Starlight is refracted by air as it passes through the Earth's atmosphere. Smaller than the apparent size of stars as seen from the Earth's surface. Why did it take over 200 years for someone to measure the parallax to another star? Astronomers had been looking through telescopes since the time of Galileo, in the early 1600s. The relationships between these units depend on the fact that there is a simple linear relationship between a tiny parallax angle, in ANY units, and the tangent of that angle.Īctually, 1838 isn't all that long ago. Why am I belaboring this point? Because astronomers have chosen a set of units for parallax calculations which look strange, but turn out to simplify the actual work. Take a look for yourself: Table 2 angle (degrees) As usual, make estimates of the range (uncertainty) of your length measurements, convert them to percentages, employ the weakest link protocol, and see if the two experiments agree.\tan(\pi)\]Īnd, in general, there is a linear relationship between the tiny angle π and its tangent, regardless of the units.For both ray-trace-with-nails portions, include a photo of the traces you created in your lab report.Please don't put the sharp side of the nail against the block when doing the parallax location – scratching the surface of the block makes it less usable for future optics experiments.Use it as a confirmation of two other rays. You get the center-line ray trace (the one that passes straight through the block undeflected) "for free".Percentage uncertainties are reduced when the object & image lengths are longer.For the image of the flat refractor portion:.There are two places where the light bends – you can use this extra data to potentially improve (or at least confirm) your result.Remember that \(\theta\) is measured with the normal to the surface.Moving your eye farther away should also help a bit. It may help to look to the left and right of this nail, to see if the perspective with the other nails is symmetric. The last nail you place looks "fatter" than the previous nails due to perspective (it is closer to your eye), and the fact that it obscures those nails can make it difficult to align it accurately.Keep in mind that two nails are needed for any straight line you need to draw.Please use a piece of paper, and not the styrofoam pad for drawing the rays.When using the nails to trace the path of the light:.You will want to trace out the border of the block on the paper, both to make the later work easier, and so that you know where to place the block in the event that it moves off its original position while you are in the middle of taking data.Find the image location using the parallax method (trial-and-error with another nail that you can move around).Find the image location using the nails-in-the-path-of-the-light from two different eye perspectives.In both cases, the object (a nail) is placed in contact with one side of the block, so that the light only really bends at one block/air interface. The next two methods involve finding the location of an image created when looking at an object through the block, and using the known image & object distances (and the appropriate equation) to compute the index of refraction.With a trace of a ray, the angles that the light bends at the two surfaces can be measured, and from that data (and the fact that the index of refraction of air is 1.0) one can use Snell's law to compute \(n\) for the block. Use the nails-placed-along-the-line-of-sight approach to trace the path that the light takes from the object to your eye (through the block, of course).In Part 1, you will experimentally determine the index of refraction of a transparent block, using three separate methods:
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