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EXPERIMENT 403
REFRACTION FROM A SPHERICAL SURFACE:THIN LENS
Amof Paul, Phy13L/B5
[email protected]
This experiment determines the focal length, point of focus, magnification of images and the focal length, 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 optical 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.

Key Words: Concave, Convex, Spherical surfaces, Refraction
Introduction
The above explained experiment was simple yet very reliable since it was proven by Snell’s law which was stated that: As the further object passes through a spherical surface, its 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 as a result, the focal point was formed and calculated. This scenario won’t be used here however the same application applies. Using the equations used earlier in the previous equations such as 1f=1s’+1s we were able to calculate the focal point and also if the effects their differences in distances affected the magnification of the objects figure.

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Methodology
Whenever we are discussing about mirrors, we must take into consideration that mirrors consist of lenses. Because of those lenses, images are produced due to the type or lenses that are being used in the mirrors. For instance, in a plane mirrors, the lenses use is plane, as a result, the reflected images seems like the actual things if seen through our eyes. Where else on the other hand are the spherical mirrors, which as will be discussed below, are their effects they produce whenever lights pass through them. One of which as described by the topic itself is called refraction. Here are the equipment’s we used during this experiment.

Fig 1: Shows the equipment’s used during the experiment
336550952500For 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.

Fig 2: Shows the Image taken at an infinite distance
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For the second part is the determination of the focal length using an object at a finite distance? 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.

Fig 3: Shows the Focal length using an object at an Infinite Distance
left762000As 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.

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.

As shown below on Table 1, we have observed that, whenever we are determing the focal length at an infinite distance, the focal length is just as equal as the image distance. This is because of the property at infinity which states that, any object divided by infinity is zero. As a result, using the formular 1f=1s’+1s in which s’ is the object distance and s is the image distance.

Table 1 Shows the Determination of Focal Length using an Object at Infinity
LENS 1 LENS 2
Trial Object Distance Image Distance Focal Length Trial Object Distance Image Distance Focal Length
1 ?10.00 cm 10.00 cm 1 ?20.00 cm 20.00 cm
2 ?9.90 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) 10 cm Focal Length (Actual) 20 cm
Percent Error 0.25 % Percent Error 0.25 %
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 of1f=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 Shows the Determination of Focal Length using an Object at a Finite Distance
Distance between Screen and Light Source is 100 cm LENS 1 LENS 2
Position 1 Position 2 Position 1 Position 2
Object Distance, s 11.10 cm 88.90 cm 26.80 cm 73.00 cm
Image Distance, s’ 88.90 cm 11.10 cm 73.20 cm 27.00 cm
Focal Length, f 9.8679 cm 9.8679 cm 19.6176 cm 19.71 cm
Focal Length (Average) 9.8679 cm 19.4438 cm
Focal Length (Actual) 10 cm 20 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’hi100 cm 11.1 cm 88.9 cm 35.6 cm 88.9 cm 11.1 cm 0.5 cm
95 cm 11.3 cm 83.7 cm 33.6 cm 84.0 cm 11.0 cm 0.6 cm
90 cm 11.4 cm 78.6 cm 30.8 cm 78.9 cm 11.1 cm 0.6 cm
Gap between the Screen and Light Source Position 1 Position 2
1s1s’1s1s’100 cm 0.09 cm-1 0.0112 cm-1 0.0112 cm-1 0.09 cm-1
95 cm 0.0855 cm-1 0.0119 cm-1 0.0119 cm-1 0.09 cm-1
90 cm 0.0877 cm-1 0.0126 cm-1 0.0127 cm-1 0.09 cm-1
x–intercept 0.10014 cm-1 Focal Length 9.986 cm
y-intercept 0.10143 cm-1 Focal Length 9.859 cm
Focal Length (Average) 9.9225 cm
Focal Length (Actual) 10 cm
Percentage Error 0.1405 %
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 %
Conclusion
Suppose that the rays of light are traveling towards the focal point on the way to the lens. Because of the negative focal length for double concave lenses, the light rays will head towards the focal point on the opposite side of the lens. These rays will reach the lens before they reach the focal point. These rays of light will refract when they enter the lens and refract when they leave the lens. As the light rays enter into the denser lens material, they refract towards the normal; and as they exit into the less dense air, they refract away from the normal. These specific rays will exit the lens traveling parallel to the principal axis.

References
Book
1 Young & Freedman University Physics 13th (2012)

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