yc6 SPECTACLES. 



focal distance When the lens by the energy of accommodation is rendered more powerfully re- 

 fractive the increase (B) can readily be eliminated by placing before the eye a mncave lens 

 which possesses exactly the opposite optical effect of the increase of accommodation (B). Hence, 

 it is possibleto indicate the power (force) of accommodation of the eye by a lens of a definite 

 focal distance, i.e., by the optical effect produced by the latter. Therefore, according to 

 Donders the measure of the force of accommodation of the eye is the reciprocal value of the 

 focal distance of a concave lens, which, when placed before the accommodated eye, so refracts 

 the rays of light coming from the near point (p) as if they came from the far point. 



Example. We may calculate the force of the accommodation according to the following for- 

 mula : - = - - -, i.e., the-force of accommodation, expressed as the dioptric value of a lens (of 



j- inch focal distance), is equal to the difference of the reciprocal values of the distances of the 

 near point (j>) and of the far point (r) of the eye. In the emmetropic eye, as already mentioned, 



j) -5, r=. Its force of accommodation is therefore - = ---, so that x=5, i.e., it is equal 



to a lens of 5 inches focal distance. In a myopic eye, p = 4, r12, so that - = - - , i.e., x = 



6. In another myopic eye, with p=4 and / =20, then .x--=5, which is a normal force of accom- 

 modation. Hence, it is evident that two different eyes, possessing a very different range of 

 accommodation, may nevertheless have the same force of accommodation. Example. The one 



eve has = 4. r=oc, the other, ?; = 2, r = i. In both cases, - = -, so that the force of accom- 



j r i i 4 



modation of both eyes is equal to the dioptric value of a lens of 4 inches focal distance. Con- 

 versely, two eyes may have the same range of accommodation, and yet their force of accommo- 

 dation be very unequal. Example. The one eye has p=* 3, r = 6 ; the other p=6, r = 9. Both, 

 therefore, have a range of accommodation of 3 inches. For these, the force of accommodation, 



111 ,111 



- ---, x-6 ; and -=---, =18. 



x 3 6 ' x 6 9 ' 



Relation of range to force of accommodation. The general law is, that, the ranges of 

 accommodation of two eyes being equally great, then their forces of accommodation are equal, 

 provided that their near points are the same. If the ranges of accommodation for both eyes 

 are equally great, but their near points unequal, then the forces of accommodation are also un- 

 equalthe latter being greater in the eyes with the smallest near point. This is due to the 

 fact that every difference of distance near a lens has a much greater effect upon the image as 

 compared with differences in the distance far from a lens. The emmetropic eye can see dis- 

 tinctly objects at 60 to 70 metres, and even to infinity, without accommodation. 



While p and r may be directly estimated in the emmetropic and myopic eyes, this is impos- 

 sible with the hypermetropic (long-sighted) eye. The far point in the latter is negative ; indeed, 

 in very pronounced hypermetropia even the near point may be negative. The far point may 

 be estimated by making the hypermetropic eye practically a normal eye by using suitable 

 convex lenses. The relative near point may then be determined by means of the lens. 



Even from the 15th year onwards, the power of accommodation is generally diminished for 

 near objects perhaps this is due to a diminution of the elasticity of the lens (Donders). 



390. SPECTACLES. The focal distance of concave (diverging), as well as convex (converg- 

 ing) spectacles, depends upon the refractive index of the glass (usually 3 : 2), and on the length 

 of the radius of curvature. If the curvature of both sides of the lens is the same (biconcave or 

 biconvex), then, with the ordinary refractive index of glass, the focal distance is the same as the 

 radius of curvature. If one surface of the lens is plane, then the focal distance is twice as 

 great as the radius of the spherical surface. Spectacles are arranged according to their focal 

 distance in iiwhes, but a lens of shorter focal distauce than 1 inch is generally not used. They 

 may also be arranged according to their refractive power. In this case, the refractive power of 

 a lens of 1 inch focus is taken as the unit. A lens of 2 inches focus refracts light only 

 half as much as the unit measure of 1 inch focus ; a lens of 3 inches focus refracts as 

 strongly, &c This is the case both with convex and concave lenses, the latter, of course, 

 having a negative focal distance ; thus, "concave ," indicates that a concave lens diverges 

 the rays of light one-eighth as strongly as the concave lens of 1 inch (negative) focal distance. 



Choice of Spectacles. Having determined the near point in a myopic eye, of course we 

 require to render parallel the divergent rays coming from the far point, just as if they came 

 from infinity. This is done by selecting a concave lens of the focal distance of the far point. 

 The greatest distance is the far point of the emmetropic eye. Suppose a myopic eye with a far 

 point of 6 inches, then such a person requires a concave lens of 6 inches focus to enable him to 

 see distinctly at the greatest distance. Thus, in a myopic eye, the distance of the far point 

 from the eye is directly equal to the focus of the (weakest) concave lens, which enables one to 

 see distinctly objects at the greatest distance. These lenses generally have the same number 

 as the spectacles required to correct the defect. Example. A myopic eye with a far point of 



