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Principles of Optics and Refraction

This page reviews the basic principles of physics that underpin optical science. It includes some important formulae and ray diagrams. It may appear complex at first glance but this content is straightforward marks on the exam.


Refraction and Reflection

Refraction and reflection describe changes in light with respect to the angles of travel.


Simple ray diagrams demonstrating refraction and reflection. n1 is a material with a higher refractive index. By Josell7, CC BY-SA 3.0


Incidence and Refraction

  • Light rays bend when moving between mediums of different refractive index
    • Refractive index describes the speed of light through a material, relative to a vacuum
    • The refractive index of the cornea is 1.376, which means the light travels 1.376 times slower through the cornea than in a vacuum
  • The angle of incidence (θ1) is the angle made between the incident ray and a line that is perpendicular to the surface at the point of incidence (dotted line)
  • When a ray moves from a material of higher refractive index to a material of lower refractive index, the ray is refracted away from the normal (dotted line)

Critical Angle

  • The critical angle (θc) is the angle of incidence at which light is first reflected instead of refracted
  • The critical angle for normal spectacles is 41°

Total Internal Reflection

Total internal reflection of light in a semicircular acrylic block. By Zátonyi Sándor, CC BY-SA 3.0 .

  • Total internal reflection is when the angle of incidence exceeds the critical angle
  • Light is not refracted
  • Light is reflected back into the medium with the higher refractive index

How gonioscopy allows the visualisation of the anterior chamber angle. By Mick lucas , CC BY-SA 3.0.

The anterior chamber angle is an important clinical structure in glaucoma. It cannot be seen directly because the light coming out of it is totally internally reflected by the corneal/air interface. A gonioscope changes the refractive index of this interface such that the angle becomes visible.


Vergence

Vergence is the amount of spreading (divergence) or coming(convergence) together of light. It is measured in diopters (D), where D is the reciprocal of the distance to the point where light rays would intersect if extended in either direction (focal length). D=1/f(m)

Converging rays have a plus vergence. Diverging rays have a minus vergence. Parallel rays have 0 vergence

Vergence where the ray of light is moving left to right. The focus is where the light intersects and the image is formed. By Boris Považay, CC BY-SA 2.5 , via Wikimedia Commons


Lens Power

A minus lens diverging light. By Fir0002, CC BY-SA 3.0.

A plus lens converging light. By Fir0002, CC BY-SA 3.0.

  • A lens changes the vergence of light, whether it’s the crystalline lens, spectacles, contact lenses or IOL implants
  • A plus lens converges light
  • A minus lens diverges light

Basic Lens Formula

  • U+D=V
  • U → vergence of light entering the lens (object rays)
  • D → vergence added to light by the lens (lens power)
  • V → vergence of light leaving the lens (image rays)

Example

Light from an object 2m away is travelling to a +2D lens. At what distance is the image going to be formed?

- U= 1/2 = -0.5D   
    - Light coming from a natural object is divergent (minus)  
- D = +2D  
- V = -0.5+2 = +1.5D  
- Recall that D=1/f(m), therefore, 1/1.5 = 0.67m  
- The image will form 0.67m on the other side of the lens  

The rays on the left of the lens are object rays. The rays on the right of the lens are image rays. This is a plus len

Where questions involve distance and diopters, take the reciprocal to switch between the units


Image Qualities

The image produced by a lens can be real/virtual, erect/inverted and magnified/diminished. The underlying principles of image projection are discussed in this section.

The most important this you should know is that the image created by a minus lens (biconcave) is virtual, erect and diminished. The image created by a plus lens (biconvex) can be real or virtual, erect or inverted, and magnified or diminished; all depending on the distance of the object relative to the focal point of the lens.


This diagram shows an object producing a real image through a biconvex lens. The rays are travelling left to right. The rays on the left of the lens are object rays and on the right are image rays. The image is formed on the same side as the image rays, this makes the image real

This diagram shows an object producing a virtual image on a biconcave lens. The rays are travelling left to right through this lens. The image rays are on the right but the image is formed on the left, this makes the image virtual


A biconcave lens will produce a diminished, erect, virtual image - irrespective of the object distance

Object distance

Image type

Magnification

Orientation

Less than focal length(f)

Virtual

Magnified

Erect

Between f and 2f(2 times focal length)

Real

Magnified

Inverted

Further than 2f

Real

Diminished

Inverted


A ray diagram showing the formation of a virtual image. F = focal point. This diagram shows that when an object is placed between f-2f, the image that will be produced is erect, virtual and diminished. By Kvr.lohith, CC BY-SA 4.0.


Visual Acuity Testing

Visual acuity is a measure of the clarity of vision. There are subjective and objective methods of testing. Retinoscopy is the most commonly used objective test of visual acuity. The other tests that are discussed in this section are all subjective (depend on the patient’s response)

An Ishihara plate. This is a test for colour blindness. If you cannot see a number in the middle of this plate then you are likely to be red-green colourblind.


Snellen Chart

A Snellen chart in feet (20ft = 6m). You might have heard of the phrase ‘perfect 20/20 vision, this is where that comes from. By Jeff Dahl, CC BY-SA 3.0.

  • Most commonly used test in clinics
  • Patients stand 6m away and read the letters on the chart.
  • A score is given as a fraction where the numerator is the distance away from the chart
    • 20/200 = 6/60
      • This means that the patient can read at 6m, what the average person can read at 60m.
    • 20/20 = 6/6
      • This means that the patient can read at 6m what the average patient can read at 6m
  • 6/12 (line 6) is the minimum driving requirement
    • This is crudely tested by asking the patient to read a number plate at 20m during the driving test

LogMAR Chart

A LogMAR chart. The letter spacing = width. Row spacing = height of letter from the row below. Each letter is worth 0.02units.

  • More accurate than Snellen but mainly used in research settings.
    • There are 5 letters in each row at equidistance, this accounts for the crowding phenomenon, and makes LogMAR more accurate than snellen
  • Patients stand 4m away
  • A score between 1-0 is given where 0 is best.
    • 0 LogMAR = 6/6 snellen
    • 1 Logmar = 6/60 snellen
  • Each letter is worth 0.02units, which are accumulated and subtracted from 1 to give the final score.

Duochrome Test

Duochrome test. By ORT5CLA TEAM H, CC BY-SA 4.0 .

  • The chart has black letters on either a red background or a green. The patient is asked to determine which background makes the letters clearer
    • No difference → no refractive error
    • Red background is clearer → hyperopia
    • Green background clearer → myopia
  • The principle underlying this test is chromatic aberration
    • Red has a longer wavelength and focuses behind the retina
    • Green has a shorter wavelength and focuses in front of the retina

Retinoscopy

  • A retinoscope is similar to an ophthalmoscope. The key difference is that the light source of the retinoscope can be quickly moved off the visual axis.
  • Retinoscopy is an objective measure of visual acuity.
  • The examiner shines the light from the retinoscope and aims to observe the red retinal reflex. Different lenses are added in front of the light to achieve the perfect perfect red reflex.
    • The power of these lenses tells you the amount of refractive error
    • The direction of the red reflex against the direction of the light from the retinoscope tells you the type of refractive error
      • Myopia → red reflex moves against the direction of light
      • Hyperopia → red reflex moves with the direction of light
        A retinoscope. By Janee, CC BY-SA 3.0, via Wikimedia Commons.

Visual Acuity in Children

Testing in Children

Situation

Test

Preverbal infants

Keeler cards (Preferential looking)

Preverbal children

Cardiff cards

Verbal but illiterate children

Kay picture cards

Verbal and semi-literate children (3-5years)

Sheridan-Gardiner and Sonksen (single letter cards)

Verbal and Literate children (>4years)

Snellen and LogMar

Visual Acuity Development

Age

Snellen Score

Description

Birth

>6/60

Poor vision

3 months

6/60

Fixate on objects and aces

6 months

6/30

Develops colour vision

1-2years

6/6

Adult level vision


Optics of Ophthalmoscopes

Ophthalmoscopes are also known as fundoscopes because they allow you to visualise the fundus of the eye - the interior surface of the retina behind the lens. There are 2 main types of fundoscopy: direct and indirect. Direct ophthalmoscopy provides a magnified view of the central fundus. Indirect ophthalmoscopy provides are wider stereoscopic view, up to the ora serrata. It is useful in cases where the direct fundus view is obstructed by hazy media or cataracts.

A direct ophthalmoscope. By Janee, CC BY-SA 3.0 via Wikimedia Commons.


Types of Fundoscopy

Characteritics

Direct

Indirect

Lens

Not required

Required

Image produced

Erect and virtual

Inverted and real

Depth perception (stereopsis)

Absent

Present

Fundus view

Slightly beyond the centre

All the way to the periphery and ora serrata

Examination distance

Close to the eye

At arm’s length

Magnification

15x

2-5x

An ophthalmologist using an indirect ophthalmoscope. The light is attached to the headband and a handheld lens is used to provide a wide view. This lens is typically +20D.

In indirect ophthalmoscopy, the field of view is largest in cases of high myopia and smaller in hyperopia


Optics of Slit Lamps

Slit lamps are the staple tool of examination in ophthalmology. They allow you to examine the ocular structures in detail. The patient is dilated during the exam. There are several different illumination techniques which allow the examiner to focus on various structures. This section will review these structures and techniques

A slit lamp. The clinician sits on the right and uses the optics. The patient sits on the left with their forehead on the white band. By Ben Schumin, CC BY-SA 3.0


Diffuse Illumination

Diffuse illumination. By Imran kabirhossain, CC BY-SA 4.0, via Wikimedia Commons.

  • Wide beam of light diffusely illuminating the eye and external structures.
  • Used for general examination

Direct Focal Illumination

  • This is the most commonly used type of illumination
  • It focuses a beam of light directly on the part of the eye being examined

Retroillumination

Direct illumination of the cornea. The arrows point toward superficial corneal lesions. You can see the beam of light passing through the cornea (left) onto the iris (right). The beam is focused on the cornea (blue arc). By Imran kabirhossain, CC BY-SA 4.0 , via Wikimedia Commons.

  • Light is reflected back from structures to posteriorly illuminate structures in front. E.g from the iris to the cornea or the retina to the iris/lens
    Retroillumination from the fundus showing an anterior subcapsular cataract. By Imran kabirhossain, CC BY-SA 4.0 , via Wikimedia Commons.

Specular Reflection

  • Focuses the view on the corneal endothelium
  • Useful in corneal endothelial diseases such as Fuchs’ endothelial dystrophy

Sclerotic Scatter

Sclerotic scatter illumination shows keratic precipitates in the cornea. By Imran kabirhossain, CC BY-SA 4.0 , via Wikimedia Commons.

  • The beam of light from the slit lamp is projected onto the corneal limbus. This light is scattered throughout the cornea and illuminates corneal lesions

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