Optics and Refraction










CHAPTER 3 Optics and Refraction


Elementary Optics


Electromagnetic Spectrum


It ranges from short ionizing radiations (1×10-16 meter) to longest radio waves (1×106 m). Visible light represents a small portion of electromagnetic spectrum with wavelengths ranging between 400 and 700 nm [1 nanometer (nm) = 10-9 meter].


Visible light appears white but is actually composed of:































V


I


B


G


Y


O


R


Violet


indigo


blue


green


yellow


orange


red

(400 nm)




(700 nm)

The red end has the longest and the violet end the shortest wavelength in visible spectrum. Light with shorter wavelengths has more energy and vice versa.


Waves of smaller wavelength <400 nm are ultraviolet (UV) rays.


Waves of longer wavelength >700 nm are infrared (IR) rays.


Cornea absorbs rays of wavelength <320 nm. Lens absorbs rays of wavelength <350 nm.


Vitreous absorbs rays of wavelength with maximum of 270 nm (Fig. 3.1).


So, in normal eye, rays between 400 and 350 nm can reach the retina and also stimulate photoreceptors. But in aphakic (eyes without crystalline lens) or pseudophakic eyes (eyes with an intraocular lens) without a UV-absorbing filter, rays between 400 and 320 nm reach the retina.


Intraocular lenses (IOLs) made up of PMMA (polymethyl methacrylate) absorb only UV rays ≤320 nm, so all modern IOLs (PMMA, silicone, and foldable acrylic) are impregnated with UV-absorbing substances called chromophores which absorb wavelengths of <400 nm. Knowledge of basic optics is necessary for an understanding of the functioning of the eye.




Fig. 3.1 Absorption of radiations by different ocular media.


Properties of Light


Speed of Light


The speed of light in vacuum (c) = 3 × 108 m/s and is constant.


The light travels slower in any medium compared with its speed in air or vacuum. The speed of light in a given medium (v) depends on the density of medium (Table 3.1).


Speed of light in air/vacuum, c = n × v; n = refractive index (RI)


When traveling through a substance, frequency of light remains unchanged but wavelength (and speed) becomes shorter. A medium is said to be optically denser if the speed of light becomes less in that medium.


Reflection


When light wave encounters an optical interface (boundary between two medium of different refractive index), it is partly reflected and partly refracted. The reflected ray bounces off the interface in the same medium. Greater the difference in RI between two media, the greater is the reflection and the angle of incidence is equal to the angle of reflection.


Laws of Reflection


For all surfaces, the angle of incidence is equal to the angle of reflection.


The rays (incident and reflected) and the normal at the point of incidence lie in the same plane.


The cornea acts as a convex mirror.


Refraction


It is the change in the direction of light traveling across an optical interface. A media with high refractive index is said to be optically denser than the media with low refractive index which is said to be optically rarer.


When a ray passes from optically rarer to a denser medium, the ray bends toward the normal. When a ray passes from optically denser to a rarer medium, bending of ray is away from the normal (Fig. 3.2). Greater the difference in optical density between the two media, greater is the deviation.
























Table 3.1 Refractive index of various media


Media


Refractive index


Air


1.0


Crown glass


1.52


Flint glass


1.65


Water


1.33




Fig. 3.2 Laws of refraction.


RI of crown glass which is used for optical purposes = 1.52.


For a ray traveling from optically denser to a rarer medium, if the angle of incidence is gradually increased, the angle of refraction also increases. The angle of incidence at which the incident light is bent exactly 90° away from normal (i.e., angle of refraction = 90°) is called the critical angle (Fig. 3.3).


When angle of incidence exceeds the critical angle, all light is reflected back into the same (denser) medium. This phenomenon is called total internal reflection (TIR). This happens at cornea–air interface, preventing direct visualization of angle structure without a special gonioscopy lens.


Prisms


In prisms, light rays are diverted toward the base, and the image is displaced toward the apex. The angle of deviation (D) of an ophthalmic prism is made of crown glass = (refracting angle (A) of the prism/2).




Fig. 3.3 Refraction at critical angle and total internal reflection.


The angle of deviation is least when angles of incidence and emergence are equal (angle of minimum deviation).


The power of prism is measured in prism dioptres (∆) (Fig. 3.4).


One ∆ is the strength of prism which produces a linear displacement of an object by 1 cm when the object is kept at a distance of 1 m.


Two displacement of arc


If prism angle (A) = 10°, then deviation = 5° or 10 ∆, that is, prism has a power of 10 ∆.


Thus, greater the angle at apex of prism (refracting angle of prism), the stronger is the prismatic effect.


Prismatic effect also varies with wavelength. Light of shorter wavelength is deviated more than the light of longer wavelength. Chromatic aberration results with blue light closer to the base (short wavelength bent most) and red light closer to the apex.


Uses of Prisms in Ophthalmology


Diagnostic uses in the following:


Many ophthalmic equipment such as gonioscope, keratometer, and applanation tonometer.




Fig. 3.4 Refraction by prism.


Objective measurement of the angle of deviation (prism bar cover test and Krimsky test).


Measurement of fusional reserve.


Therapeutic use in patients afflicted with phorias and diplopia.


Lenses


Lenses may be spherical or cylindrical.


Spherical Lenses


A simple lens is a piece of glass with spherical surfaces. These may be:


Convex lens (converging lens/plus lens): It acts like two prisms placed base to base. It may be biconvex or plano.


Convex and concavo–convex (Fig. 3.5).


Concave lens (diverging lens/minus lens): It acts like two prisms aligned apex to apex. It may be biconcave, plano–concave, and convexo–concave (meniscus) (Fig. 3.6).




Fig. 3.5 Types of convex lenses.


On moving a lens away from the eye,


The effective power of convex lens increases, so a plus lens becomes stronger.


The effective power of concave lens decreases, so a minus lens becomes weaker.


To find out whether the lens is convex or concave, hold the lens near the eye and move it from side to side.


If distant object seems to move in the opposite direction to that of lens, then the lens is convex.


If distant object seems to move in the same direction as the lens, then the lens is concave.


To determine the refractive power (strength) of lens after determining the nature of lens by the above method, neutralize the movement of image with a lens of opposite sign. For example, if there is no movement at all with –4.0 D lens (concave lens), it means that the original lens was +4.0 D lens (convex lens).


Ophthalmic Uses of Spherical Lenses


Convex lens is used:


In correction of hypermetropia, aphakia, and presbyopia.


In indirect ophthalmoscopy.


In magnifying lens.


Concave lens is used:


In correction of myopia.


As Hruby lens (with slit-lamp) for fundus examination.


Cylindrical Lenses


Cylindrical lenses are the lenses taken out from the surface of a cylinder like a tumbler. These lenses have an axis associated with them which is parallel to that of the cylinder, of which these lenses are a segment. A cylindrical lens focuses light into a line instead of a point as a spherical lens would. These may also be convex or concave.




Fig. 3.6 Types of concave lenses.


In cylindrical lenses, one axis has zero power, while the power is incorporated in the direction at right angle to the axis. So, the object will move with/opposite to the lens only in one direction.


Ophthalmic Uses of Cylindrical Lenses


Cylindrical lenses are used:


To correct astigmatism.


As a cross cylinder (to check refraction).


If the object is at infinity, the image will be formed at principal focus which is very small, real, and inverted. As the object is gradually brought nearer to the lens, the image recedes further from it. The size of the image increases likewise.


Optical Aberrations


The lenses behave ideally near their optical axis (the line passing through the centers of curvature of the surfaces). Aberrations occur peripheral to the optical axis. Aberrations may be:


Spherical aberration: It is caused by increasing the prismatic effect of the lens periphery. Peripheral rays are refracted more than paraxial ones (Fig. 3.7a).


Chromatic aberration: It occurs between light of different wavelengths which are refracted by different amounts. Shorter wavelengths are bent more. This effect in eye, however, is small (Fig. 3.7b).


The eye has the following compensatory mechanisms to reduce the spherical aberrations of crystalline lens:


Size of pupil: Pupillary constriction eliminates the peripheral rays.




Fig. 3.7 (a) Spherical aberration. (b) Chromatic aberration.


Shape of cornea: Cornea is progressively flatter in periphery. So, peripheral rays are refracted equal to the paraxial ones.


RI of lens: RI is higher centrally in nucleus. So, paraxial rays bend more and all rays are brought to a focus at a single point.


Optics of Normal Eye


The optical system of the eye comprises several refracting structures (Table 3.2):


Cornea.


Aqueous humor.


Crystalline lens.


Vitreous humor.


RI of aqueous is equal to that of vitreous and RI of air = 1.000.


Refracting interfaces in the eye are:


Air—cornea.


Aqueous—lens.


Lens—vitreous.


Total dioptric power of the eye = + 60 D


Out of +60 D, refractive power of the
cornea = +43 D


and refractive power of the lens = +17 D.


Cornea is a major refractive component because the difference in refractive indices is maximum at anterior corneal surface interface. The centers of the corneal curvature and the two surfaces of the lens are all in the same straight line, which is called optic axis. Instead, of a simple convex lens with the same medium (air) on either side, the optical system of eye is quite complicated to understand the optics of human eye. The medium in front is air, while behind the lens, it is the vitreous having a higher RI than air.






























Table 3.2 Refracting structures of the eye with their refractive indices


Refracting structure


Refractive index


Cornea


1.376


Aqueous humor


1.336


Lens


Anterior and posterior cortex


1.386


Nucleus (core)


1.406


Vitreous humor


1.336


Schematic Eye (Gullstrand)


Schematic eye is a mathematical model used to provide a basis for theoretical studies of the eye as an optical instrument. From the optical point of view, the entire system can be defined by its “cardinal points.” Every optical system has six cardinal points (Fig. 3.8 and Table 3.3):


1.Focal points (F1 and F2)–primary and secondary.


2.Principal points (P1 and P2)–primary and secondary.


3.Nodal points (N1 and N2)–primary and secondary.


When an optical system is bounded on both sides by air (same refractive index both side), the nodal points coincide with the principal points.


Listing simplified it theoretically and introduced the concept of reduced eye.


Reduced Eye (Listing and Donder)


In the reduced eye, the eye is regarded as one convex lens having characteristics as mentioned in Fig. 3.9 and Table 3.4.






























Table 3.3 Cardinal points


Cardinal points


Location


F1 (primary focus point)


15.7 mm in front of cornea.


F2 (secondary focus point)


24.13 mm behind the cornea.


P1 (primary principal point)


Located in anterior chamber 1.35 mm behind the anterior surface of cornea.


P2 (secondary principal point)


Located in anterior chamber 1.60 mm behind the anterior surface of cornea.


N1 (primary nodal point)


Located in posterior part of lens 7.08 mm behind the anterior surface of cornea.


N2 (secondary nodal point)


Located in posterior part of lens 7.33 mm behind the anterior surface of cornea.




Fig. 3.8 Schematic eye.


Measured from the principal point:


The anterior focal length (F1) is equal to 17.05 mm (15.7 + 1.35).


The posterior focal length (F2) is equal to 22.78 mm (24.13–1.35).


So, the refracting system of the eye separates the two media of refractive indices 1 (air) and 1.33 (eye).


Since the rays enter and leave the refracting system through media of different refractive indices, the anterior and posterior focal distances are different. The parallel rays falling upon cornea will be brought to a focus 24 mm behind it, coinciding with position of retina/posterior focal point in the normal eye. The optic axis passing through center of both lenticular curvatures, when produced backward, cuts the retina exactly at fovea centralis.




Fig. 3.9 Reduced eye.

































Table 3.4 Characteristics of reduced eye


Total power


+ 58.6 D


Radius of curvature


5.73 mm


Single principal point (P)


1.35 mm from anterior surface of cornea


Single nodal point (N)


7.08 mm from anterior surface of cornea
(1.35 + 5.73 mm)


Two focal points


Anterior focal point (F1) (anterior focal distance)


–15.7 mm in front of anterior surface of cornea (minus sign by sign convention)


Posterior focal point (F2) (posterior focal distance)


+24.13 mm behind the anterior surface of cornea


Refractive index


1.333


The reduced eye is clinically useful in:


Calculation of IOL power.


Localization of intra ocular foreign body.


Designing the instruments.


Determining the size of retinal image since nodal point (N) corresponds to the optical center of convex lens.


Accommodation


The parallel rays coming from infinity come to a focus on retina in the emmetropic eyes, but divergent rays falling upon cornea will not come to a focus on retina and are focused behind it. Light rays from an object within 6 m are divergent. If an object is brought nearer to the eye at reading distance (≈ 30 cm), divergent rays from object at reading distance focus behind the retina and blurred image is formed.


There are only two ways by which this image can be seen properly:


By an increase in axial length of eye ball, which is not possible.


Eye should increase its dioptric power to cause greater convergence of rays to focus the image of near object on retina. This is what actually happens.


This ability of eyes to change their refractive power to ensure a clear retinal image is known as accommodation.


Snellen’s acuity test is traditionally performed at a distance of 20 ft (6 m). At this distance, very little accommodation is required by the patient.


Physiology of Accommodation


Accommodation is accomplished by increase in convexity of lens. Radius of curvature of the anterior surface of lens R1 = 10 mm and that of the posterior surface of lens R2 = 6 mm.


At rest, the curvature of surfaces of the lens is approximately spherical.


In accommodation, the central part of anterior lens surface becomes more convex in relation to the peripheral part of lens because the capsule is thinner at the center and thicker at the periphery. In strong accommodation, the radius of curvature of anterior surface becomes 6 mm. The curvature of posterior lens surface remains almost the same. Posterior surface of lens undergoes little change in curvature as it is well-supported by the anterior face of the vitreous (Fig. 3.10).


Mechanism of Accommodation


When the eye is at rest for distant vision, the ciliary muscle is relaxed and zonules are kept tense. It keeps the lens in a flattened shape and the rays are focused on retina.


When the eye is at rest for near vision, a blurred image is formed on the retina. The blurred retinal image is the stimulus to accommodation, which is a reflex action regulated by an accommodation reflex.




Fig. 3.10 (a, b) Physiology of accommodation.




If a person looking at a distant object, focuses on to a near object, three responses are associated with this accommodation reflex:


Increase in anterior curvature of lens (due to contraction of ciliary muscle).


Constriction of pupil (due to contraction of sphincter pupillae).


Convergence of eyeballs (due to contraction of medial recti).


The association of accommodation, convergence, and pupillary constriction in fixation at near is termed as near response or near vision complex (Fig. 3.11).


Pathway for Near Response (Near Reflex)


Thus, a person with normal vision can see not only distant objects but also near ones. Accommodation reflex involves both skeletal muscle (medial recti) and smooth muscles (ciliary muscle and sphincter pupillae; Flowchart 3.1 and Fig. 3.12).


The nearest point at which an object can be seen clearly by accommodation is called the near point or punctum proximum. At this point, accommodation is exerted to its maximum.




Fig. 3.11 Near vision complex. (a) Eye at rest with object at reading distance. (b) For distant objects. (c) Eye in accommodation for object at reading distance.




Flowchart. 3.1 Pathway of near response.




Fig. 3.12 Pathway of near response. Source: Clinical Features. In: Scott I, Regillo C, Flynn H et al., ed. Vitreoretinal Disease: Diagnosis, Management, and Clinical Pearls. 2nd Edition. Thieme; 2017.


The farthest point which can be brought to focus on to the retina is called the far point or punctum remotum. The distance between the near point and far point is called range of accommodation.


Amplitude of Accommodation (A)


It is the difference between refractive power of the eye at near point (P) and far point (R).



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Nov 20, 2022 | Posted by in OPHTHALMOLOGY | Comments Off on Optics and Refraction
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