Physics problem of junior two: exploring the imaging law of convex lens

In optics, an image gathered by actual light, called a real image, can be accepted by the light curtain; On the contrary, it is called a virtual image, which can only be felt with the eyes. Experienced physics teachers, when talking about the difference between real images and virtual images, often mention such a distinction method: "Real images are upside down, and virtual images are upright." The three virtual images formed by plane mirror, convex mirror and concave lens are all positive; The real image formed by concave mirror and convex lens, and the real image formed by pinhole imaging are all inverted without exception. Of course, concave lenses and convex lenses can also form real images, and the two real images they form are also inverted. So is the image of the human eye a real image or a virtual image? We know that the structure of the human eye is equivalent to a convex lens, so the image formed by external objects on the retina must be a real image. According to the above rule of thumb, the image of the object on the retina seems to be upside down. But anything we usually see is obviously upright. This problem, which conflicts with experience and law, actually involves the regulation of cerebral cortex and the influence of life experience.

When the distance between the object and the convex lens is greater than the focal length of the lens, the object becomes an inverted image. When an object approaches the lens from a distance, the image becomes larger and the distance from the image to the lens becomes larger. When the distance between the object and the lens is less than the focal length, the object becomes an enlarged image. This image is not the convergence point of the actual refracted light, but the intersection point of their opposite extension lines, which can not be received by the light screen and is a virtual image. The contrast of the virtual image formed by the flat mirror (which can't be received by the light screen, but can only be seen by the eyes). When the distance between the object and the lens is greater than the focal length, the object becomes an inverted image. This image is formed by the light from the candle converging on the convex lens, which is the convergence point of the actual light and can be accepted by the light curtain. This is a real image. When the distance between the object and the lens is less than the focal length, the object becomes an upright virtual image.

Edit the difference between this paragraph and concave lens.

Different structures

The convex lens is composed of transparent mirror surfaces polished into spherical surfaces on both sides, and the convex lens is thin on both sides and thick in the middle. A concave lens consists of a transparent mirror body, two sides of which are polished into concave spherical surfaces, and the concave lens is thick on both sides and thin in the middle. .

Have different effects on light.

Convex lenses mainly converge light, while concave lenses mainly diverge light.

Different imaging characteristics

The convex lens is refractive imaging, and the image can be positive or negative; Virtual and real; Expansion and contraction. Play the role of spotlight. Concave lens is refractive imaging, which can only be reduced to vertical virtual image. Play the role of astigmatism.

Lens and mirror

Lenses (including convex lenses) are instruments that transmit light and form images by folding the light. Light obeys the law of refraction. Mirror (including convex mirror) is an instrument that does not transmit light, but reflects back the image, and light obeys the law of reflection. The convex lens can be an inverted enlarged, equal-sized and reduced real image, or an upright enlarged virtual image. Parallel light can converge on the focal point, and the light emitted from the focal point can also be refracted into parallel light. The convex mirror can only form a vertical and reduced virtual image, which is mainly used to expand the field of vision.

Edit the details of this paragraph.

The application characteristics of object distance (U) and image distance (V) are inverted, positive, small, virtual and real.

U & gt2f f<v & lt2f Inverted Miniature Real Image Camera

U=2f v=2f Measure the demarcation point of the focal length of the inverted real image.

F<u & lt2f v & gt2f Inverted Magnifying Real Image Projector

slide projector

U = FV-∞-// The searchlight obtains the virtual and real boundary points of parallel light sources.

Inverted demarcation point

U<f v>u stands upright on the same side as the object, and magnifies the virtual image magnifying glass, and the virtual image is on the same side as the object.

(1) times the focal length, inverted to reduce the real image; The first focal length here refers to the distance from the point where the parallel light sources converge through the lens to the optical center of the lens, and then the second focal length refers to the real image where it is twice as far away. Double focal length to double focal length, inverted to enlarge the real image; There is no imaging at one focal length; Enlarge the virtual image of the vertical position within a focal length; The real image and the image are on different sides of the convex lens, and the virtual image is on the same side of the convex lens. (2) A focal length is divided into virtual focal length and real focal length; The size is divided into two focal lengths; The close-up image of the object becomes larger; The close-up image of the object becomes smaller; The law of convex lens imaging forms the distance u from the object to the center of the lens; The distance v between the virtual and real images of the positive and negative images and the lens center should be based on the relationship between the object distance and the image distance (u is the object distance v and the image distance f is the focal length) U >；; The real image of the inverted image 2f >:v>；; F camera u> real image v u=2f, if inverted, can be used to measure the focal length of convex lens U = V2F >；; U> Inverted magnification real image v & gt2f projector, slide projector and projector u < V u=f Non-imaging parallel light source: searchlight \ u；; Inverted reduction of the reverse side of 2f real image f

Real image, the near image of the object becomes larger than the virtual image, and the far image of the object becomes larger than the virtual image (4) When the virtual image is used, the left and right sides of the object and the image are consistent, and the top and bottom are consistent; As real images, things and images are left and right relative, and up and down relative. (5) Two demarcation points of convex lens imaging: 2f point is the demarcation point of real image enlargement and reduction; Point f is the dividing point between real image and virtual image.

Deductive method of editing this paragraph law

The imaging rule of convex lens is1/u+1/v =1/f (that is, the sum of the reciprocal of object distance and image distance is equal to the reciprocal of focal length. ) * * * There are two kinds of derivation methods. They are "geometric method" and "functional method"

Geometric method

The title is shown in the right picture. It is proved by geometric method that1/u+1/v =1/f. The imaging law of convex lens is deduced by geometric method.

Solution ∵△ ABCO ∽△ A 'b 'o ∴ AB: A 'b' = u: v ∵△ COF ∽△ A 'b 'f ∴ Co: A 'b' = f: (v-f). Uvf) = VF/UVF ∴1/f-1/v =1/u, that is,1/u+1/v =1/f.

structuralfunctionalism

The problem is as shown in the figure on the right. Prove1/u+1/v =1/f by the function method.

Solution 1 The picture on the right shows the schematic diagram of convex lens imaging. Where c is the length of the imaged object and d is the length of the image formed by the object. U is the object distance, v is the image distance, and f is the focal length. Step 2 (1) In order to solve this problem by the function method, the main optical axis of the convex lens is related (i.e. coincident) with the horizontal coordinate axis (X axis) of the plane rectangular coordinate system, the ideal refractive surface of the convex lens is related with the vertical coordinate axis (Y axis), and the optical center of the convex lens is related with the coordinate origin. Then: the coordinates of point A are (-u, c), point F is (f, 0), point A' is (v, -d), and point C is (0, c). (2) AA' and A'C extend in two directions into a straight line l 1, l2, which are regarded as two function images. As can be seen from the image, the straight line l 1 is a direct ratio function image, and the straight line l2 is a linear function image. (3) Let the analytical formula of the straight line l 1 be y=k 1x and the analytical formula of the straight line l2 be y = K2x+B, and substitute A (-u, c), A' (v, -d) and C (0) according to the meaning of the question. C) Substituting the corresponding analytical formula to obtain the equations: c =-u. K2 as the unknown solution, k 1=-(c/u)k2=-(c/f) ∴ The two resolution functions are: y =-(c/u) x y =-(c/f) x+.

Edit this routine memory

1 . u & gt； 2f, inverted reduced real image f < v & lt2f The abbreviation of the camera is: small outside and small inside (or the close-up image of the object is smaller) 2.u=2f. The inverted real image v=2f can be used to measure the focal length of the convex lens. Abbreviations are: paired inverted solid 3.2f & gtu> inverted magnified real image v & gt2f projector, slide projector, and projector. Abbreviations are: Chinese and foreign inverted images are stereoscopic (or the distant image of an object becomes larger). 4.u=f Non-imaging parallel light source: searchlight. Abbreviations are: no imaging at the point. 5.u.

Application of convex lens in editing this paragraph

The lens of a camera is equivalent to a convex lens, and the photographic negative is the image formed when taking pictures. Projectors, slide projectors, projectors, magnifying glasses and searchlights all use convex lenses, which have improved our lives and have been used all the time. Common application of concave lens: myopia glasses have written so much, don't forget to vote when passing by! Hope to adopt! ! !