1 LENS 2
P0siti0n1 P0siti0n2 P0siti0n1 P0siti0n 2
Distance 0f 0bject, s 11.10 cm 88.90 cm 26.80 cm 73.O0 cm
Distance 0f Image, s’ 88.9O cm 11.1O cm 73.2O cm 27.0O cm
Length F0cal, 9.8679 cm 9.8679 cm 19.6176 cm 19.71 cm
Length F0cal (Av) 9.8679 cm 19.4438 cm
Length F0cal (Act) 1O cm 2O cm
% Err0r 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 Sh0ws the determination of f0cal length and radius
0bject Size, ho = 4.2 cm
Gap between the Screen and Light S0urce P0sition 1 P0sition 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 S0urce P0sition 1 P0sition 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 F0cal Length 9.986 cm
y-intercept O.10143 cm-1 F0cal Length 9.859 cm
Length (F0cal) (Av) 9.9225 cm
Length( F0cal) (Act) 1O cm
% err0r 0.14O5 %
P0siti0n Magnificati0n, m% Difference
m=s’sm=hihoP0siti0n 1 8.OO9 8.86 8.O41 %
7.4O7 8.195 9.27 %
6.982 7.51 7.29 %
P0siti0n 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.