牛顿环实验报告(英文版)

1、Newtons Rings(Caution: the report still have some mistakes inevitably.)1. Purpose of the experimenta) Applying Newtons rings to observe the phenomenon of equal thickness interference with reflected light and transmitted light respectively, then analyze the physical principles.b) Get familiar with im

2、age processing and learn to use software concerned, such as Image J and Visio.c) Analyze reasons for different patterns resulted from different light sources.2. Apparatusa) Sodium lamp (with a central wavelength of 589.3nm)b) Other illuminant (purple, white and red leaser)c) Newtons ringsd) Imaging

3、lense) Frosted glass screenf) Camera (CCD)g) Rulers used for calibration (smallest tick interval is 0.1mm)h) Computer3. Principles of the experimenta) BackgroundNewtons rings is named after Isaac Newton, who first studied them in 1717. When viewed with monochromatic light, Newton's rin

4、gs appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. When viewed with white light, it forms a concentric-ring pattern of rainbow colors, because the different wavelengths of light interfere at different thicknesse

5、s of the air layer between the surfaces.b) Principle of Newtons ringsNewtons ring is composed of a segment of large-radius convex lens with its convex side to a glass plane (Fig.3.b.(a). The light source is usually monochromatic light. Because of the gap between the plane lens and the convex lens, t

6、he reflected ray and the incident ray will have optical path difference. As a result the two rays will interfere with each other. The whole process is called equal thickness interference, which is one type of film interference. When two beams interfere with each other, there will

7、 be a superposition of waves due to the characterization of light waves. If the optical path difference s is integral multiple of the wavelength , i.e., the superposition will cause the maximum amplitude and result in the brightest region of the image on the screen. On the other hand, if t

8、he optical path difference s is integer and a half multiple of the wavelength, the two beams will counteract each other and result in the dark region of the image on the screen (Fig.3.b.(b). The air film between the convex lens and glass plane is curved instead of uniform, so the rings on

9、the pattern is not uniformly distributed. Further, we apply sodium lamp for the expand surface light source. The advantage is that there are numerous wave vectors and the interference area is small, thus the interference will be localized. Fig.3.b. (a) The structure of a Newtons ring (b) The pattern

10、 of Newtons rings c) Half-wave lossWhen a wave transfers from wave thinner medium to a wave denser medium and reflected back, the reflected wave has the vibrating direction half period later than the incident wave. Such phenomenon is called half-wave loss. d) The meaning of the patter

11、nFrom (b) we can see, the two beams causing one bright ring have the optical path difference where d is the thickness of the air film. For dark rings, . Considering the half-wave loss when the beam reflect on the glass plane, to dark rings we haveThe thickness of the air film between the g

12、lass plane and the convex lens as shown in Fig.3.b. (a) can be calculated From (1) and (2) we haveEquation (3) is the main equation for the data analysis below.If pressure is applied to the contact point of the lens and the glass plane, a small distortion d0 should be introduced as correction into e

13、xpression(2), givingd=r2/2R-d0 ( r2>=2R-d0 ).(4)For dark fringes, expression (3) becomesr2=kR+2Rd0.(5) k=0, 1 ,2 ,3Similar analysis can be applied to the Newtons rings in transmitted light, which has a bright central spot. For the bright fringes in transmitted light, r2=kR.(6)k=0, 1 ,2 ,3(bright

14、fringes)Expression (3) and (6) indicate that the radius of the dark Newtons rings in reflected light equals to the radius of the bright Newtons rings in transmitted light, which means these two sets of interference pattern are complementary. The visibility of the fringes in reflected light is differ

15、ent from that in transmitted light. The amplitude reflection coefficient is r when the light travels from the air to the glass, and the amplitude transmission coefficient is t. According to Stokes relations, the amplitude reflection coefficient is r when the light travels from the glass to the air,

16、and the amplitude transmission coefficient is t, which satisfies tt+r2=1. The visibility V is defined as V=(Imax-Imin)/(Imax+Imin), in which Imax and Imin are the maximum and minimum light intensity respectively in the interference pattern. From simple calculation we can get Expression (7) indicates

17、 that the visibility is related to r. In our experiment, the refraction index of the air and the glass is respectively n1=1.0, n2=1.55, giving r=(n2-n1)/(n2+n1)=0.22. Use this value of r in (7), we get Vtran approximately 10 percent, and Vref approximately 100 percent. Therefore in this experiment w

18、e use the image of Newtons rings in reflected light to measure the radius of curvature R of the plano-convex lens.e) Point to Point imaging and image enlargementThe Newtons rings are generally too small for direct observation and measurements, hence usually reading microscope is applied to observe a

19、nd measure them. When illuminated with expanded plane light source, the Newtons rings are localized interference pattern of equal thickness, so we can consider the fringes as the object, and use lens to get its image on the screen, which can be image sensor on the camera. The photosensitive surface

20、of this image sensor is usually called the target surface. There is a variety of working mechanisms of this kind of sensor. One of the most commonly applied image sensors is CMOS image sensor.Usually the target surface is the integration of hundred thousands or millions of photoelectric sensors. Eac

21、h photoelectric sensor is named as a pixel, and its function is to translate the light intensity its area into electric signals. These signals are translated by electric circuits into digital coding, transferred to the computer, and then point-to-point displayed by certain software. Point-to point m

22、eans that one pixel on the target surface corresponds to one pixel on the computer screen where the processed image is displayed. This widely applied method makes observation and precise measurement convenient, but it does not enhance the resolution of the image, which depends primarily on the ampli

23、fication coefficient of the optical system, the quality of the image and the pixel density on the target surface.When we take a photograph, large aperture size, which gives lower depth of focus, can be used to achieve blurring at the adjacent area of the image surface and highlight on the object. Th

24、erefore during the experiment we should adjust the aperture carefully to a proper size that improves the image quality.f) The reduction of the random noise of the imageAccording to the theoretical background about the Newtons rings discussed earlier in this section, while the visibility of the fring

25、es in reflected light is high, the light intensity on the target surface would be weak since the beams are transmitted backwards from the device, resulting in strong influence on the image from the background noise of the sensor. If we observe carefully we would find small randomly moving or twinkli

26、ng spots on the displayed image, called the random noise of the image. It appears randomly, which allows us to reduce it through performing arithmetic average over time, which is, taking multiple photos when all the experimental conditions are kept unchanged, and calculating point-to-point arithmeti

27、c mean of these photos, which gives a higher quality image. g) Calibration and measurementsBecause of the inevitable frequent adjustments to the optical path, it is hard to keep the optical elements at fixed positions, rendering it difficult to directly calculate the magnification coefficient. If we

28、 use a ruler with known scale length in the place of the object, we can get the magnification coefficient through their comparison. This method is named as the calibration of the system. In this way, the measurement of the pixels can substitute for the measurement of the geometric size of the object

29、. Facilitated by the computer, images of objects with complex geometry can be processed through this way. 4. Procedure of the experimenta) Observe and record Newtons rings in transmitted lighti. Use your eyes to observe Newtons rings in reflected and transmitted white light. Pay specific attention t

30、o the pattern of the 0th order ring and the size of the rings. If it is not in the center of the device, then further adjustments are required. Estimate the ratio between the image distance and the object distance from the size of the rings and the size of the target surface of the camera.1.Sodium l

31、amp; 2.lens; 3.Newtons ring; 4.lens; 5.CCD; puter systemFig.4 the optical path diagram of the experimentii. Arrange the optical elements for observation of the fringes in transmitted light according to the optical path diagram illustrated in Fig.4. Adjust the aperture size of the imaging lens to the

32、 largest value.iii. Adjust the optical elements to concentric and equal-altitude position. First, draw the optical elements close to roughly adjust them to be concentric and on the same altitude. Then adjust them until they meet this requirement precisely, using the method the small image followed b

33、y the large image.iv. Adjust the ratio between the image distance and the object distance to get sharp image with proper size and with a bright 0th order spot. Adjust this ratio so that the 3rd to 10th ring area is the sharpest. v. Adjust the aperture of the imaging lens, and observe the resolution

34、change of the whole image of Newtons rings. Adjust it so that the panorama view of the rings is the sharpest, and prevent the saturation of brightness in the brightest area.vi. Fix the position of the device of Newtons rings, the lens and the camera, and adjust the parameters in the video software.

35、Record after satisfactory image quality is achieved. More detailed procedure of this step is available in The Newtons rings experiment software users Manual. b) Observe and record Newtons rings in reflected lighti. Keep the image distance and the object distance constant. Arrange the optical path fo

36、r the observation of the fringes in reflected light as illustrated in Fig.4. Add a plate-glass between the Newtons rings and the lens, and adjust the angle between the optical axis and the plate-glass to be approximately 45°. Move the sodium lamp so that the light illuminates the plate-glass an

37、d reflects vertically to travel to the Newtons rings. Newtons rings in reflected light with a dark 0th order spot should appear on the computer screen. In the mean time, adjust the position of the device to make the 0th order spot center the image. ii. Turn the aperture size to the largest value, an

38、d adjust the position of the Newtons rings device precisely to acquire sharpest image in the 3rd to 10th ring area. After that, adjust the aperture size to proper value.iii. Adjust the parameters in the video software to get satisfactory image quality. Due to the low intensity of the reflected light

39、, the image noise will be bigger in this step. Therefore keep the recording conditions unchanged, and take 10 photographs, or record a video that lasts approximately 5 seconds. c) Record the image for calibrationi. Since the ticks on the ruler is not transparent, the image of the fringes in transmit

40、ted light will have better quality than that in reflected light. Keep the image distance constant, move away the Newtons rings and the plate-glass, and put the ruler on the object plane.ii. Turn the aperture size to the largest value. Move the ruler back and forth, and fix its position precisely. Th

41、en adjust the aperture size again to get sharp image. In the mean time, the amplification of the entire optical path should be the same as when the Newtons rings are recorded. Record the image of the ruler.d) Newtons rings in polychromatic lightUse the tricolored LED light as the light source to rec

42、ord the fringes in reflected light. The monochromatic light can be chosen as R, G and B, and bi-chromatic light can be chosen as R-G, G-B, G-B or R-G-B. White LED light or the work lamp can be used as the light source in the recording as well.i. Compare the regions in which the interference orders a

43、re sharp when the sodium lamp and the three kinds of LED monochrome are used as the light source respectively.ii. Interpret the change of the interference orders in the bi-chromatic light.5. Dataa) Sodium lightThe wave length of the sodium light is 589.0 nm and 589.6 nm, and we choose the mean wavel

44、ength 589.3 nm, the reason of which will be illustrated in discussion. With transmission-type method (Fig.5.(a).1), the figure we attain is not very clear for further analysis. Fig.5.(a).1.The pattern attained by transmission-type methodSo we apply the reflection-type method (Fig.5.(a).2)Fig5.(a).2.

45、The pattern attained by reflection-type methodAfter processed by Visio we can have the radius of each ring (Fig.5.(a).3).Fig5.(a).3.The image after processThe diameters of the 10th to 24th rings are shown in the table below:198.624 207.136 214.505 221.953 229.067 236.191 243.390 250.263 256.734 263.

46、038 269.310 275.220 281.395 287.487 293.188 Then we process the image of ruler (Fig.5.(a).4)Fig.5.(a).4.The processed image of the rulerFrom the figure we can get the distance between 2mm is 80.71 units.b) Purple lightWe apply the reflection-type method (Fig.5.(b).1)Fig.5.(b).1.The pattern attained

47、by reflection-type method after processBecause the rings far from the center is not clear enough for analysis, we choose 4th to 13th rings, whose diameters are shown in the table below:67.93373.72879.45784.4889.48594.00398.184102.435106.323109.954Then we process the image of ruler (Fig.5.(b).2)Fig.5

48、.(b).2.The processed image of the rulerFrom the figure we can get the distance between 2mm is 91.50 units.c) Red light We apply the reflection-type method (Fig.5.(c).1)Fig.5.(c).1.The pattern attained by reflection-type method after processThe diameters of the 1st to 10th rings are shown in the tabl

49、e below:51.10763.60674.26883.61591.93999.929105.812112.067118.216123.177Then we process the image of ruler (Fig.5.(c).2)Fig.5.(c).2.The processed image of the rulerFrom the figure we can get the distance between 2mm is 91.04 units.d) White lightFor white light is not monochromatic light, so we just

50、choose two kinds of colors - purple and yellow, then we apply the reflection-type method (Fig.5.(d).1&2)Fig.5.(d).1.The pattern of purple rings attained by reflection-type method after processFig.5.(d).2.The pattern of yellow rings attained by reflection-type method after processThe diameters of

51、 the 1st to 4th rings are shown in the table below:purplek1234D48.51759.61968.04676.55yellowk1234D43.12955.25164.88973.205Then we process the image of ruler (Fig.5.(d).2)Fig.5.(d).2.The processed image of the rulerFrom the figure we can get the distance between 2mm is 55.44 units.6. Data analysisa)

52、Sodium light:The data concerned is shown in the table below.k11121314151617k(mm)0.0070740.00766350.0082530.00884250.0094320.01002150.010611r(mm)2.46096 2.56642 2.65773 2.75001 2.83815 2.92642 3.01561 r2(mm2)6.05632 6.58653 7.06350 7.56253 8.05509 8.56391 9.09391 18192021222324250.01120050.011790.012

53、37950.0129690.01355850.0141480.01473750.0153273.10077 3.18094 3.25905 3.33676 3.40999 3.48649 3.56197 3.63261 9.61476 10.1184 10.6214 11.1340 11.6280 12.1556 12.6877 13.1959 Then we can apply Origin to draw the figure of d2 and kWe can learn from the figure that the radius of the convex lens is We a

54、lso apply MATLAB to analyze the data, the result is shown below and the code is attached in the appendix. We can see the result is The difference is because the Origin result is the slope of the d2-k, while the MATLAB result is the radius calculated respectively. We think the latter is more precise

55、and apply the result afterwards. b) Purple lightThe data concerned is shown in the table below.k45678910111213kR(mm)3431.64289.55147.46005.36863.27721.185799436.910295 11153 r(mm)1.4849 1.6115 1.7368 1.8466 1.9560 2.0547 2.1461 2.2390 2.3240 2.4034 r2(mm2)2.2049 2.5971 3.0164 3.4098 3.8258 4.2218 4.

56、6057 5.0132 5.4010 5.7762 Then we can apply Origin to draw the figure of d2 and kRWe can conclude from the figure that the slope is the wavelengthc) Red lightThe data concerned is shown in the table below.k12345678910kR(mm)857.91715.82573.73431.64289.55147.46005.36863.27721.18579r(mm)1.1227 1.3973 1

57、.6315 1.8369 2.0197 2.1953 2.3245 2.4619 2.5970 2.7060 r2(mm2)1.2605 1.9525 2.6619 3.3741 4.0794 4.8192 5.4034 6.0611 6.7445 7.3224 Then we can apply Origin to draw the figure of d2 and kRWe can conclude from the figure that the slope is the wavelengthd) White light Because there are only 4 sets of data, we choose MATLAB to analyze th