Lab 11-tue. 1pm sec B

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201L

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Mechanical Engineering

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Dec 6, 2023

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Loudenridge Sundling Lab #11 Thick lenses II Tuesday Am Lab

Objectives: Ultimately, the primary goal of this lab is to further our understanding of thick lenses and their effect on the lens maker equations that are used for ideal thin lenses. Moreover, throughout this lab we will be required to display our understanding of how thick lenses require us to use the two different principal planes as reference points when calculating the other defining characteristics of the lens system. Furthermore, because the principal planes are usually located inside the lens, they are generally difficult to measure from which sometimes requires us to use the front and rear focal points as reference points. Consequently, throughout this lab we will use an autocollimation technique in which collimate beams of light are shined onto each side of the lens which allows us to easily locate both F and F’. Then, using these values and their relationship to the front and rear focal lengths, we should be able to calculate for the principal planes which we can then use to find the rest of the cardinal points. Therefore, this will display our understanding of how the principal planes are dependent on the radius of curvature and thickness of their respective side of the lens surface. Additionally, throughout this lab, we are expected to use our knowledge of principal planes in their relationship to thin lenses to calculate for 3 different known focal lengths using a three lens system and a point source. Procedure: Within this lab, we have two different experimental procedures. The first procedure requires us to display our knowledge of our the back and front focal lengths relate to the principal planes and the rear and front focal lengths. Consequently, we must set up an optical system with one of the two lenses given, the xerox copy lens or SLR zoom camera lens, and use autocollimation as well as adjusting the microscope to focus on the dust on the front of lens to calculate the front focal distance. Then, after removing the microscope and replacing it with the point source, we will adjust the lens until a focused image is on the back notecard. We will record the position of the microscope and subtract the original position from it to find our x value in the Newtonian equations. Then, in order to find the x’ value, we will repeat our process of autocollimation to find the position of the lens which we will then subtract the previous position of the lens. Finally, we will repeat the original process to find the front focal distance but flipped around on the optical system in order to find the back focal distance. Then, we will repeat this process for the other provided lens system. The second procedure requires us to setup a three lens system. Therefore, we must first place our first lens, focal length of 100 mm, 100 mm away from the object source and then place the imaging notecard a random distance away from the first lens. Then, we will adjust the second lens using trial and error until we find the arbitrary distance between the first lens and the imaging notecard which makes the image focused. Thus, in order to find the focal length of a given lens, we will place this lens 100 mm away from the first lens and proceed to adjust the object location until the image is in focus again. Then, using the new object location subtracted from the original object location, we have found the location of the first principle plane. Consequently, using the equations provided for us in the lab manual, we can calculate for the values of f2 using our know value of d (first principle plane) which will inevitably be the focal length of our second lens. Finally, by taking the inverse of this f2 value, we will calculate for the power of the second lens as well. Summary: Overall, throughout this lab, we are using Newtonian image equations in order to calculate for the cardinal points of two provided lenses, a xerox copy lens and a SLR zoom

camera lens. Consequently, we are tested on our understanding of the relationship between the front and back focal distances, the rear and front lengths, and the principal planes. Additionally, we are also expected to use a three lens system to compare principal planes to the power of the lens system in order to calculate for the focal lengths of three known lenses. Data: Q1: BFD FFD d d’ VN V’N’ Xerox Copy Lens 170 mm -153 mm 24 mm -28 mm 24 mm -28 mm SLR zoom camera lens 55 mm -41 mm 544 mm 30 mm 544 mm 30 mm Q2: KPX100 KPX106 KPC031 Principle plane shiŌ (d) 63 mm 45 mm -68 mm Focal Length 158.7 mm 222.22 mm -147.1 mm OpƟcal Power 6.3 m^-1 4.5 m^-1 -6.8 m^-1 Q3) For positive test lenses, why must f2 > 100 mm in the focometer? Because the second lens is exactly 100 mm away from the first lens which has a focal length of 100 mm, the second lens must have a focal length greater than 100 mm because if it doesn’t, the system will be afocal. This is due to the fact that the 100 mm focal length lens brings all parallel rays to focus 100 mm away from the lens. Therefore, if all the rays of light come to focus right at the center of a lens with the same focal length as before then the remaining rays will refract a focal point way in front of the third lens. (Q4) For negative test lenses, what practical limitations are there for f2? The practical limitations for f2 is the power of the lens. If the power of the negative lens is much greater than the overall power of the two other positive lenses in the system combined then the system will not focus the picture onto the notecard and there will be no way to effectively calculate the focal length using the focometer setup. Moreover, this is due to the fact that if the overall power of the lens system is negative then it will actually refract the rays away from the optical axis and essentially scatter the rays away from the imaging notecard.

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