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course PHY 202
I think I am a little confused about how many steps there are and which indexes of refraction I should be using. Should I think about the index of refraction of the glass cylinder as well as the water and the air? I think I understand how snell's law works, but I am confused about this specific situation. Do you have to calculate 4 separate angles of refraction?
This experiment uses a cylindrical container and two lamps or other compact light sources. Fill a cylindrical container with water. The cylindrical section of a soft-drink bottle will suffice. The larger the bottle the better (e.g., a 2-liter bottle is preferable to a 20-oz bottle) but any size will suffice.
Position two lamps with bare bulbs (i.e., without the lampshades) about a foot apart and 10 feet or more from the container, with the container at the same height as the lamps. The line separating the two bulbs should be perpendicular to the line from one of the bulbs to the cylindrical container. The room should not be brightly lit by anything other than the two bulbs (e.g., don't do this in front of a picture window on a bright day).
The direction of the light from the bulbs changes as it passes into, then out of, the container in such a way that at a certain distance behind the container the light focuses. When the light focuses the images of the two bulbs will appear on a vertical screen behind the cylinder as distinct vertical lines. At the focal point the images will be sharpest and most distinct.
Using a book, a CD case or any flat container measure the distance behind the cylinder at which the sharpest image forms. Measure also the radius of the cylinder.
As explained in Index of Refraction using a Liquid and also in Class Notes #18, find the index of refraction of water.
Then using a ray-tracing analysis, as describe in Class Notes, answer the following:
1. If a ray of light parallel to the central ray strikes the cylinder at a distance equal to 1/4 of the cylinder's radius then what is its angle of incidence on the cylinder?
20cm diameter: 10cm radius
24cm distance to image on screen
305cm from lens to source
¼ of radius = 2.5cm
Tan(theta)=2.5/305
Angle of incidence = 0.00014293927
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It doesn't matter how far the object is from the lens, the angle of incidence of a ray parallel to the central ray which strikes at 1/4 of the cylinder's radius from the central ray will be the same.
The angle of incidence will be the angle between the incoming ray and a radial line from the center of the lens to the point of incidence (i.e., the point at which the ray strikes the lens).
What is this angle?
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2. For the index of refraction you obtained, what therefore will be the angle of refraction for this ray?
Using Snell’s Law and index of refraction for air and water:
Sin(angle of incidence)n_air=Sin(angle of refraction)n_water
Sin(.00014293927)1.00029=Sin(angle of refraction)1.33
Angle of refraction = 1.87622931 × 10-5 degrees
3. If this refracted ray continued far enough along a straight-line path then how far from the 'front' of the lens would it be when it crossed the central ray?
140,000 cm
4. How far from the 'front' of the lens did the sharpest image form?
From what I measure: 24 cm…
5. Should the answer to #3 be greater than, equal to or less than the answer to #4 and why?
These should be equal to one another because it is the distance to the focal point behind the lens.
6. How far is the actual refracted ray from the central ray when it strikes the 'back' of the lens? What is its angle of incidence at that point? What therefore is its angle of refraction?
My answer does not seem consistent with striking the back of the glass. Can you help me figure out where I have gone wrong???
7. At what angle with the central ray does the refracted ray therefore emerge from the 'back' of the lens?
8. How far from the 'back' of the lens will the refracted ray therefore be when it crosses the central ray?
It “should” be the same as the distance from the original object to the lens. So, 305cm.
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You used the wrong triangle to answer the first question.
See my note and please revise accordingly.
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