Lab #5: Geometric Optics Chi Shing Tsui 11/23/2009 Physics 4bl
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Lab #5: Geometric Optics Chi Shing Tsui 11/23/2009 Physics 4BL Lab Partner: Ester Introduction: In this experiment, we investigate the behavior and physical properties of light rays. This includes a study on reflection, total internal reflection, magnification, and refraction phenomenon. We conduct the experiment using a multitude of geometric lenses, laser, and light box. It should be noted though – the results from our lab should support Snell’s Law of Refraction. Experimental Results: Lab #, Section #, Part # Section 5.2.1.: This section uses the light box with one slit, producing one light ray. It’s then directed to a trapezoidal prism that’s been rotated roughly to 45°. The angle between the reflected light ray and the incident ray is measured to be 76.5°. The angle between the transmitted ray out of prism and its perpendicular comes out to be 40°. Knowing that Θincident = Θreflected and that the total Θ is 76.5°, we can calculate that Θi = Θr = 38.25°. We will use this and other measured angles to calculate n of the trapezoidal prism in future analysis. Everything described above is traced and scanned into the figure below (Figure 1):
The second part uses the same single ray, except this time we rotate the trapezoidal prism until there is total internal reflection. At this point, the transmitted ray disappears. Again, we traced the prism, its angles, and the incident light ray as shown in the following diagram (Figure 2):
Section 5.2.2.: In this part of the lab, we worked with thick lenses. Although thick lenses are avoided in most cases of actual scientific research, we will use them as a learning tool. It’s much easier to observe the behavior of light rays with big lenses we can see. We first measured focal lengths of three different lenses, of a convex, concave, and plano-convex lens. To do this, we traced the shape of the lens and its corresponding incident light rays. Then we measured the distance between the convergence point and the edge of lens. For the convex lens, the focal length was 4.15cm+/-.05cm; for concave, the focal length is 2.4cm; for plano-convex, the length is 10.2 cm. The light rays, the measured focal length, convergence pts, and the shape of prism traces are that of the following Figures. (Figure 3, convex): (Figure 4, concave):
(Figure 5, plano-convex):
In continuation of the investigation of the properties and behavior of light hitting thick lenses, we explore the phenomenon of spherical aberration. We do this by putting the bi-convex lens back in front of the ray box with now 5 incident rays. Take notice of the two focal points that occur. This phenomenon is called spherical aberration. The first focal length is 3.9cm; the next is .5cm away (@ 4.4cm). Figure 6, will be the physical representation of what I had just described:
The last part of this section looks into magnification and demagnification caused by lenses. We place a concave in front of light source, then a plano-convex lens behind. The result is magnification of the image (light rays). In our lab, the distance between slits (and therefore light rays) were initially .995cm, which about equals to 1cm from each other. But after magnification, the distance between rays split up to around 1.505cm. Demagnification occurs when the lens are put in opposite order. The demagnification ratio is from .995cm to .495cm. All of this is illustrated in scanned Figure 7:
Section 5.3.3.: Though thick lenses allow for easy interpretation of how light behaves, it is the thin lens properties that are more important to understand. We study the thin lens properties in a similar manner. We use a laser and a beam splitter as opposed to a light box. First we test for the focal length of two thin lenses individually, then we test for their focal length when put together one after the other. With a lens that has a 2cm diameter lens, the focal length was 16cm. The lens that has a 4.5cm diameter shows a focal length of 41.5cm. In the case of both, the experimental result was a focal length of 11.5cm. These collected data will be put to further analysis. Section 5.2.4.: Most of the knowledge learned from previous parts will be utilized in this final section. We use a shine an image from a film grating through a known lens onto a screen. Then we measure the object distance from lens, the focal distance, and the magnified image of the film grating. The data collected are:
28.3cm for object distance, 36.95cm for the focal distance, and 1.8mm for distance between magnified film gratings. In later analysis, we will verify the expression 1/f = 1/o + 1/i. But for now, the following data should help put things into perspective for both part 3 and part 4. Data 8:
Analysis: Section 5.3.1.: Let me make this clear from the beginning: the data taken from Figure 1 are erroneous. We traced everything and followed the directions correctly up until the one crucial step – drawing of the normal. We ignored to use a
protractor, and instead eyeballed the perpendicular normal line to which we compared our angles with. From this seemingly slight mistake during lab procedure produced a whole section of bad data. But I will run through the calculations as though the data were correct; and I will explain the difference between the numbers that “should be” and that we experimentally calculated. First off, Figure 1, shows a difference between incident and reflected angles. This is false as the laws of reflection decrees that θincident = θreflected. So as explained in experimental results, what I needed to do is to add up and average the angles, and set θincident and θreflected equal to each other. This resulted in a θincident angle of 38.25⁰. The θtransmitted, which was measured with the eyeballed normal, is 40⁰. Using Snell’s Law, nairsin(θincident) = nprismsin(θtransmitted). So, nprism = (1)(sin(38.25)/sin(40)). In the case that we had the right data, nprism should be between 1.3 – 1.8. However, my calculations gave n = 0.963; which is impossible for the prism to have lower n of air and with the given range of what nprism should be. However, even if we had thought that nprism = 0.963 is correct, the next calculations for the expected TIR (total internal reflection) angle would show the error in data. Since θTIR is sin-1(nair/nprism), and nair/nprism is greater than 1, we know that it is impossible to have arcsin of a value greater than 1. Hence, the data is unreliable due to the one mistake we made to assume it was okay to eyeball the normal perpendicular to the trapezoidal prism. We also cannot compare the “estimated θTIR” with “actual θTIR”, which is 45⁰ as shown in Figure 2, because we don’t have a value to compare to. Unfortunately, we have no way to fix the mistake, so all I can do is to end the analysis with the results from my erroneous data (which is above). Section 5.3.2.: In the second part of the lab, we used thick lenses to really grasp an understanding of how different lenses affect the image. Most of the data is qualitative, and shown in Figure 3, 4, 5. The focal lengths, as shown in those respective figures, are 4.15cm for convex, 2.4cm for concave, and 10.2cm for plano-convex lens. The next part is spherical aberration, and as shown in Figure 6, and the difference between the focal points is 0.5cm or 11.4%. The magnification and demagnification from concave and plano-convex lenses are easily by dividing the distance between original light rays and resultant light rays. The first combination of lenses produce a magnification factor of 1.505/0.995 = 1.51. The second combination of lenses produce a demagnification factor of 0.495/0.995 = 0.497. Section 5.3.3.: From the experimental data collected, we have the focal lengths and diameter of two individual thin lenses. The 2cm diameter lens has a focal pt of 16.0cm. The 4.5cm diameter lens has a focal point of 41.0cm. Given that Dtotal = D1 + D2, and Di = 1/fi, we can substitute known values and change the equation to 1/ftotal = 1/(16cm) + 1/(41cm) + e/(16*41), where e = .0207. After the calculations, ftotal = 11.5cm. This theoretical value completely matches with the experimental focal length of both lenses, which was 11.5cm. The error must have been negligible because of the exact match on experimental and theoretical values. Section 5.3.4.: Since we used the smaller lens, we know that the focal length of 16cm. We will prove that 1/f = 1/o + 1/i, where o is 28.3 and i is 36.95. If we calculate focal length using the values of o and i, we will have the experimental value of 16.03cm. Comparing to the focal length that we knew from another
experiment, we have confirmed that the expression is valid. The image size is magnified, as apparent by data. Conclusion: This lab builds upon the understanding of light by teaching the behavior of light rays through geometric optics. We used both thick and thin lenses, and laser/light box as the source. The first part of the lab explored application of Snell’s Law of Refraction. Unfortunately, a critical error in experimental procedure produced a set of data that is not applicable or correct for analysis. We “eyeballed” the normal perpendicular that we measured the incident and transmitted angles with. In doing so, the data are not reliable and as predicted produced erroneous and impossible results. The second part of the lab, we used thick lens to grasp other properties of light, including the concept of focal lengths, magnification/demagnification, and spherical aberration. The data are as shown Figure 3, 4, 5, 6. The magnification factor is 1.51 and demagnification factor is 0.497. In the third part, we wanted to verify 1/ftotal = 1/f1 + 1/f2 + e/(f1f2), where e = 0.0207. Using data of focal length from individual lenses, we compared the calculated ftotal with experimentally measured ftotal. They turned out to be exactly the same at 11.5cm, supporting the relation we had to prove. In the last part of the lab, we set up to prove 1/f = 1/o + 1/i. Since we know the focal length of the lens we chose to work with, all we had to do was follow the instruction and measure o and i distances. By plugging in the values, as done in analysis section 5.3.4., we were successful too in proving that relation.
The second part uses the same single ray, except this time we rotate the trapezoidal prism until there is total internal reflection. At this point, the transmitted ray disappears. Again, we traced the prism, its angles, and the incident light ray as shown in the following diagram (Figure 2):
Section 5.2.2.: In this part of the lab, we worked with thick lenses. Although thick lenses are avoided in most cases of actual scientific research, we will use them as a learning tool. It’s much easier to observe the behavior of light rays with big lenses we can see. We first measured focal lengths of three different lenses, of a convex, concave, and plano-convex lens. To do this, we traced the shape of the lens and its corresponding incident light rays. Then we measured the distance between the convergence point and the edge of lens. For the convex lens, the focal length was 4.15cm+/-.05cm; for concave, the focal length is 2.4cm; for plano-convex, the length is 10.2 cm. The light rays, the measured focal length, convergence pts, and the shape of prism traces are that of the following Figures. (Figure 3, convex): (Figure 4, concave):
(Figure 5, plano-convex):
In continuation of the investigation of the properties and behavior of light hitting thick lenses, we explore the phenomenon of spherical aberration. We do this by putting the bi-convex lens back in front of the ray box with now 5 incident rays. Take notice of the two focal points that occur. This phenomenon is called spherical aberration. The first focal length is 3.9cm; the next is .5cm away (@ 4.4cm). Figure 6, will be the physical representation of what I had just described:
The last part of this section looks into magnification and demagnification caused by lenses. We place a concave in front of light source, then a plano-convex lens behind. The result is magnification of the image (light rays). In our lab, the distance between slits (and therefore light rays) were initially .995cm, which about equals to 1cm from each other. But after magnification, the distance between rays split up to around 1.505cm. Demagnification occurs when the lens are put in opposite order. The demagnification ratio is from .995cm to .495cm. All of this is illustrated in scanned Figure 7:
Section 5.3.3.: Though thick lenses allow for easy interpretation of how light behaves, it is the thin lens properties that are more important to understand. We study the thin lens properties in a similar manner. We use a laser and a beam splitter as opposed to a light box. First we test for the focal length of two thin lenses individually, then we test for their focal length when put together one after the other. With a lens that has a 2cm diameter lens, the focal length was 16cm. The lens that has a 4.5cm diameter shows a focal length of 41.5cm. In the case of both, the experimental result was a focal length of 11.5cm. These collected data will be put to further analysis. Section 5.2.4.: Most of the knowledge learned from previous parts will be utilized in this final section. We use a shine an image from a film grating through a known lens onto a screen. Then we measure the object distance from lens, the focal distance, and the magnified image of the film grating. The data collected are:
28.3cm for object distance, 36.95cm for the focal distance, and 1.8mm for distance between magnified film gratings. In later analysis, we will verify the expression 1/f = 1/o + 1/i. But for now, the following data should help put things into perspective for both part 3 and part 4. Data 8:
Analysis: Section 5.3.1.: Let me make this clear from the beginning: the data taken from Figure 1 are erroneous. We traced everything and followed the directions correctly up until the one crucial step – drawing of the normal. We ignored to use a
protractor, and instead eyeballed the perpendicular normal line to which we compared our angles with. From this seemingly slight mistake during lab procedure produced a whole section of bad data. But I will run through the calculations as though the data were correct; and I will explain the difference between the numbers that “should be” and that we experimentally calculated. First off, Figure 1, shows a difference between incident and reflected angles. This is false as the laws of reflection decrees that θincident = θreflected. So as explained in experimental results, what I needed to do is to add up and average the angles, and set θincident and θreflected equal to each other. This resulted in a θincident angle of 38.25⁰. The θtransmitted, which was measured with the eyeballed normal, is 40⁰. Using Snell’s Law, nairsin(θincident) = nprismsin(θtransmitted). So, nprism = (1)(sin(38.25)/sin(40)). In the case that we had the right data, nprism should be between 1.3 – 1.8. However, my calculations gave n = 0.963; which is impossible for the prism to have lower n of air and with the given range of what nprism should be. However, even if we had thought that nprism = 0.963 is correct, the next calculations for the expected TIR (total internal reflection) angle would show the error in data. Since θTIR is sin-1(nair/nprism), and nair/nprism is greater than 1, we know that it is impossible to have arcsin of a value greater than 1. Hence, the data is unreliable due to the one mistake we made to assume it was okay to eyeball the normal perpendicular to the trapezoidal prism. We also cannot compare the “estimated θTIR” with “actual θTIR”, which is 45⁰ as shown in Figure 2, because we don’t have a value to compare to. Unfortunately, we have no way to fix the mistake, so all I can do is to end the analysis with the results from my erroneous data (which is above). Section 5.3.2.: In the second part of the lab, we used thick lenses to really grasp an understanding of how different lenses affect the image. Most of the data is qualitative, and shown in Figure 3, 4, 5. The focal lengths, as shown in those respective figures, are 4.15cm for convex, 2.4cm for concave, and 10.2cm for plano-convex lens. The next part is spherical aberration, and as shown in Figure 6, and the difference between the focal points is 0.5cm or 11.4%. The magnification and demagnification from concave and plano-convex lenses are easily by dividing the distance between original light rays and resultant light rays. The first combination of lenses produce a magnification factor of 1.505/0.995 = 1.51. The second combination of lenses produce a demagnification factor of 0.495/0.995 = 0.497. Section 5.3.3.: From the experimental data collected, we have the focal lengths and diameter of two individual thin lenses. The 2cm diameter lens has a focal pt of 16.0cm. The 4.5cm diameter lens has a focal point of 41.0cm. Given that Dtotal = D1 + D2, and Di = 1/fi, we can substitute known values and change the equation to 1/ftotal = 1/(16cm) + 1/(41cm) + e/(16*41), where e = .0207. After the calculations, ftotal = 11.5cm. This theoretical value completely matches with the experimental focal length of both lenses, which was 11.5cm. The error must have been negligible because of the exact match on experimental and theoretical values. Section 5.3.4.: Since we used the smaller lens, we know that the focal length of 16cm. We will prove that 1/f = 1/o + 1/i, where o is 28.3 and i is 36.95. If we calculate focal length using the values of o and i, we will have the experimental value of 16.03cm. Comparing to the focal length that we knew from another
experiment, we have confirmed that the expression is valid. The image size is magnified, as apparent by data. Conclusion: This lab builds upon the understanding of light by teaching the behavior of light rays through geometric optics. We used both thick and thin lenses, and laser/light box as the source. The first part of the lab explored application of Snell’s Law of Refraction. Unfortunately, a critical error in experimental procedure produced a set of data that is not applicable or correct for analysis. We “eyeballed” the normal perpendicular that we measured the incident and transmitted angles with. In doing so, the data are not reliable and as predicted produced erroneous and impossible results. The second part of the lab, we used thick lens to grasp other properties of light, including the concept of focal lengths, magnification/demagnification, and spherical aberration. The data are as shown Figure 3, 4, 5, 6. The magnification factor is 1.51 and demagnification factor is 0.497. In the third part, we wanted to verify 1/ftotal = 1/f1 + 1/f2 + e/(f1f2), where e = 0.0207. Using data of focal length from individual lenses, we compared the calculated ftotal with experimentally measured ftotal. They turned out to be exactly the same at 11.5cm, supporting the relation we had to prove. In the last part of the lab, we set up to prove 1/f = 1/o + 1/i. Since we know the focal length of the lens we chose to work with, all we had to do was follow the instruction and measure o and i distances. By plugging in the values, as done in analysis section 5.3.4., we were successful too in proving that relation.
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