This document discusses different types of lenses used in ophthalmology. It describes spherical lenses and how they are either convex or concave, forming converging or diverging images. It also discusses astigmatic lenses, including cylindrical lenses which have one curved and one plane surface, and toric lenses which have two curved surfaces of different curvatures. The key concepts of focal length, power, vergence, and magnification of lenses are defined.

1. Spherical & Astigmatic lenses
Dr.Mohammad Dmour- PGY1
Supervised by : Dr.Dema Otoom
Ophthalmology Department- Islamic Hospital

2. Outlines…
1. Types of lenses
2. Convex and concave lenses
3. Construction of the image
4. Vergence
5. Dioptric Power of Lenses
6. Magnification Formulae
7. Spherical Lens Decentration
8. Cylindrical and toric lenses
9. Spherical Equivalent

4. Introduction
• A lens is defined as a portion of a refracting
medium bordered by two curved surfaces which
have a common axis and at least one of these
two surfaces is curved.

5. Spherical lenses :
• A spherical lens is
a lens in which
each spherical
surface forms part
of a sphere and so
all meridians of
each surface have
the same curvature
and the refraction
is symmetrical
about the principal
axis.

6. Forms of spherical lenses
A. Convex lenses:
• A convex lens may be considered as a
collection of prisms base to base i.e. it
is built of prisms of gradually
increasing angles.
B. Concave lenses:
• A concave lens may be considered as a
collection of prisms apex to apex i.e. it
is built of gradually decreasing angles.

10. • A convex lens causes convergence of incident
light while a concave lens causes divergence of
incident light.
Forms of spherical lenses

12. Construction of the image by spherical lenses:
• Diagrammatic construction of image using two rays :
• A. A ray parallel to the principal axis which after
refraction passes either:
• Through F2 of a convex lens; or
• Away from F2 of a concave lens.
• B. A ray from the top of the object: Which passes
through the principal point undeviated.

16. • The Image formation by a concave lens:
• If the object is at ∞, the image is at F.
• If the object is at any finite distance on the principal axis of the lens:
The image is virtual, erect, diminished and inside F2.

19. Power of the lens
• The total vergence power of a spherical lens
depends on:
1. The vergence power of each surface.
2. The thickness of the lens:
A. Thin lenses:
• The thickness factor may be ignored and the total
power of a thin lens is the sum of the two surface
powers.
B. Thick lenses:
• Refraction by thick lenses is more complicated.

20. The power of convex or concave meniscus:
is the sum of the power of the two surfaces.

21. Vergence:
• A measure of the amount of spreading (or
gathering) of a bundle of light rays (wavefront)
emerging from (or heading to ) a single point
• It is the measure of the amount of convergence
or divergence of a bundle of light rays coming
from or heading to a single point.

22. Vergence:
• Direction of light travel
must be specified (by
convention, left to right)
• Convergence
(converging rays): plus
vergence; rare in nature;
must be produced by an
optical system
• Divergence (diverging
rays): minus Vergence
• Parallel rays: zero
vergence

23. Dioptric Power of Lenses
• Lenses of shorter focal length are more powerful
than lenses of longer focal length. Therefore the unit
of lens power, the dioptre, is based on the reciprocal
of the second focal length.
• The reciprocal of the second focal length expressed
in metres, gives the vergence power of the lens in
dioptres (D) thus :
• where F is the vergence power of the lens in dioptres
and f2 is the second focal length in metres.

24. Vergence of rays
(a) Vergence at the lens (b) Vergence at the lens

25. • A converging lens of second focal length +5 cm
has a power of
• Likewise, a diverging lens of second focal length
–25 cm has a power of

26. Magnification Formulae
• Linear Magnification
• The linear magnification produced by a
spherical lens can be calculated from the basic
formula:
• where I is the image size, O is the object size, v
is the distance of the image from the principal
plane, and u is the distance of the object from
the principal plane .

28. Spherical Lens Decentration and Prism Power
• Definition: The use of non-axial portion of the lens
to gain a prismatic effect.
• Indication:
• 1. convergence insufficiency e.g.
• 1. Old presbyobe
• 2. High myope
• 2. Convergence excess.
• 3. In asymmetrical eyes:
We bring the optical center to coincide with visual
axis of each eye separately.

29. The prismatic effect of a spherical lens:
• light rays passing through the peripheral portion
of the lens is deviated more than those passing
through its axial zone.
• Therefore, the peripheral portion of the lens acts
as a prism.
• The refracting angle grows larger as the edge of the
lens is approached.
• Therefore, the prismatic effect increases towards
the periphery of the lens.

31. • The prismatic power gained by decentration
of a spherical lens (Prentice`s rule):
• Prentice`s rule: At any point of spherical lens
there is a prismatic effect except at the optical
center.
• The prismatic effect is 1 Δ for every 1 cm
decentration per 1D lens power

35. Astigmatic Lens
• All the meridians of each surface of a spherical
lens have the same curvature (as parts of a
sphere), and refraction is symmetrical about the
principal axis.
• In an astigmatic lens, all meridians do not have
the same curvature, and a point image of a point
object cannot be formed.
• There are two types of astigmatic lenses, namely
cylindrical and toric lenses.

36. Cylindrical Lenses
• These lenses have one plane surface and the
other forms part of a cylinder.
• Thus, in one meridian the lens has no vergence
power and this is called the axis of the cylinder.
In the meridian at right angles to the axis, the
cylinder acts as a spherical lens.
• The total effect is the formation of a line image
of a point object. This is called the focal line. It is
parallel to the axis of the cylinder.

38. Toric Surface
• Imagine that the cylindrical is picked up by its ends
and bent so that the axis XY becomes an arc of a
circle.
• The previously cylindrical surface is now curved in
both its vertical and horizontal meridians, but not
to the same extent. It is now called a toric surface.
• The meridians of maximum and minimum
curvature are called the principal meridians and in
ophthalmic lenses these are at 90° to each other.
• The principal meridian of minimum curvature, and
therefore minimum power, is called the base curve.

40. Toric Lenses
• Lenses with one toric surface are known as toric
lenses, or sphero-cylindrical lenses. Such lenses do
not produce a single defined image because the
principal meridians form separate line foci at right
angles to each other.
• Between the two line foci the rays of light form a
figure known as Sturm's conoid . The distance
between the two line foci is called the interval of
Sturm.
• The plane where the two pencils of light intersect is
called the circle of least confusion or the circle of least
diffusion. Blur circle images only are formed at all
other planes lying between FH and FV.

42. Spherical Equivalent
• The spherical equivalent power is calculated from the
toric lens prescription by algebraic addition of the
spherical power and half the cylindrical power,
e.g. the spherical equivalent of +2.00 DS/+2.00 DC is
+3.00 DS, while that of +2.00 DS/–2.00 DC is +1.00 DS.
• The focal point of the spherical equivalent would coincide
with the circle of least confusion of the toric lens's
Sturm's conoid.
• This consideration is especially important in the choice of
intraocular lens power for the individual patient.