2. The refractive system of eyeball is an adjustable "convex lens", so its shape can be changed. When the concave lens is placed in front of the eyes, the eyeball still has the function of self-adjustment, which shows that the eyes can see objects at different distances, and patients with myopia or presbyopia can adapt to wearing glasses.
3. Because ordinary glasses are separated from eyeballs, the images are intuitive and easy to calculate. This section focuses on the influence of glasses on eyeball refraction, and the discussion about glasses is aimed at ordinary glasses. The refractive effect of wearing contact lenses is the same as that of ordinary glasses, and its principle and technology are very mature in the glasses industry, so I won't repeat them here.
4. In refractive optics, only in some special cases can the combination of two lenses with diopters of P 1 and P2 produce the refractive effect of lenses with diopters of P 1+P2. In the optical path composed of eyeball and lens, P 1+P2 can also be found in effect or qualitative calculation, which is not the actual refractive effect after lens combination, but a simplification and approximation, because the eye has the ability to change diopter by itself. Although it is difficult to be verified by experiments, it should be able to offset the diopter of the lens from the perspective of the adjustment function of the eyeball, but this formula can simplify the calculation. For the system composed of eyeball and lens, it is a refractive system composed of two lenses at most, so it can be calculated by refractive optics theory. When wearing a lens, due to the special adjustment function of the eyeball, we can add or subtract the diopter of the lens and the diopter adjusted by the eyeball, or we can get an approximate value. Although there is still a long way to accurately measure the refractive power of the eyeball, the effect is close. In this demonstration, although it is theoretically deduced, it is very difficult to experiment and measure, just like myopia glasses need to be tried on, and experiments need to be carried out in the process of guiding glasses.
5. According to the refractive characteristics of the eyeball, the static refractive power of the eyeball is+58.6 d. Although this is a special case, it basically reflects that the refractive power of the eyeball is very strong, and its adjustment is relatively small. The normal eye is about 0- 10d, and the myopia is about N- 10d(N refers to the myopic refractive power of the eyeball). It can be considered that the distance from the center of the refractive system of the eyeball-the lens to the retina is constant, and in the later calculation, the image distance can be considered as a constant K. For the refraction of the eyeball, if a clear image can be formed on the retina, the refractive system still meets the lens imaging formula.
1/u+ 1/k=P
Where k is a constant, p is the refractive power of the eyeball, which is a variable, meaning that different people look at targets at different distances, and the refractive power of different people's eyeballs is different, and u refers to the distance from the target to the eyeball.
The condition of this formula is that at a certain moment, the eyes look at the target at a certain distance, and the target is between the near point and the far point of the eye.
According to the formula, when looking straight at infinity, 1/u=0, the above formula can be changed to P= 1/K, so that 1/k=P0, that is, P0 is the static diopter of eyeball. When looking at a target with a distance of L from the eyeball, the imaging formula of "lens" becomes 1/L+1/k =1/L+P0, where1/L is the diopter of the eyeball when looking at the target with a distance of L.
For the wearer, under normal circumstances, the distance from the eyeball to the center of the glasses is about 1.2-2.4 cm, which is denoted by H below, but the value at a certain moment is certain for someone. Let the focal length of a lens with a diopter of p' be f, and when looking at a target with a distance of l, the lens imaging formula is as follows:
1/L+ 1/V = P ' = = & gt； 1/V=P'- 1/L ①
At this time, the distance from the lens to the eyeball is |V|+h, and the refractive condition of the eyeball satisfies the formula:1(| v |+h)+1/k = p2.
According to the formula, if |V| is much greater than h, according to formula ①, formula ② can be approximately simplified as:
1/| V |+ 1/K = D = | D '- 1/L |+ 1/K③
Because the eyes see the virtual image through the lens, V.
According to this formula, the size of |V| depends on the object distance L and the focal length of the lens. Considering the actual situation, the diopter of myopia glasses is mostly greater than -6D, and the reading and writing distance of students is mostly greater than 0.25m. Moreover, according to the lens imaging formula, the refractive power of concave lens is P' (Note D'
In other words, for thin lenses, if the distance from the eyeball to the lens is ignored, it can be considered that the added accommodation of wearing myopia glasses is equal to the refractive power of the lens. In the optical system composed of eyeball and glasses, the diopter produced by each part can be approximately increased or decreased. This analysis can simplify the calculation and simplify the problem. In the following discussion, we will use this result for qualitative analysis and approximate calculation.
6. Error analysis. If the formula is taken as the standard, there are many reasons for the error, which are analyzed now.
(1) Because the adjustment and deformation of the eyeball are carried out at the same time, if there is adjustment, there will be deformation, and if there is deformation, there will be changes in the anterior and posterior diameter of the eyeball, as well as changes in the cornea, aqueous humor and the optical center of the lens caused by the deformation of the lens and cornea itself. Although myopia or presbyopia itself can't explain the change of the anterior and posterior diameter of the eyeball (myopia is that the eyeball images in front of the retina, but it can be achieved if the close adjustment is too strong or the ciliary muscle can't relax, and it can't fully explain the elongation of the anterior and posterior diameter of the eyeball), nor can it explain its invariance. The existence of these factors determines that k in the formula is only an approximation, and the larger the tuning range, the greater the change of k value, which is also one of the reasons for the error. However, considering that the diopter adjustment of the lens is far from the diopter of the eyeball (about 60 diopters), and the adjustment range of the eyeball is generally less than 10 diopter, the change of corneal diopter is smaller, so it can be considered that the distance from the optical center of the "lens" to the retina is almost unchanged.
(2) Because the anterior-posterior diameter of eyeball varies from person to person, K is not a constant, so it is difficult to measure it accurately. For a certain stage of a person, the anterior and posterior diameter of the eyeball remains the same, so K can be considered as a constant.
(3) For different people, the distance between the lens and the optical center of the "convex lens" is a difficult variable to measure, which also affects the accuracy of calculation. It can be seen from the calculation that when h increases, the error increases, and vice versa.
7. When the lens is placed in front of the eyes, if the eyes can still see the target clearly compared with the normal eyes, from the regulatory role of the eyeball, the glasses first offset the lack of regulation of the eyeball. So in the future calculation, as long as the effect of the offset lens is within the normal adjustment range of the eyeball, it can be established in theory, and we don't need to pay attention to the change of the actual diopter of the eyeball. For the eyeball, no matter how many diopters of glasses you wear, you must reduce the role of glasses and increase the diopter adjustment to see the target in front.
8. Because of the error and adaptation of glasses, even if all factors are taken into account, theory is only an approximation to practice. When the range of eyeball accommodation is large, this simplified and idealized theory will increase the error due to its own deformation. Moreover, the distance from the lens to the optical center of the eyeball varies from person to person, which cannot be expressed by physical formula. The specific problems are to be analyzed in detail.
9. For the refractive system composed of eyeball and lens, the refractive power of lens is certain, but the refractive power of eyeball is a variable. Therefore, the eyeball is regarded as an adjustable convex lens, which means that the refractive power of the eyeball is determined when the eye can see a certain target clearly through glasses, so it can be calculated by refractive theory, but when the distance between the eyeball and the target changes, its refractive power also changes.
10. For the refractive system composed of eyeballs and glasses, there are only two "lenses", which can be regarded as an equivalent lens group, and the degrees of the lenses can be increased or decreased. For example, the +5D lens can be regarded as a (+2D)+(+3D) lens group. Although it is not true in most cases, it provides convenience for us to solve the problem in theory.