The equation of the thin lens says
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| where f = focal lenght, x = the distance from the object to the lens, and y = the distance from the vision to the lens. |
The vision on the retina is formed only when the retina is in the required distance from the
lens. It is hard to imagine an eye in which the distance between the retina and the lens could
change freely. It depends on the structure of the eye and its ability to change is limited. So
what can we do to see ‘well’ and what do we mean by "good sight"? We see well if the light
rays coming from the object undergo a process of bending (refraction) in the lens and become
focused on the retina. If we change the distance between the object and the lens (that is x in
the equation) the focal lenght (f) also has to change, in order not to change the distance
between the vision and the lens (y). The focal lenght depends directly on the structure of
the lens itself. If the lens is limited by two special surfaces whose radiuses are
respectively r1 and r2 and the coefficient of the refracting angle of the substance the
lens is made up of is n the focal lenght of the thin lens can be calculated by means of the
following equation :
1 1 1
--- = (n-1) [ ---- + ---- ] [ 2 ]
f r1 r2
In everyday life the focal lenght is more often refered to as the dioptrics of the lens and it is represented by the equation Z=1/ f . Its unit is a diopter [1 D = 1/m] so, if the lens has the dioptrics equal to 1 D the parallel rays aimed perpendiculary at the lens after being refracted in it will focus in the distance of 1 m. The point the rays focus in is called the focus.
Beams of light (parallel if an object is 6m away or more, and divergent if an object is nearer) from any one point in an object are falling on the surface of the cornea which converges them. In normal vision the lens brings them to a focus and is variable to enable us to see close and distant objects equally well. When old-age leads to the loss of this power of accommodation the eye is said to be presbyopic.
The adjustment of the dioptrics of the eye, whereby it is able to focus the image of both
distant and close objects, is brought about by a change in the convexity of the anterior
surface of the lens.. When the eye is accommodated for distant vision the ciliary muscle
relaxes, pulling the suspensory body or zonule taut, which results in a flattening of the
anterior surface of the lens. Conversely, in accomodation for near vision the ciliary
musclecontracts and the anterior surface of the lens becomes more convex. The complete
act of accomodation for a near object comprises, besides an increased convexity of the
lens, convergence of the eyes and constriction of the pupil. Six muscles move the eyeball,
four "recti" and two "obliqui". By means of the contractions of these muscles the eyeball
may be moved in any desired direction.
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Refractions, in the case of vision, are due to constitutional or pathological abnormalities in the cornea, crystalline lens, or shape of the eye which cause abnormal refraction in light rays: or to muscular changes leading to deficient accomodation.
MYOPIA
Myopia, or short sight, is a defect in vision due to a faulty structure of the eye. When the
eyeball is long, the focus lies in front of the retina. Distant objects are indistinct and near
objects have to be brought close to the eyes.
MYOPIA BEFORE |
MYOPIA AFTER USING SPECTACLES |
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This defect is corrected by use of spectacles with concave lenses adjusted so that parallel rays
are focused on the retina as in ordinary vision. You can calculate yourself what dioptrics of the
lens of your spectacles you should use. The distance between the eye-lens and the retina is
constance. If you "see well" only words, which are not more distant from your eye than 16 cm,
you should use correct lenses. The "normal" distance is to 24 cm.
So :
Z1 - the dioptics of the eye
Z2 - the dioptrics of the spectacles
X1 - the distance from the eye without spectacles (here: 16 cm)
X2 - the distance from the eye with spectacles (here: 24 cm)
Y - the distance between the lens and the retina
Now the equation no.1 we can write as :
Z1 = 1/X1 + 1/Y
From the physical rules we know that :
Z1 + Z2 = 1/X2 + 1/Y
When you substract those two equations you will have :
Z2 = 1/X2 - 1/X1
So in this example you will obtain that you have to use spectacles :
Z2 = 1/0.24 - 1/0.16 [D] = - 2.08 D =~ - 2D
The concave lanses have a negative dioptrics. By slightly diverging the rays before entering
the eye, spectacles can throw the focus on the retina, producing correct vision.
PRESBYOPIA & HYPERMETROPIA
Presbyopia (old sight) is due chiefly to changes in the mechanical properties and shape of the
lens and contractile power of the ciliary muscles, with advancing age; near objects are indistinct.
PRESBYOPIA & HYPERMETROPIA BEFORE |
PRESBYOPIA & HYPERMETROPIA AFTER USING SPECTACLES |
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In hypermetropia (long sight) the eyeball is short and the focus of the rays lies behind the retina, producing a condition similar to presbyopia, but applying to objects at all distances. Both are corrected by convex lenses. Here the dioptrics of the spectacles you can obtain in the same way as you have done it in myopia .
EYE SENSIBILITY
The human eye sees only the rays, which lenght is 360 - 780 micrometers. Every colour has its own lenght. For example : Violet about 400, blue - about 470, green - about 520, yellow - about 585, orange - about 600, red - about 680. If the lenght of the ray is longer than 700, we can’t see it with our eyes. We call them infrared. Rays, which are shorter than 350 are called ultraviolet and we also doesn’t see them with our eyes.
COLOUR - BLINDNESS
An affection of the eyes which renders them unable to distinguish certain colours. In an extreme form, which is very rare, everything appears monochromatic. Colour-blindness is nearly always congenital. More common in the male than the female sex, it is transmitted through the female to male children. About 10 per cent of the male population have some defect of colour-vision. The colour-blind woman is rare. The most common form of defect consists of difficulty in distinguishing differences between red, green ,and yellow. People with this defect are sometimes called red-green blind. They can see colours, but have difficulty in distinguishing which is which. There is also a defect in which blue, green, and yellow are confused. The cause of colour-blindness is in some cases a defect in the function of the rods or cones of the retina, and in others the defect lies in the nerve cells of the visual centre in the brain.
ASTIGMATISM
A condition of the eye in which rays of light from one source are not brought to a focus at a point. It is usually due to inequality of curvature of the meridians of the cornea. Sometimes it is due to imperfection of the lens or faulty action of the ciliary muscles. Astigmatism may be simple, compound or mixed. It is due to the abnormal shape of the cornea or lens, and the rays of light in different planes are not refracted to the same focus. It exists in every degree of complexity, but is simple when one meridian has correct refraction but the other is myopic or hyprmetropic. Compound when both meridians show errors of the same kind but differ in degree. Mixed when one gives myopic, the other hypermetropic vision. Cylindrical glasses, correcting corneal curvature, are used to correct astigmatism.
