O Lab O Snells Law and the Index of Refraction Introduction - Description

1 Lab O3 Snells Law and the Index of Refraction Introduction The bending of a light ray as it passes from air to water is determ ined by Snell s law This law also applies to the bending of light by lenses and to t ID: 26008 Download Pdf

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O Lab O Snells Law and the Index of Refraction Introduction

1 Lab O3 Snells Law and the Index of Refraction Introduction The bending of a light ray as it passes from air to water is determ ined by Snell s law This law also applies to the bending of light by lenses and to t

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O Lab O Snells Law and the Index of Refraction Introduction

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O3.1 Lab O3: Snell's Law and the Index of Refraction Introduction. The bending of a light ray as it passes from air to water is determ ined by Snell' s law. This law also applies to the bending of light by lenses and to the guiding of light by the fiber optic cables that carry m odern com unications signals. In part 1 of this lab you will investigate the bending of light as it travels from air to plastic and plastic to air. Your data will illustrate Snell' s law. In part 2, you will find that the speed of light in plastic varies slightly with the wavelength. The speed of light

in a vacuum is c = 3.00 x 10 m s. Because of a com lex interaction between an electrom gnetic wave (light) and the charges in tter(electrons and protons), a light signal travels re slowly in transparent m terials, such as glass or water, than in vacuum . The ratio of c, the speed of light in a vacuum , to v, the speed of light in a m dium , is called the index of refraction, n, of the dium medium vacuum CF 1.461 diam (1) . Note that n 1, always. In m st applications, the index of refraction of air can be taken to be one, with negligible error. A ray of light passing from one m dium to another

(say, from air to water) is bent or refracted from its original path according to Snell' s Law, which states medium 1, n medium 2, n interface between two media normal to surface (2) 11 sin in , where n and n are the indices of refraction in m dium 1 and m dium 2, and the angles are m asured with respect to the norm l (the perpendicular) to the interface. The light is always bent m re toward the norm l in the m terial with the larger n, and, in the diagram to the left, we have drawn the angles for the case . Note that if the ray strikes the interface perpendicularly, at an angle of = 0 , then

it is not refracted and exits perpendicularly with = . Although Snell' s Law can be proven from fundam ntal principles, we will consider it to be an experim ntal fact and use it to determ ine the index of refraction of Lucite (a transparent plastic). Fall 2004
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O3.2 Consider a ray of light passing from air (n air = 1) into another m dium such as Lucite with an index of refraction n (n >1). In this case, the ray is incom ng (incident) on the air side and outgoing (refracted) on the Lucite side of the interface, and we have (3) sin in TT ir , n sin si (air Lucite) where and are

the angles of the incident and refracted rays, respectively. Suppose now a ray of light passes from a m dium (Lucite) with index of refraction n > 1 into air . W then have (4) ir sin in TT , si sin (Lucite air) In the two cases just considered, if instead of labeling the angles as and , we label the angles ( in air) and ( in Lucite plastic), then both form ulas (3) and (4) becom (5) sin si . The index of refraction is, in general, a function of the wavelength of the light. It turns out that n is sm aller for long wavelength (red) light and larger for short wavelength (blue) light. That is,

blue light is bent m re by glass or plastic lenses and red light is bent less. This is the cause of chrom tic aberration in sim le lenses. Multi-elem ent lenses which correct for chrom tic aberration are called achrom ts and are rather expensive. wavlength, red violet This spread in the values of n, or dispersion , is the cause of the rainbow of colors produced by a prism This effect was first studied quantitatively by Isaac Newton when he was still a student. red violet yellow white monochromatic The colors of the spectrum in order from longest to shortest wavelength are: red, orange, yellow,

green, blue, violet. Procedure In this lab, using a sem circular Lucite lens, we will m easure the angles and as a ray of light passes between the flat side of the Lucite and air. The angles are easily m easured because the lens sits Fall 2004
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O3.3 at the center of a circular platform with an angle scale along its perim ter. A ray of light, defined by a slit on the side of the platform , passes through the lens and the angles and are read by noting where the shaf t of light touches the angle scale. The apparatus is shown below. The lam and the slit are fixed in position, while

the lens and the platform with the angle scale can be rotated with a handle under the platform . lamp slit lucite lens angle scale normal 90 90 View from above Note that refraction of the light ray takes place only on the flat side of the sem -circular lens. On the circular side, the ray strikes the interface exactly norm l to the surface and there is no refraction. that is the angle on the air side of the flat interface and is the angle of the plastic side of the interface. So if the flat side is facing the slit, is the incident angle, but if the curved side is f acing the slit, then is the

incident angle. Bef re taking m easurem ents, it is crucial that the lam and the lens be caref ully positioned with respect to the angle scale platform . Unless the alignm ent is perfect, your data will have system atic errors. The alignm ent procedure is as follows: 1. Begin by adjusting the lam to give a good parallel beam . Point the lam at a distant wall (at least 30 feet away) and observe the im age of the light bulb fila nt. Slide the bulb back and forth slightly, with the knob on the underside of the lam , to get a sharp im age of the filam nt on the distant wall. Adjust the orientation

of the lam to m ke the im age of the f ilam nt vertical (so that m xim light passes through the vertical slit on the platform ). Fall 2004
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O3.4 filament lens lamp 2. Rem ove the Lucite lens f om the platf rm and then position the lam and rotate the platf rm so that a fine, sharp shaft of light is seen entering at 0 , passing over the exact center of the platform , and exiting at 0 . You have to get the light slightly higher than the platform and angle it down slightly to get a bright shaft of light showing on the platform . 90 90 Fall 2004
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O3.5 3. Now place

the Lucite lens on the platform with the flat edge centered on the platform and perpendicular to the 0 line. Adjust the position of the lens slightly until the ray of light exits at 0 when it enters at 0 . Check that this occurs when both the f at side is toward the slit and when the platf rm is rotated 180 so that the rounded side is toward the slit. 90 90 4. As a further check of the alignm ent, rotate the platform to the 45 position and observe the reflected ray, which should also be at 45 . 90 90 45 45 reflected refracted incident Part 1. Index of Refraction of Lucite At last, you are

ready to take data. W ith the flat side toward the slit, take several m easurem ents of and for various ’s from 5 up to about 70 . Estim ate the angles to the nearest 0.1 . For each value of , take two m easurem ents of for both possible orientations of the lens, as shown below, and average your two values for . If your alignm ent is good, the two values should be very close, within a few tenths of a degree. Record both in your handwritten notes, but enter only the average into your Mathcad docum ent. Fall 2004
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O3.6 90 90 90 90 Now repeat all these m easurem ents, with the

circular side of the lens toward the slit. Take data for values of from 5 to about 40 , every 5 or so. W en is near 75 , which occurs when is near 40 , you will notice that the refracted beam is no longer a narrow beam of white light, but has broadened into a rainbow of colors. Use a white piece of paper as a screen to see this clearly. Use the position of the m ddle of the broadened light beam to determ ine . Now com ine all your data to m ke a single table of and . Flat side toward slit Curved side toward slit All data combined To m ke the new arrays with the com ined data, sim ly enter the

data again. You can avoid ch tedious typing by using copy and paste. Be sure that all the air side angles are in one colum and all the plastic side angles are in the other colum . Using all the data m ke a plot of vs. , with both angles in degrees. Now convert the angles from degrees to radians, and then m ke a plot of sin vs sin . [The default m ode of Mathcad assum s that angles are in radians when co puting sine and cosine.] The plot should be a straight line. Fall 2004
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O3.7 For each / pair, com pute sin( sin( , and graph n vs. . The index of refraction n should be a

constant, independent of ; however, for sm all , the fractional errors are large, and you will probably observe large deviations of n f om the average value n avg when is sm all. [The curve of n vs. should be flat, except for random fluctuations; if not, there is som system atic error, probably due to m salignm ent.] By exam ining the graph of n vs. , decide which sm all- values of n to throw out, and then use your “good” data to com pute the m ean of n, standard deviation, the standard deviation of the m ean. nn avg nn me ia VV Part 2. Dispersion of Lucite In this part, you will m easure n

red and n violet , the values of n at the extreme red and violet ends of the visible spectrum To do this, orient the platf rm so the circular side of the lens is f acing the slit, and then adjust the angle so that the refracted beam is close enough to 90 o to give a good spectrum of colors, but not so close that som of the colors are lost to internal reflection. Make m easurem ents of the angles of the refracted beam at the red and violet edges of the spectrum red and , as well as . Com pute viole incident red red vi ol vi olet si n( si n( sin( sin( . Make m easurem ents at 2 or 3 slightly

different inci dent angles and repeat each m easurem ent for the two orientations of the lens. You now have three values of n for three different wavelengths: n avg in the m ddle of the visible spectrum (yellow , n red , and n violet . Look at the spectrum chart on the wall to estim ate the wavelengths of the red, yellow, and violet light. Make a pl ot of n vs. wavelength with your three points. PreLab Questions: 1. at is Snell’s Law? Your answer should include a diagram 2. A ray of light in air strikes the surface of a pool of water at an angle of 30 f om the norm l. W at is the angle (m

easured from the norm l) of the refracted ray in the water? 3. In this experim nt, why is there no refraction of the light ray on the circular side of the Lucite lens? Fall 2004 4. en a light ray passes from a m terial of higher n to a m terial of lower n (for instance, a light ray passing from glass to air), the refracted angle is larger than the incident angle. In this case, the angle of
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O3.8 the incident ray can exceed a critical angle , at which the angle of the refracted ray is 90 . For incident angles greater than the critical angle, there is no re fracted ray, only a

reflected ray. This phenom enon is called total internal ref ection. W at is the critical angle f r w ter w ith n = 1.33? W at is the critical angle for glass n = 1.50? 5. Show with a sketch what the graph of sin( ) vs. sin( ) for Lucite should look like (for a given fixed wavelength ). Your sketch should show the shape of the curve (linear, parabolic, etc.) as well as indicate whether the curve goes through the origin. W at can you say about the slope of this curve? 6. Suppose you m easured n vs. using a red light source and a blue light source. On the sam graph, sketch both n red vs. and n

blue vs. , where n red is the index m easured with red light and n blue is the index m easured w ith blue light. (Q ualitative sketch only! N num bers.) 7. at does a graph of n vs. wavelength look like for glass or plastic? 8. en the curved side of the lens is tow rd the slit, w ich angle is W ich angle is ? Indicate your answers with a diagram 9. If a piece of clear glass with an index of refraction n is placed in a clear liquid with the sam index of refraction n, the glass becom s com letely invisible. W hy? n's different n's identical glass tube glass of liquid 10. W en a light ray passes

from air through the Lucite sem -circular lens and back into air the ray path appears as shown below, with > . Suppose that a Lucite lens with n = 1.55 is subm erged in a clear liquid with n liq =1.70, so the ray path is now liquid Lucite liquid, and the angle should now be labeled liq . Is greater than, less than, or equal to liq Suppose liq = 20 , what is Fall 2004