3.12.3 Experimental principles
The interference of light is one of the important optical phenomena,which provides important experimental evidence for the wave property of light.In order to obtain optical interference phenomenon,the two beams must satisfy coherent conditions,such as the same frequency,the same vibration direction and constant phase difference.Since ordinary light sources are not coherent,a stable interference field cannot be obtained from two-point light sources or two independent parts of a plane light source.In order to guarantee coherent conditions,the common method is to divide one light beam into two by using a set of optical components and make them meet again after passing different paths.Since the two beams are from one source,they meet the coherent conditions,and then a stable visible interference field is formed.As an interference phenomenon based on division-of-amplitude,the equal thickness interference has many applications,i.e.testing the surface finish and flatness of high-precision optical surface,measuring the thickness of a thin film and a small angle,measuring the curvature radius of curved surface and the sample’s expansion coefficient,studying components’internal stress distribution,etc.For these measurements,the typical devices that Newton’s rings and wedge film are required necessarily.In this experiment,as one of the typical devices of the equal thickness interference,Newton’s rings are employed to measure the curvature radius of the lens.
Figure 3.12.1 shows the structure of Newton’s rings,which is composed of a plano-convex lens with a curvature radius R in the upper part,a piece of planar glass in the lower part,and a thin air film with a variable thickness between the lens and the planar glass.The thickness of the air film increases gradually along the center to the edge,and keeps unchanged on the same circle.When the device is vertically irradiated by a parallel monochromatic light,two beams of reflected light from the upper and lower surfaces of the middle air layer will meet to cause the interference phenomenon because of their constant optical path difference.As a result,a group of circular interference fringes centered at the contact point O are observed,being sparse at the center and dense at the outer.These fringes are called Newton’s rings,as displayed in Figure 3.12.2.
Figure 3.12.1 Structure diagram of Newton’s rings
Figure 3.12.2 Newton’s rings
According to the optical path analysis,the corresponding optical path difference of the two light beams related to the k order interference ring(assuming the contact point is zero order)can be expressed as follows:
Where λ/2 is an additional optical path difference,which is caused by the half-wavelength loss during the reflection when the light comes into an optically dense medium from an optically spare medium,and the refractive index of air is n0=1.According to the geometry relation,it can be expressed as:
Considering dk≪R,the second order small quantity can be ignored,so it is expressed as:
Substitute Equation(3.12.2)into Equation(3.12.1),we can obtain:(https://www.daowen.com)
It can be seen from the interference conditions that the interference fringe is dark if the optical path difference satisfies the following conditions:
Thus,the radius of k order dark fringe can be expressed as follows:
If the λ is known,the curvature radius will be obtained through measuring the radius rk of k order dark ring.
In fact,it is highly difficult to measure the radius rk accurately,for the obvious deviation of R.There are two reasons for the deviation:one is that the center of Newton’s rings is hard to fix when there is a face rather than a point at the contact place because of the dust and the deformation caused by the contact press between two pieces of glass;the other one is that the fringes are not thin enough to assist in counting the number of dark rings exactly.In order to avoid the systematic deviation,we will employ the interference differential to calculate the curvature radius.Assuming that the radius of the n order dark ring is rn and the radius of the m order dark ring is rm,we can get:
Assuming m＞n,according to the two formulas above,we can get:
As the center of Newton’s rings is difficult to fix,it is necessary to measure the diameters Dn and Dm instead of rn and rm.Thus,the formula of the curvature radius of plano-convex is:
