Lab 8 Geometrical OpticsMickey RazaLab Partner: Kelly A GordonLab TA: Sajjad TahirLab Date: 3rd April, 2014

TheoryWhen a lens is placed in front of an object, depending on the type of lens, the image of the object that can be seen is either shrunk or magnified, inverted or same direction, real or virtual. All of these properties of the image also depend on the distance of the object from the lens, the focal length of the lens, etc.

Experimental DescriptionIn the first part of the experiment, we set up the apparatus and measure the width of the object, yobj. Then we place a lens with a focal length of 10 cm almost 20 cm from the object and measure the distance between the object and the lens and record this distance as dobj. Then we place the screen on the other side of the lens and move the image till the image is the sharpest and then measure the width of the image that is produced on the screen, yimg. We see that the image is inverted and therefore the value of the width of the image is negative. We then record the distance of the image from the lens as dimg. Using these values we calculate the experimental focal length and the expected and calculated magnification of the image produced. We then repeat the process several times to get an average value of the magnification and focal length and compare it to the given focal length.In the next part we aim to check Astigmatism. We hold the lens in a slanted position near the image and then move the screen to obtain a vertical and a horizontal line. We then check which is closer to the lens and calculate the difference in position of the vertical and horizontal lines.In the next part, we use two lenses, so that the image produced by the first lens acts as an object for the second lens. Using the different distances, we aim to find the focal length of the second lens.In the next part, we move the lens so close to the object that wherever the screen is put on the opposite side of the lens, there is no image produced. This is because a virtual image is produced on the same side as the object. We calculate the expected width of the virtual image and then view the virtual image and roughly verify that our calculated value is correct.

ResultsIn the first part of the experiment, we found the width of the object to be 0.80 0.10 cm, and the initial distance of the object from the lens to be 20.00 0.10 cm. The distance of the screen where the image was the sharpest was found to be 47 cm and therefore the image distance from the lens was measured to be 26.00 0.10 cm. Since the image was inverted, the width of the image produced was measured to be -0.90 0.10 cm. Using the formula for focal length, the focal length was calculated to be 11.30 cm. Using the ratio of the image width and object width, the magnification was calculated to be -1.13 0.27, while using the formula , the calculated magnification was -1.30 0.01. This process was repeated several times by moving the lens closer and closer to the object, and finding the focal length, measured magnification and calculated magnification for each attempt. The average focal length therefore obtained was 10.24 0.55 cm, with an uncertainty of 5.32%. The average measured magnification was found to be -2.45 and the average calculated magnification was found to be -2.23, therefore giving an uncertainty of 2.39%.When finding Astigmatism, we found that the vertical line was closer to the lens and the position of the vertical line was 37.60 cm, while the horizontal position was 32.40 cm, therefore the difference in the positions was measured to be 5.20 cm.In the next part, the first lens was placed 20.00 cm away from the object and the position, S1, of the screen, where the sharpest image was seen was at 41.00 0.10 cm. This position also acts as the object location for the second lens. The other lens with a focal length of 5.00 cm is placed 50 cm away from the object. The location of the second lens, L2 is measured to be 51.00 0.20 cm. Therefore the object distance for the second lens is L2 S1, which is 10.00 cm. Then the screen is placed at a location where the image is sharp on the screen, and this is denoted by S2 which is 61.10 0.20 cm. The image distance is then found by S2 L2, which is 10.10 cm. Using the formula , the focal length is calculated to be 5.02 cm. The percentage error between the expected value of 5.00 cm and the calculated value is 0.50%.In the last part, the lens with a focal length of 10.00 cm is used. The lens is placed at a position of 7.00 cm from the object, and using the equation, the distance of the image is calculated. Since there is no image on the screen on the other side of the lens, it is a virtual image and is formed on the same side as the object, and therefore gives a negative value of -23.33 cm. Using the ration of distance of the image and the object, the magnification is found to be 3.33 and the image location is found to be -17.33 cm. Upon verification, we see that the image is indeed approximately 3 times bigger than the object.

ConclusionIn the first part, we see that when a lens with the focal length of 10 cm is used, we calculate the focal length experimentally to be 10.24 cm with an uncertainty of 5.32%, which is very close to the given value. Also the measured magnification and the calculated magnification only have an uncertainty of 2.39%.When a lens with the focal length of 5cm is used, the percentage difference between the calculated value and the actual value is only 0.50 %.When the virtual image in the last part is viewed, it is seen that it is indeed about 3 times magnified.Data