3.11.3 Experimental principles
Lens is the most common basic element in optical instruments.Focal length,the distance from the center point to the focus of the lens,is an important physical quantity for reflecting the optical characteristics of the lens.Lens or lens groups with different focal lengths are used in many optical instruments according to different purposes.Thus,learning to measure the focal length of the lens,mastering the imaging law of lens and the analysis and adjustment methods of simple optical paths are very necessary for the proper usage of optical instruments.Several methods of measuring the focal length of a thin lens are listed in the following content.
1)Measurement of convex lens focal length
(1)Plane mirror method.As shown in Figure 3.11.1,if the object is placed in the focal plane of the convex lens L,the light will be the parallel light after the lens.Then the parallel light is reflected back by the plane mirror M,passing through the lens L again and imaging in the object surface.It can be obviously inferred that the focal length f of the convex lens is the distance u.
(2)Conjugate method(also called double imaging method).According to the imaging law of the convex lens,if the relative distance between the object and the screen remains unchanged and is more than 4 times the focal length(d＞4f ),two imaging positions can be found when the convex lens is moved between the object and image screen.When the object distance is u1,the enlarged image is obtained on the image screen.When the object distance of u2,the reduced image is obtained on the image screen.The schematic diagram of the conjugate method is shown in Figure 3.11.2.
Figure 3.11.1 Plane mirror method
Figure 3.11.2 Conjugate method
According to the lens imaging formula:
According to the conjugate relations:
Then:
2)Measurement of concave lens focal length
Since the virtual image of the concave lens cannot be received on the screen,the convergence effect of the convex lens is used to measure the focal length of the concave lens.
(1)Plane mirror method.As shown in Figure 3.11.3,the light is converged by the convex lens L1 and then is diverged by the concave lens L2.As long as the distance between L1 and L2 is appropriate,parallel light can be obtained after the light goes though concave lens L2.With a plane mirror M,the parallel light will be reflected back,then the focal length f of concave lens is the difference between the image distance v1 of the convex lens L1 and the distance l between the two lenses,i.e.
(2)Object distance method.As shown in Figure 3.11.4,the light from object AB passes through the convex lens L1and converges into a reduced image(A′B′).Then a concave lens L2 is inserted between L1 and position A′B′.The image A′B′is considered to be a virtual object of the concave lens.According to the concave lens imaging rule,the virtual objects in the concave lens focal length have a real image(A″B″).If u,v and f represent the object distance,image distance and focal length of concave lens L2 respectively,then:(https://www.daowen.com)
Figure 3.11.3 Plane mirror method
It should be noted that the real image can only be obtained when u＜f.
Figure 3.11.4 Object distance method
3)Settings of objects and reception of images
(1)Settings of objects.Objects in the beam path diagram must be luminescent.However,real illuminant is often three-dimensional and not easy to accurately determine the center.Therefore,planar transparent figures are usually used as objects,such as a hollow arrow on a thin plate.The hollow arrow illuminated by a small lamp is regarded as the luminous object,and the transmitted light is regarded as the light from the luminescent object.In this condition,the solid angle of the beam emitted by each point on the object is greatly limited,and the projection direction is different(Figure 3.11.5).Light from the object center participates in imaging,while light from edge locations cannot pass through it.
In this way,an incomplete image is obtained with bright in the middle and dark around the edge.In order to improve this phenomenon,a ground glass can be added near the object between the object and the light source,so that the light passing through the object can diffuse in all directions and the solid angle of emission is increased,leading to the uniform brightness of the image(Figure 3.11.6).
Figure 3.11.5 Object imaging schematic
Figure 3.11.6 Schematic diagram for improving the imaging quality
(2)Reception of image.Similarly,a diffused white paper or ground glass(one side is rough while the other side is smooth)is used as the image screen to facilitate the observation of the image from all angles.When the ground glass screen is used,the image should be observed from the direction of transmittance because the transmittance of light intensity is much greater than the reflectivity when the incident angle is small.
4)Coaxial adjustment
(1)Coarse adjustment.Firstly,keep the lens,image screen,object,light source in the optical bench close to each other at the center of the various components into roughly in the same line,using our eyes to make a rough observation.The screen is vertical to the guide direction,and the lens optical axis is parallel to the guide rail.
(2)Fine adjustment.Based on the lens imaging adjustment,if the light source,the center of the object,the center of the lens and the center of the screen are coaxial,then the centers of the large and small images obtained by moving the lens will coincide(both on the optical axis).If the center of the object is not on the optical axis,the center of the large image and small image will be biased to the same side of the optical axis,and the large image will deviate farther.If the image is inverted,the center of the large image is higher than the center of the small image,indicating that the lens is high or the object is low,then the lens should be lowered or the object should be raised.Otherwise,the position of the lens should be raised or the object should be lower(Figure 3.11.7).Transverse adjustment rules are consistent with the methods mentioned above.If there are more than two lenses in the optical system,the coaxial of the two lenses should be firstly adjusted and keep unchanged.Then add the other lenses one by one,and use the same principle for coaxial adjustment.
Figure 3.11.7 Diagram of coaxial adjustment
