How to write the report of college physics experiment (measuring lens curvature radius with Newton ring)

Measurement of lens curvature radius with Newton's ring

The interference of light is a manifestation of the fluctuation of light. If the light emitted by the same point light source is divided into two beams and meet again after passing through different paths, interference will generally occur when the optical path difference is less than the coherent length of the light source. Interference phenomenon is widely used in scientific research and industrial technology, such as measuring the wavelength of light waves, accurately measuring the length, thickness and angle, testing the surface smoothness of samples, studying the distribution of internal stress in mechanical parts and measuring the thickness of oxide layer on silicon wafers in semiconductor technology. Newton ring and optical wedge are very typical examples, which belong to the interference phenomenon produced by amplitude segmentation method and are also typical equal thickness interference fringes.

Experimental purpose

1. Observe and study the phenomenon and characteristics of equal thickness interference.

2. Learn to measure the curvature radius and film thickness of plano-convex lens by equal thickness interferometry.

3. Skillfully use the reading microscope.

4. Learn the method of processing experimental data by step-by-step difference method.

Laboratory instrument

Measuring microscope, sodium light source, Newton ring instrument, Newton ring and wedge device.

Figure 1 Physical Diagram of Experimental Instrument

Experimental principle

Newton's ring is a kind of equal thickness interference phenomenon realized by fractional amplitude method, which was first discovered by Newton. In order to study the color of the film, Newton carefully studied the experimental device composed of convex lens and plane glass. His most valuable achievement is that by measuring the radius of concentric circles, the thickness of air layer at the corresponding position between convex lens and plane glass plate can be calculated. The air layer thickness corresponding to bright rings is proportional to 1, 3,5 …, and the air layer thickness corresponding to dark rings is proportional to 0,2,4 …. However, he failed to explain it correctly because he advocated the particle theory of light (the interference of light is a manifestation of light fluctuation). Until the beginning of19th century, Thomas Young explained Newton's ring phenomenon with the interference principle of light, and calculated the corresponding wavelengths and frequencies of light waves of different colors with reference to Newton's measurement results.

Newton's ring device consists of a plano-convex lens with a large radius of curvature, and its convex surface is placed on an optical glass plate (flat crystal), as shown in Figure 2. An air film is formed between the convex surface of the plano-convex lens and the glass plate, and its thickness gradually increases from the central contact point to the edge. If parallel monochromatic light shines vertically on Newton's ring, there will be optical path difference between the two beams reflected from the upper and lower surfaces of the air layer, and interference will occur when they meet on the convex surface of the plano-convex lens. Its interference pattern is a series of concentric rings with alternating light and shade centered on the glass contact point (as shown in Figure 3), which is called Newton's ring. Because the thickness of air layer is the same everywhere on the same interference ring, it is called equal thickness interference.

Fig. 2 Newton ring device fig. 3 interference ring

The optical path difference between two coherent beams corresponding to horizontal stripes is

( 1)

Is the air film thickness corresponding to the first-order stripes; Half wave loss.

According to the interference condition, when = (2k+ 1) (k = 0, 1, 2,3, ...), the interference fringe is dark, that is.

get

(2)

Let the radius of curvature of the lens be r, and the thickness of the air layer at r from the contact point O be d, which can be obtained from the geometric relationship shown in Figure 2.

D2 can be omitted because of R>& gtd.

(3)

According to equations (23-2) and (23-3), the radius of the K-class dark ring is:

(4)

According to formula (4), if the wavelength of monochromatic light source is known, the curvature radius r of plano-convex lens can be calculated only by measuring the radius rm of the first dark ring; On the other hand, if r is known, the wavelength of the incident monochromatic light wave can be calculated after measuring rm. However, because the convex surface of the plano-convex lens and the plane of the optical flat glass can not be in ideal point contact; Contact pressure will cause local elastic deformation, making the contact point a circular plane and the center of the interference ring a dark spot; Or the existence of dust in the air gap layer makes an optical path difference added to the dark ring formula, assuming that the additional thickness is (a0, A) when there is dust.

Through the dark stripe condition

get

Replace (4) with the above formula.

The above formula cannot be measured directly, but it can be eliminated by taking the square difference of the radii of two dark rings, such as removing the first ring and the second ring, and the corresponding radii are

You can get the subtraction of two expressions.

So the radius of curvature of the lens is

(5)

Because the center of the dark ring is not easy to determine, the diameter of the dark ring is calculated.

(6)

As can be seen from the above formula, as long as the values of Dm and Dn (the diameters of the m-th and n-th dark rings respectively) are measured, R or can be calculated.

Divide the tip equally.

When two optical flat glasses are stacked together and one end is padded with a sheet (or filament) to be tested, an air wedge is formed between the two glass plates. When illuminated vertically with monochromatic light, like Newton's rings, two coherent beams reflected from the upper and lower surfaces of the air wedge interfere with each other. The interference fringes are a cluster of parallel light and dark fringes with equal spacing and width, which are parallel to the intersection line of two glass plates (that is, the edge of the wedge), as shown in Figure 4.

Fig. 4 air wedge interference

Through the dark stripe condition

(=0, 1,2,...)

It can be obtained that the thickness of the air wedge corresponding to the first-order dark line is

The thickness of air wedge corresponding to+1 dark texture is

Subtract these two expressions.

The above formula shows that the thickness difference of air wedge corresponding to any two adjacent interference fringes is. It can also be concluded that the thickness difference of the air wedge corresponding to two interference fringes separated by fringes is

According to the geometric similarity condition, the thickness of the plate to be measured can be obtained as follows

Among them, the distance between the intersection line of two glass plates and the edge of the glass plate to be measured (that is, the effective length of the wedge tip) and the distance between stripes can be measured by a reading microscope.

Introduction of experimental instruments

1. Reading microscope

As shown in fig. 5, the main parts of the reading microscope are the microscope for magnifying the object to be measured and the main ruler and auxiliary ruler for reading. Rotating the micrometer handwheel can move the microscope left and right. Microscope consists of objective lens, eyepiece and crosshair. When in use, the measured object is placed on the workbench and fixed by tabletting. Adjust the eyepiece to adjust the visibility to make the fork wire clear. Turn the focusing handwheel and observe from the eyepiece to make the image of the measured object clear. Adjust the measured object so that the transverse plane of the measured part is parallel to the moving direction of the microscope. Turn the micrometer handwheel so that the longitudinal line of the crosshair is aligned with the starting point of the measured object, and take a reading (the reading is the sum of the readings of the main ruler and the micrometer handwheel). The reading ruler is marked with a line of 0-50mm, and the value of each cell is 1mm, and the circumference of the reading cylinder is equally divided into 100 cells. Every time the drum rotates, the scale moves one grid, that is, 1mm, so the value of each grid on the drum is 0.01mm. In order to avoid the return error, one-way moving measurement should be adopted.

1 .eyepiece 2. Lock ring 3. Lock screw 4. Focus handwheel 5. Lens barrel holder 6. Goal 7. Spring pressure 8. Desktop glass 9. Turn the handwheel 10. Mirror 1 1. Cardinality 12. Changed hands 13.

2. Sodium light source

There are two layers of glass bulbs in the lamp tube, which contain a small amount of argon and sodium. When the filament is heated, argon emits lavender light, and sodium vaporizes after heating, gradually emitting two strong spectral lines, 589.0 and 589.3, which are usually called sodium double lines. Because the two spectral lines are very close, it can be considered as a good monochromatic light source in the experiment, and the average value of 589.3 is usually taken as the wavelength of monochromatic light source. Because of its high intensity and simple color, it is the most commonly used monochromatic light source.

Attention should be paid to when using sodium lamp:

(1) The sodium lamp must be used in series with the choke, otherwise it will burn out.

(2) After the lamp is ignited, it needs to wait for a period of time before it can be used normally (the ignition time is about 5-6).

(3) Every switch has an impact on the life of the lamp, so don't switch it easily. In addition, there is a certain consumption under normal use, and the service life is only 500. Be prepared and concentrate on using time.

(4) When the machine is turned on, it should be placed vertically, without impact or vibration. After use, it must be cooled before it can be shaken upside down, so as to avoid the flow of sodium metal and affect its performance.

Experimental contents and steps

1. Measure the curvature radius of plano-convex lens with Newton ring.

1. Place Newton's ring in the center of the ground glass of the reading microscope workbench, make the microscope barrel face the center of Newton's ring device, and light the sodium lamp to make it face the mirror of the reading microscope objective.

2. Adjust the reading microscope

(1) Adjust the eyepiece: make the reticle clearly visible on the reticle, and rotate the eyepiece to make the reticle parallel to the moving direction of the microscope barrel.

(2) Adjusting the mirror surface: the brightness is the largest in the field of view of the microscope, which basically meets the requirement that the incident light is perpendicular to the lens to be measured.

(3) Turn the handwheel 15: Move the lens barrel to the middle of the scale, and adjust the focusing handwheel 4 to make the objective lens close to the surface of Newton's ring device.

(4) Focusing the reading microscope: slowly rotate the focusing handwheel 4 to make the lens barrel move from bottom to top for focusing until Newton's ring interference fringes are clearly seen from the eyepiece field of view, and the error is ignored; Then move the Newton's ring device so that the intersection of the crosshairs in the eyepiece roughly coincides with the center of Newton's ring.

3. Observe the distribution characteristics of stripes. Whether the thickness of stripes at all levels is consistent and the spacing of stripes is the same, and explain. Observe whether the center of Newton's ring is bright or dark. If it is bright, how do you explain it?

4. Measure the diameter of the dark ring. Rotate the reading cylinder of the reading microscope and observe in the eyepiece at the same time, so that the crosshair moves slowly from the center of Newton's ring to the 23rd ring and then back to the 22nd ring, and moves the crosshair unidirectionally from the 22nd ring, and records the corresponding reading every time it moves to the 13 ring, and then records it from the 10 ring on the same side to the 1 ring; Through the central dark spot, from the number of 1 rings on the other side to 10 rings, and then from 13 rings to the 22nd ring. And record the measured data in the data table.

Second, use a wedge to measure the thickness of the sheet.

1. Remove Newton's ring from the reading microscope workbench and replace it with a wedge, so that the intersection of two glass sheets and the edge of the sheet are within the measurable area.

2. Focusing microscope, clear interference fringes can be seen from the eyepiece. If the interference fringe is not parallel to the intersection line of two glass plates, it may be that the compression screw is not tight enough or there is dust on the plates. Adjust the tightness of the compression screw or clean the thin slice properly, so that the interference fringe is parallel to the intersection line of two pieces of glass.

3. Adjust the position of the splitting tip on the workbench so that the interference fringe is parallel to the longitudinal line of the crosshair.

4. Turn the drum 15, move the lens barrel to one end of the scale and then reverse it, and measure the effective L of the wedge tip (that is, the distance from the intersection of two pieces of glass to the edge of the plate).

5. Where the middle stripe of the wedge is clear, count from the first dark stripe, and then count every five dark stripes, and record the reading of 12, and record it in the self-made data table. Processing data by difference method.

Matters needing attention

1. The optical surfaces of Newton's ring instrument, optical wedge, lens and microscope are not clean, so gently wipe them with special mirror cleaning paper.

2. The micrometer drum of the reading microscope can only rotate in one direction during each measurement, and cannot be reversed in the middle.

3. When focusing the measured object with the lens barrel, in order to prevent the microscope objective from being damaged, the correct adjustment method is to move the lens barrel away from the measured object (that is, lift the lens barrel).

Data recording and processing

I. Data processing

According to the calculation formula, yes, measure n times respectively, then you can get n Ri values, so there are, we want to get the measurement results. The following will briefly introduce the calculation of. According to the definition of uncertainty

Where is component a

The b component is (the b component of a single measurement)

The measurement accuracy can be obtained from the reading mechanism of the microscope (mm).

So there is

Second, the data record table

1. Measure the radius of curvature of lens with Newton ring.

Packet I 1 23455 6789 10

Grade number mi 222120191716151413.

Set to the left

correct

Direct diameter Dmi

GradeNo. Ni121109876543