3
Spherical Lenses
A lens is defined as a portion of a refracting medium bordered by two curved surfaces which have a common axis. When each surface forms a part of sphere, the lens is called a spherical lens. There are various forms of spherical lens, some of them also have one plane surface. This is acceptable because a plane surface can be taken as part of a sphere with infinite radius. (Fig. 3.1)
Fig. 3.1: Basic forms of spherical lens
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Spherical surfaces are either convex or concave. A convex lens causes convergence of incident light, whereas a concave lens causes divergence of incident light (Fig. 3.2).
Figs 3.2A and B: Light passing through a lens obeys Snell’s Law at each surface (A) Convex lens, (B) Concave lens
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The total vergence of a spherical lens depends on the vergence power of each surface and the thickness of the lens. Since, most of the lenses used in ophthalmology are thin lenses, thickness factor is ignored (Fig. 3.3). Thus, the total power of a thin lens is the sum of the two surface powers. Refraction can be thought of as occurring at the principal plane of the lens. In Figures 3.4A and B principal plane of the lens is shown as AB. The point at which the principal plane and the principal axis intersect is called the principal point or nodal point, of the lens which is denoted by N. Rays of light passing through the nodal point is undeviated. Light rays parallel to the principal axis is converged to or diverged from the point F, the principal focus (Fig. 3.5).
Fig. 3.3: Vergence power of thin lens
Figs 3.4A and B: Cardinal points of thin spherical lenses (A) Convex (B) Concave
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Fig. 3.5: The principal foci of thin spherical lenses
Since, the medium on both sides of the lens is the same, i.e., air, parallel rays incident on the lens from the opposite direction, i.e., from the right in Figure 3.4 will be refracted in an identical way. There is, therefore, a principal focus on each side of the lens, equidistant from the nodal point. The first principal focus F1, is the point of origin of rays which, after refraction by the lens, are parallel to the principal axis. The distance F2N is the first focal length. Incident rays parallel to the principal axis is converged to or diverged from the second principal focus – F2. The distance F2N is the second focal length. By the sign convention, F2 has a positive sign for convex lens and negative sign for the concave lens. Lenses are designed by their second focal length. Thus, the convex or converging lenses are also called “Plus Lenses” and are marked with “+”, while concave or diverging lenses are also called “Minus Lenses” and are marked with “–”. If the medium on either side of the lens is the same, i.e. air, then F1 = F2. However, if the second medium differs from the first, e.g. in case of contact lenses, then F1 will not be equal to F2.
DIOPTERIC POWER OF LENSES, VERGENCE
Lenses of shorter focal length are more powerful than lenses of longer focal length. Therefore, the unit of lens power, the diopter, is based on the reciprocal of the second focal length expressed in metres, gives the vergence power of the lens in diopters (D).
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Figs 3.6A and B: Vergence of rays
Thus, F = 1/ f2
Where F = Vergence power of lens in dioptres. f2 = Second focal length in metres.
So, in the above Figure 3.6A vergence at the lens is: F = 1 / 0.25 = 4.00 D.
And in Figure 3.6B vergence at the lens is: F = 1/ 0.10 = 10.00 D.
A converging lens of second focal length + 5 cm has a power of + 1/ 0.05 or + 20.00D, and a diverging lens of second focal length 25 cm has a power of
– 1/ 0.25 or – 4.00 D.
SPHERICAL LENS DECENTRATION AND PRISM POWER
Rays of light incident upon a lens outside its axial zone are deviated towards (Convex lens) or away from (Concave lens) the axis. Thus, the periphery portion of the lens acts as a prism. The refracting angle between the lens surfaces grows larger as the edge of the lens is approached (Fig. 3.7). Thus, the prismatic effect increases towards the periphery of the lens. Use of paraxial portion of a lens to gain a prismatic effect is called decent ration of the lens. Lens decent ration is frequently employed in spectacles where a prism is to be incorporated. On the other hand, poor centration of spectacle lenses, may produce an unwanted prismatic effect. The prismatic power of the lens is given by the formula:
P = D / d Where, P = Prismatic power in prism dioptre.
D = Deviations produced by lens in cms. d = Distance in metres.
The increasing prismatic power of the more peripheral parts of a spherical lens is the underlying cause of spherical aberrations.
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Fig. 3.7: Prismatic deviation by spherical lenses
DETECTION OF SPHERICAL LENS
It is possible to determine the spherical lens by studying the image formed when two lines crossed at 90º, are viewed through the lens. Spherical lens causes no distortion of the cross. However, when the lens is moved from side to side and up and down along the axis of the cross, the cross also appears to move. In the case of a convex lens, the cross appears to move in the opposite direction to the lens, termed as “against movement”, while a movement in the same direction termed as “with movement” is observed if the lens is concave (Fig. 3.8). Rotation of a spherical lens has no effect upon the image of the crossed lines. The power of a lens can also be found using the neutralization method. Once the nature of the unknown lens is so determined, lenses of opposite type and known power are superimposed upon the unknown lens until a combination is found which gives no movement of the image of the cross line when the test is performed. At this point the two lenses are said to “neutralize” each other and the dioptric
Fig. 3.8: Movement test for detection of spherical lens
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power of the unknown lens must equal that of the trial lens of opposite sign, e.g, a + 2.00 D lens neutralizes a – 2.00 D lens. To measure this accurately, the neutralizing lens must be placed in contact with the back surface of the spectacle lens. However, with highly curved lenses, this is not possible and an air space intervenes. It is, therefore, better to place the neutralizing lens against the front surface of the spectacle lens. Neutralization is, thus, somewhat inaccurate for curved lenses of more than about 2.00D. An error of up to 0.50D may be possible with powerful lenses. Nevertheless for relatively low power lenses, neutralization is still a very useful technique.
The Geneva lens measure can be used to find the surface powers of a lens by measuring the surface curvature (Fig. 3.9). The total power of a thin lens equals the sum of its surface powers. However, the instrument is calibrated for lenses made of crown glass and a correction factor must be applied in the case of lenses made of materials of different refractive indices.
Focimeter is used to measure the vertex power of the lens. The image of the target is seen as a ring of dots when a spherical lens is tested (Fig. 3.10).
Fig. 3.9: Geneva lens measure watch
Fig. 3.10: Target as seen in Focimeter